Addition and. subtraction. given a number, identify one more and one less. balance pans. non-standard measuring equipment.

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Addition and. subtraction. given a number, identify one more and one less. balance pans. non-standard measuring equipment."

Transcription

1 Year 1 Number and Addition and Multiplication, Measures place value subtraction division and fractions Year 1 number and place value Statutory requirements count to and across 100, forwards and backwards, beginning with 0 or 1, or count, read and write numbers to 100 in numerals, count in different multiples given a number, identify one more and one less identify and represent numbers using concrete objects and pictorial representations language of: equal to, more than, less than (fewer), most, least Read and write numbers from 1 to 20 in digits and words. Resources numicon balance pans non-standard measuring equipment multilink real life objects

2 bead strings NRICH ACTIVITIES: Core pedagogy Counting using Children make Drawing links Children practise various apparatus, numbers between 1 between concrete subitising regular IDENTIFY AND including stick, and 100 using representations to dot patterns. Use REPRESENT physical and numicon without pictorial irregular patterns. NUMBERS USING pictorial counting. Then use representations of Investigate that si OBJECTS AND representations. multiple values, leading to does not affect PICTORIAL Counting songs and representations using abstract associations quantity e.g REPRESENTATIONS. bounce counting. real life objects. of number. multiple Children to say representations of teen numbers explicitly. Thinking pedagogy Same and What do you notice Find all the pictures What do you see? different- 3 and when we add 1? that show 5 Agree/disagree 13 3 big cars are mo

3 Statutory requirements read, write and interpret mathematical statements involving addition (+), subt represent and use number bonds and related subtraction facts within 20 add and subtract one-digit and two-digit numbers to 20 (9 + 9, 18-9), including zero solve simple one-step problems that involve addition and subtraction, using concr missing number problems. Resources numicon balance pans non-standard measuring equipment multilink real life objects dice counting sticks bead strings NRICH ACTIVITIES: Core pedagogy Children make Through a grounding Explore concept of Children explore

4 CONTEXT, numicon without how addition and holder. Explore counting back as CONCRETE counting and explore subtraction acts upon what happens when subtraction. RESOURCES AND number bonds with quantities. zero is added or PICTORIAL complementary subtracted. REPRESENTATIONS. numcion shapes. Thinking pedagogy Using numicon Agree/disagree- Give me an example Give me a hard a show me different when I add my of- a number with a easy addition ways to make 20 number gets bigger. zero in the ones column

5 LINKS CHILDREN SHOULD BUILD UPON THEIR UNDERSTAND MEASURE CONTEXTS FOR ADDITION AND SUBTRACTIO Year 1- multiplication and division Statutory requirements Solve simple one-step problems involving multiplication and division, calculating the a representations and arrays with the support of the teacher. Resources numicon balance pans non-standard measuring equipment multilink real life objects dice counting sticks bead strings arrays NRICH ACTIVITIES: Core pedagogy Build upon their Children explore Practise doubling Link halving wit

6 CONCRETE addition and to begin to and then move onto equality within RESOURCES AND subtraction by using understand numicon fractions. Ensure PICTORIAL real life situations multiplication and strong links betwe REPRESENTATIONS. to see how division. division and simpl operations act upon fractions. quantities. Thinking pedagogy The answer is 16. Agree/disagree- How many different Odd one out- ½ How many multiplication is the ways are there to divide by 2, different operations opposite of addition. double 6? multiply by 2 can make this number?

7 LINKS Opportunities to use measure as a context for multiplication and division should be fo Year 1- fractions Statutory requirements recognise, find and name a half as one of two equal parts of an object, sha recognise, find and name a quarter as one of four equal parts of an object, s Resources numicon balance pans non-standard measuring equipment multilink real life objects dice counting sticks geometric shapes

8 NRICH ACTIVITIES: Core pedagogy Explore concept of Explore concept of a Provide children Fractions explored USE REAL LIFE fractions through whole with a range with opportunities to in terms of a rang CONTEXT, real life problems in of objects. explore equality in of objects that ca CONCRETE stories and using different contexts. be equally shared RESOURCES AND food. produce a half an PICTORIAL a quarter. Childr REPRESENTATIONS. to record their findings with own notation

9 wholes set of smarties have to include half the colours? LINKS Opportunities to use measure and shape as a context for fractions to be used. Year 1- measures Statutory requirements compare, describe and solve practical problems for: lengths and heights (e.g. long/short, longer/shorter, tall/short, double/half) mass or weight (e.g. heavy/light, heavier than, lighter than) capacity/volume (full/empty, more than, less than, quarter) time (quicker, slower, earlier, later) measure and begin to record the following: lengths and heights mass/weight

10 sequence events in chronological order using language such as: before and after, next, first, today, yesterday, language relating to dates, including days of the week, weeks, months and years tell the time to the hour and half past the hour and draw the hands on a clock face to show these times. Resources numicon balance pans non-standard and standard measuring equipment multilink real life objects dice counting sticks clocks, calendars and timetables money NRICH ACTIVITIES: Core pedagogy Children recognise different Children explore Use language relating to Explore measuring using USE REAL LIFE denominations of coins and notes through practical chronological order vocabulary and comparative dates. Read and record time to closest hour and half hour non-standard equipment, CONTEXT, experience (real and vocabulary e.g before, next, CONCRETE plastic) then use money to first, today, yesterday, solve number problems. tomorrow, morning, RESOURCES AND afternoon, evening, long, PICTORIAL short, longer, shorter.

11 Thinking pedagogy Agree/ disagree- Odd one out- give Order these dates Show me toys tha the bigger the coin a list of language are smaller than m the more it is worth hand. LINKS THROUGH MEASURES BUILD UPON CORE AREAS O POSSIBLE. Year 1- geometry Statutory requirements recognise and name common 2-D and 3-D shapes, including: 2-D shapes (e.g. rectangles (including squares), circles and triangles) 3-D shapes (e.g. cuboids (including cubes), pyramids and spheres). order and arrange combinations of objects and shapes in patterns

12 multilink polydron 2d and 3d representations of shapes Real life geometric shapes Bee bots Clocks Core pedagogy Rehearse vocabulary Children use 2d Children experience Children recognis CHILDREN of movement and and 3d shapes in 2d and 3d shapes in common 2d shapes EXPERIENCE, direction. Children construction and different and where you see RECOGNISE AND practise turns with design. Start to orientations. them most NAME SHAPES IN toys (whole, half, introduce frequently? VARIOUS quarter, ¾) and vocabulary. ORIENTATIONS IN then turn own THE WORLD bodies AROUND THEM.

13 Thinking pedagogy Hard/easy How many shapes Same and different Which shapes are Show me a hard do you see in this with a range of the most common i turn. picture? shapes in different our classroom? orientations. LINKS LINKS MADE BETWEEN MEASURES (CLOCKS) AND FRA UNDO THEMSELVES (DOORS). Vocabulary for movement linked to P Academic year Autumn 1 Autumn 2 Spring 1 Spring Year 2 Number and place Addition and Multiplication, Measures value subtraction division and

14 Statutory requirements count in steps of 2, 3, and 5 from 0, and count in tens from any number, forward or backward recognise the place value of each digit in a two-digit number (tens, ones) identify, represent and estimate numbers using different representations, including the number line compare and order numbers from 0 up to 100; use <, > and = signs read and write numbers to at least 100 in numerals and in words use place value and number facts to solve problems Resources numicon balance pans non-standard measuring equipment multilink real life objects dice counting sticks bead strings dienes number cards/place value cards Core pedagogy Children learn to Learn to see 10 as Learn place value in Count forwards

15 UTILIZE 10 TO in various collection of 10 this looks like with number. SUPPORT AN representation (to at ones. different UNDERSTANDING least 100). representations (use OF PLACE Learning supported distance) so it makes VALUE. by subitising and quantifiable sense to using numicon. the children. Thinking pedagogy What do you see? Give me an example Agree/disagree Find the mistake- subitising of a number with 5 I think that position count in tens and tens and another a is ten times further children spot the away mistake Year 2- addition and subtraction Statutory requirements solve simple one-step problems with addition and subtraction: using concrete objects and pictorial representatio applying their increasing knowledge of mental and written methods recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100 add and subtract numbers using concrete objects, pictorial representations, and mentally, including:

16 adding three one-digit numbers show that addition of two numbers can be done in any order (commutative) and subtraction of one number fr recognise and use the inverse relationship between addition and subtraction and use this to check calculations Resources numicon balance pans non-standard measuring equipment multilink real life objects dice counting sticks bead strings dienes number cards/place value cards Core pedagogy Number facts to 20 Mental and written Children introduced to Children explore inverse taught to fluency. methods applied to variety commutative law through calculation through Children to apply these of contexts. Children practical investigation. practical investigation. Use concrete representations facts to real life contexts, should be able to switch to build understanding of then extend facts to 100 fluently between methods. Should be able to add and addition and subtraction subtract 2 digits and one digit numbers, 2 digit and

17 show that multiplication of two numbers can be done in any order (commutative) and division of one number number bonds conditions- find Addition is the numbers that add to 4+3 opposite of 20, now one subtraction number must be 5 etc LINKS Use opportunities to consolidate understanding of place value when extending into 3 d context for learning. Year 2- multiplication and division Statutory requirements recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recogni calculate mathematical statements for multiplication and division within the multiplication tables and write equals (=) signs recognise and use the inverse relationship between multiplication and division in calculations

18 multiplication balance pans non-standard measuring equipment multilink real life objects dice counting sticks bead strings dienes arrays number cards/place value cards Core pedagogy Children to find Explore use of Children introduced Link concepts of USE REAL LIFE links between language to describe to commutative law division and CONTEXT, arrays, number multiplication and through practical fractions through CONCRETE patterns and division. Explore investigation. investigation. RESOURCES AND counting in 2 s, using known facts PICTORIAL 5 s and 10 s.,then and inverse REPRESENTATIONS children learn 2, operations. 5, 3 and

19 variety of problems. Thinking pedagogy What do you How can I use Agree/disagree What do you notice? Investigate 2x3 to help me 3x4=4x3 notice? arrays. find out 4x3? 12 3 Find 1/3 of 12 LINKS REINFORCE UNDERSTANDING OF PLACE VALUE AND L DATA HANDLING CONTEXTS FOR PROBLEM SOLVING Year 2- fractions Statutory requirements recognise, find, name and write fractions 1 /3, 1 /4, 2 /4 and ¾ of a leng

20 balance pans non-standard measuring equipment multilink real life objects dice counting sticks bead strings food clocks Core pedagogy Introduce concept Explore concept of Children count in Introduce non unit INTRODUCE through real life whole, then halves, halves and quarters up fractions. FRACTIONS USING problems and then quarters then to 10. Demonstrate with REAL LIFE stories. thirds. different OBJECTS SUCH AS representations. FOOD. EXPLORE MULTIPLE

21 Thinking pedagogy Find the correct Hard and easy List the first 10 What do you solution- show fractions numbers when notice? different halves counting in ½ s. can Show multiple with 1 wrong. we predict what the representation of a last number will be? non unit fraction

22 Statutory requirements choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); m Core pedagogy Children Children compare Links made between Children learn ti the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels (From Year 3) compare and order lengths, mass, volume/capacity and record the results using >, < and = read relevant scales to the nearest numbered unit recognise and use symbols for pounds ( ) and pence (p); combine amounts to make a particular value and m amounts of money; add and subtract money of the same unit, including giving change solve simple problems in a practical context involving addition and subtraction of money compare and sequence intervals of time tell and write the time to five minutes, including quarter past/to the hour and draw the hands on a clock fac Resources numicon balance pans non-standard measuring equipment multilink real life objects dice counting sticks bead strings number cards money clocks, calendars and timetables

23 THE VOCABULARY reliability of <and = then go addition/subtraction. OF COMPARISON standard units of over with money. Introduce to and p OF DIFFERENT measurement when symbols and explore MEASURES compared with non relationship. standard. Then use range of apparatus in practical contexts Thinking pedagogy Convince me that it Order different Hard and easy How long- see if better to measure to measures adding amounts of children can use a ruler rather money. What are estimate how long than the length of best methods to add minute is etc my finger. larger amounts of

24 LINKS Link to x5 tables and use money to reinforce concept of place value and solve additio used in other subjects such as science, history and geography. Year 2- geometry and statistics Statutory requirements Properties of shape identify and describe the properties of 2-D shapes, including the number of sides and symmetry in a vertical l identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces identify 2-D shapes on the surface of 3-D shapes, for example a circle on a cylinder and a triangle on a p compare and sort common 2-D and 3-D shapes and everyday objects. Movement order and arrange combinations of mathematical objects in patterns use mathematical vocabulary to describe position, direction and movement, including distinguishing between rot and three- quarter turns (clockwise and anti-clockwise), and movement in a straight line. statistics interpret and construct simple pictograms, tally charts, block diagrams and simple tables ask and answer simple questions by counting the number of objects in each category and sorting the categories b ask and answer questions about totalling and compare categorical data. Resources numicon balance pans non-standard measuring equipment multilink

25 bead strings Core pedagogy Explore 2d and 2d shapes Explore shapes by sorting Use a ruler to draw 2d Identify 2d shapes found Classify and sort shapes and name properties. Read and spell names correctly. and classifying them. Use everyday items. shapes in different orientations. 3d faces. Teacher to model precise Links drawn between Explore patterns in different Links made to other position vocabulary-right rotation and time- orientations anle. 3 quarter turn etc clockwise, anticlockwise curricular areas Children try to answer Children present data in Children answer questions on question without sorting of tables, pictograms and data data then introduced to block diagrams and make tally chart decision on how to present Using statistics with a purpose Thinking pedagogy Odd one out- with Agree/disagree How many questions? Which 3d shape has the properties of shape A half turn clockwise and How many were? most 2d shapes on its anticlockwise will get me How many more? faces? to the same position

26 Academic year Autumn 1 Autumn 2 Spring 1 Spring Year 3 Number, place Multiplication Fractions Measures value and and division addition and subtraction Year 3 number and place value and addition and subtraction Statutory requirements count from 0 in multiples of 4, 8, 50 and 100; finding 10 or 100 more or less than a given number (From Yea recognise the place value of each digit in a three-digit number (hundreds, tens, ones) compare and order numbers up to 1000 identify, represent and estimate numbers using different representations read and write numbers to at least 1000 in numerals and in words solve number problems and practical problems involving these ideas add and subtract numbers mentally, includi a three-digit number and ones a three-digit number and tens a three-digit number and hundreds

27 Resources numicon balance pans non-standard measuring equipment multilink real life objects dice counting sticks bead strings number cards Cuisenaire rods Place value ITP and ITP number square Core pedagogy Children read and write Children use place value Compare and order numbers Children relate x10 bigger numbers up to 1000 and charts and number racks to up to Physically to measure. create place value system combine numbers to make represent size of numbers. Place value in real life using straws. totals. contexts Use partitioning and place Model use of inverse Introduce column addition value to answer a range of calculations. When and subtraction method in addition and subtraction mentally adding and answering real life problems. problems. Children should subtracting 1, 2 and 3 digit Estimating answers and estimate first. numbers.

28 Thinking pedagogy Agree/disagree with How many different ways What number lies between What is the same and estimates can we partition 167? 2 and 3? 96 and 102? different between 36 and 360? Year 3- multiplication and division Statutory requirements recall and use multiplication and division facts for the 3, 4 and 8 multiplication ta write and calculate mathematical statements for multiplication and division using the including for two-digit numbers times one-digit numbers, using mental and progressing solve problems, including missing number problems, involving multiplication and divisi correspondence problems in which n objects are connected to m objects. Resources numicon balance pans non-standard measuring equipment multilink real life objects

29 bead strings number cards Core pedagogy Multiplication Children explore Solve problems where Learn 3,4,8 USE REAL LIFE taught in terms of commutative and m number of objects multiplication facts CONTEXT, scaling and associative laws. is related to n and use them to solve CONCRETE proportionality. number of objects. problems. they then AND PICTORIAL Rehearse vocabulary write statements RESOURCES for multiplication using 2, 5,10,3,4 and division. an8 times tables.

30 Thinking pedagogy If a ruler is 30cm How many different If there are 3 hats List all the facts what would be 4 ways can you x 12x9 and 4 coats, how that occur in the 2 times longer? many different and times tables. outfits? LINKS Links made to geometry, statistics, fractions and measure. Year 3- fractions Statutory requirements count up and down in tenths; recognise that tenths arise from dividing an object into 10 equa quantities by 10 recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fr recognise and use fractions as numbers: unit fractions and non-unit fractions with small denom recognise and show, using diagrams, equivalent fractions with small denominators add and subtract fractions with the same denominator within one whole (e.g. 5 /7 + 1 /7 compare and order unit fractions with the same denominator

31 non-standard measuring equipment multilink real life objects dice counting sticks bead strings cuisanaire rods fraction wall ITP fraction videos NCETM htt Core pedagogy Explore finding non Practise counting on Introduce mixed Learn to simplify Explore in relation to unitary fractions of and back in fractions fractions through fractions using real life contexts different ( not starting at different fraction walls representations. 0) and ordering representations Emphasise links fractions with the with division same denominator on a number line

32 Thinking pedagogy Give range of Have children count ASN- fractions are Convince me- that fraction and division in halves and less than 1 ½=3/6 calculations and they quarters- what do must match pairs they notice? LINKS Use contexts from measure, geometry and statistics. Link fractions with division. Year 3- measures Statutory requirements measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml) measure the perimeter of simple 2-D shapes add and subtract amounts of money to give change, using both and p in practical contexts tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12-hour and estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, m a.m./p.m., morning, afternoon, noon and midnight

33 Resources numicon geometric shapes standard measuring equipment money multilink counting sticks real life objects clocks and timetables Core pedagogy Learn to measure Record mixed Children compare, Introduce to roman TEACH accurately and apply measures 3.20= add and subtract numerals in the THROUGH to real life contexts. three ponds and measures. Use context of time. (I APPLICATION twenty pence. vocabulary to link to to XII) OF SKILLS TO multiplication- this REAL LIFE is 5 times as long. CONTEXTS Children measure perimeter through

34 Thinking pedagogy Same and different How many pence, If I add 1cm to each If the minute hand between different how many ten pences, side of a square, moves from XII to measuring instruments how many pounds etc how much will the VI how many perimeter go up by? minutes have past? LINKS DECIMAL NOTATION, ADDITION AND SUBTRACTION, MU DIVISION. CONTEXTS LINKED TO OTHER CURRICULAR AR Year 3- geometry and statistics

35 or less than a right angle identify horizontal, vertical, perpendicular and parallel lines in relation to other lines. interpret and present data using bar charts, pictograms and tables solve one-step and two-step questions such as How many more? and How many fewer? using information presente Resources numicon geometric shapes standard measuring equipment money multilink counting sticks real life objects protractors polydron geometric shapes clocks

36 DEVELOP description of turn. and greater than a right perpendicular lines. polygons and polyhedron. LANGUAGE Recognise 2 right angles angle. Introduce acute and Describe properties-length of FOR make a half turn etc obtuse. lines, acute, obtuse, horizontal and vertical lines CLASSIFICATION and right angles. OF PROPERTIES Read scales carefully Children interpret and Children practise solving OF SHAPE including whole number, present data using pictograms, addition and difference unmarked divisions. bar charts and tables. They questions using data presented must choose scales (make sure in a variety of formats (2 FIND PURPOSE that 3 and 5 are covered) step problems) AND CONTEXT that are appropriate to data and how they wish their data THROUGH to be presented. CROSS CURRICULAR LINKS Thinking pedagogy Same and different- ¼ turn Give me an example of an Convince me that these Children group shapes using and ¾ turn obtuse angle etc curving lines are parallel different criteria

37 LINKS Measure lines accurately and perimeter. Use real life contexts and real life shapes. Addi division in statistics. Academic year Autumn 1 Autumn 2 Spring 1 Spring 2 S Year 4 Number and place Addition and Fractions and Measures G value and rounding subtraction, decimals s multiplication and division Year 4 number and place value and rounding Statutory count in multiples of 6, 7, 9, 25 and 1000 requirements find 1000 more or less than a given number count backwards through zero to include negative numbers recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones) order and compare numbers beyond 1000 identify, represent and estimate numbers using different representations round any number to the nearest 10, 100 or 1000 solve number and practical problems that involve all of the above and with increasingly large positive numbers

38 multilink real life objects counting sticks number cards dienes Cuisenaire rods Roman numeral display Place value ITP Core pedagogy Children create place value Place value in 4 digit Children count in Children compare and order C system using art straws. Then numbers explored using 1 s.10 s,100 s.1000 s numbers beyond 1000, then n find 1000 more and 1000 multiple representations then record horizontally and physically represent size. e Linking place less than number. vertically in place value. value to relative Estimate and round numbers Children learn roman Link multiples of 100 and in different contexts to numerals to 100. Use sizes of numbers. 10,100,1000 numerals to complete calculations Use real life

39 of a number with best way to represent is happening to the this be? Place blank a 4 thousands 1456 numbers/ card on number line. 0 Year 4- Addition and subtraction, multiplication and division Statutory add and subtract numbers with up to 4 digits using the efficient written methods of columnar addition and subtraction wh requirements estimate and use inverse operations to check answers to a calculation solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why. recall multiplication and division facts for multiplication tables up to use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by recognise and use factor pairs and commutativity in mental calculations multiply two-digit and three-digit numbers by a one-digit number using formal written layout solve problems involving multiplying and adding, including using the distributive law and harder multiplication problems such as which n objects are connected to m objects. Resources measuring equipment multilink real life objects counting sticks

40 Cuisenaire rods Core pedagogy Develop mental strategies Investigate in terms of Taught formal methods for Develop a sense of taught in previous yearspartitioning, place value, arithmetic lawscommutative, associative, addition and subtraction for 4 digits with use of an answer before known facts, rounding and distributive. manipulatives. Must round calculation adjusting to gain fluency. to find approximate answers and check with inverse operations. Children use place value and Multiplication and division Children to solve harder Learn multiplication tables C known facts to x by 0, 3 taught in terms of arithmetic correspondence problems up to 12 x 12 and apply to f numbers and 3 digit numbers. laws and of scaling and problem solving contexts. c direct proportionality.to Explore multiplication and develop mental fluency. Ensure teaching is through practical investigation. division in terms of arithmetic laws

41 meal, how many options are people are there? =4 so 20 8=8 there? Is not true because LINKS Use measure, geometry and statistics as a context for learning. Year 4- fractions and decimals Statutory count up and down in hundredths; recognise that hundredths arise when dividing an object by a hundred and dividing tenths requirements solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including identify, name and write equivalent fractions of a given fraction, including tenths and hundredths add and subtract fractions with the same denominator. recognise and write decimal equivalents of any number of tenths or hundredths recognise and write decimal equivalents to 1 /4 ; 1 /2 ; 3 /4 find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer round decimals with one decimal place to the nearest whole number compare numbers with the same number of decimal places up to two decimal places solve simple measure and money problems involving fractions and decimals to two decimal places. Resources measuring equipment multilink real life objects counting sticks

42 fraction walls and cards Cuisenaire rods Core pedagogy Explore ¼, ½, Link fractions and Link fractions and Count on and back E LEARNING IS 1/3, ¾ in multiple place value by division. Explore (not starting at 0) 2 BASED ON representations and revisiting art straw fractions of 100 to in fractions and 1 REAL LIFE link vocabulary of representation of link to decimals decimals (0.1 and a CONTEXTS multiplication and place value 0.01) ensure that AND division through children understand EXPERIENCES vocabulary of factor that a hundredth is and multiple Explore rounding decimals to nearest whole number Thinking pedagogy Same and different Same and different What do you notice? Extend into negative W

43 help with rounding 3 LINKS Place value. Multiplication and division. Use measure, geometry and statistics to provide con Year 4- measures Statutory convert between different units of measure (e.g. kilometre to metre; hour to minute) requirements o measure and calculate the perimeter of a rectilinear figure (including squares) in c find the area of rectilinear shapes by counting estimate, compare and calculate different measures, including money in pounds and pence o read, write and convert time between analogue and digital 12 and 24-hour clocks solve problems involving converting from hours to minutes; minutes to seconds; years to mon Resources measuring equipment multilink

44 number cards dienes money geometric shapes clocks and timetables Cuisenaire rods Core pedagogy Children convert Convert between Measure and Calculate areas of R between units of units using addition calculate perimeter of rectilinear polygons c measurement using and subtraction, rectilinear polygons by counting squares 2 proportionality and multiplication and in m and cm place value. division and fractions. Thinking pedagogy How much larger is Agree /disagree If a pentagon has a What do you A

45 hexagon have to be to area c have the same perimeter. LINKS Proportionality, fractions and place value, multiplication and division, addition and subtracti Year 4- geometry and statistics Statutory compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes requirements identify acute and obtuse angles and compare and order angles up to two right angles by size identify lines of symmetry in 2-D shapes presented in different orientations complete a simple symmetric figure with respect to a specific line of symmetry describe positions on a 2-D grid as coordinates in the first quadrant describe movements between positions as translations of a given unit to the left/right and up/down plot specified points and draw sides to complete a given polygon. interpret and present discrete data using bar charts and continuous data using line graphs solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and simple line

46 counting sticks number cards dienes money geometric shapes clocks and timetables polydron Cuisenaire rods protractors Core pedagogy Children classify geometric Read, write and plot Children rehearse directional Build symmetrical shapes O Develop shapes (quadrilaterals and triangles) based on a variety coordinates (points and shapes) in the first and movement vocabulary to translate shapes and points. around lines of symmetry and when the mirror line does not c u visualisation skills of properties (introduce quadrant.. Draw axes dissect the shape. to identify and plot regular and irregular) including equal scales and integer labels. lines of symmetry Explore differences between Plot multiplication tables on Explore greater range of continuous and discrete data continuous charts to explore scales including unmarked and present and charts and proportional relationships. divisions. time graphs. Can they use this to find Purpose and context decimal times tables? given through cross

47 Thinking pedagogy Which definitions Find the correct ASN- when a shape Additional P match a square? solution- identify is translated its conditions- draw a o correct plots properties remain the shape with 2 lines of s same symmetry, now change it so it has 4 lines LINKS Movement linked to control technology. Multiplication and division, addition and subtractio Academic year Autumn 1 Autumn 2 Spring 1 Spring 2 S Year 5 Number and place Multiplication Fractions, decimals Measures G value and addition and division and percentages R and subtraction Year 5 number and place value, addition and subtraction Statutory read, write, order and compare numbers to at least and determine the value of each digit requirements count forwards or backwards in steps of powers of 10 for any given number up to

48 read Roman numerals to 1000 (M) and recognise years written in Roman numerals. add and subtract whole numbers with more than 4 digits, including using efficient written methods (columnar addition and add and subtract numbers mentally with increasingly large numbers use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why. Resources measuring equipment multilink real life objects counting sticks number cards dienes roman numeral display Cuisenaire rods Books- How much is a million? Core pedagogy Explore value of 6 and 7 Order whole and decimal Round numbers to Explore linier sequences C Understanding digit numbers numbers up to Count forwards and 10,100,1000,10000, , including fractions and decimals and find the term to o 1 relative value of backwards in powers of 10. term rule larger numbers Investigate addition and Increase speed and fluency Explore order of calculation- Apply formal methods to 5 subtraction in terms of through making connections Bodmas digits in problem solving arithmetic laws. and generalising about known contexts that involve 2 steps

49 calculation and correct choices when choosing methods Thinking pedagogy Prove it- it doesn t matter Order largest to smallest Hard and easy rounding Give me an example of a W which order the numbers are in sequence where the term to u in addition. term rule is add 0.5 Year 5- multiplication and division Statutory identify multiples and factors, including finding all factor pairs requirements solve problems involving multiplication and division where larger numbers are used by decomposing them into their factors know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers establish whether a number up to 100 is prime and recall prime numbers up to 19 multiply numbers up to 4 digits by a one- or two-digit number using an efficient written method, including long multiplicat multiply and divide numbers mentally drawing upon known facts divide numbers up to 4 digits by a one-digit number using the efficient written method of short division and interpret remainders appropriately for the context

50 solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates Resources measuring equipment multilink real life objects counting sticks number cards Cuisenaire rods dienes Core pedagogy Explore and reason using Explore factor pairs and Construct arrays to recognise Multiply 4 gits by 2 digits C arithmetic laws ( common factors. Introduce square and cubed numbers and by formal method and use B a(b+c)=ab+ac ) and square and prime numbers use correct notation. Then use manipulatives.to aid p Problem solving scaling. Build upon fluency through the number of factors understanding to solve understanding. Interpret non through in multiplication tables up to they have. Learn and recall problems and construct integer answers in different 12 x12 and apply to square numbers up to 144 and equivalence statements. ways to match the context of understanding of calculations. Use place value prime numbers up to 19. the problem properties of and scaling to multiply and number divide decimal numbers by 10, 100,1000. Explore equals sign to indicate equivalence.

51 Thinking pedagogy What is 1/10 th Same and different- Additional Spot the great larger than a ruler? 2 numbers, identify conditions- the mistakes common factors product of 2 numbers is 20 one of them is a square LINKS Contexts used in measure, statistics and geometry. Links to decimals and fractions and place va Year 5- fractions, decimals and percentages Statutory compare and order fractions whose denominators are all multiples of the same number requirements recognise mixed numbers and improper fractions and convert from one form to the other add and subtract fractions with the same denominator and related fractions; write mathematical statements >1 as a mixed n multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams. read and write decimal numbers as fractions (e.g o = 71 /100 )

52 solve problems involving number up to three decimal places. recognise the per cent symbol (%) and understand that per cent relates to number of parts per hundred, and write percenta decimal fraction solve problems which require knowing percentage and decimal equivalents of 1 /2, 1 /4, 1 /5, 2 /5, 4 /5 and those with Resources measuring equipment multilink real life objects counting sticks Websites Subtraction number cards Cuisenaire rods Fraction cards and walls Addition Multiplying Core pedagogy Read and write Practise mental Use a sense of Addition and R decimals as fractions. addition and proportionality to subtraction m Fractions, decimals Explore decimals to subtraction of identify, name and (dominators multiples f and percentages are thousandths using decimals with mxes of write equivalent of same number) of l different ways of place value straw whole numbers and fractions (including fractions represented

53 compare them using a model. Count on and number line. Round backwards in fraction decimal numbers with and decimal steps 2 digits- link to bridging 1. real life application Thinking pedagogy Agree/disagree Odd one out- spot Hard and easy What do you notice? G Decimals are just the non-equivalent additions and o fractions of one fraction subtractions f d m LINKS Links to place value. Contexts in measure, statistics and geometry used. Year 5- measures Statutory convert between different units of measure (e.g. kilometre and metre; metre and centimetre; centimetre and millimetre; kilogr requirements places from Year 6) understand and use basic equivalences between metric and common imperial units and express them in approximate terms

54 recognise and estimate volume (e.g. using 1 cm blocks to build cubes and cuboids) and capacity (e.g. using water) solve problems involving converting between units of time solve problems involving addition and subtraction of units of measure (e.g. length, mass, volume, money) using decimal nota Resources measuring equipment multilink real life objects counting sticks number cards Cuisenaire rods Core pedagogy Calculate perimeter Calculate and Interpret algebraic Estimate volumes U of composite estimate area of representations of using 1cm cubed c Use understanding rectilinear shapes in rectangles through missing measures for blocks to build u to solve real life cm and m then use,multiplication (first perimeter and area. cuboids s problems understanding to with scale drawings b calculate unknown and then not to a measures. scale). Use u knowledge of area to

55 Thinking pedagogy Convince me of the ASN 4+2b=20 for a Explore relationship I length of an unknown If I increase the area rectangles of sides between side length a side then the perimeter 2cm and b cm and and volume t will increase perimeter of 20cm a LINKS Place value, addition and subtraction, multiplication and division. Year 5- geometry and statistics Statutory identify 3-D shapes, including cubes and cuboids, from 2-D representations

56 angles at a point on a straight line and ½ a turn (total 180 o ) angles at a point and one whole turn (total 360 o ) ) reflex angles, and draw shapes using given dimensions and angles state and use the properties of a rectangle (including squares) to deduce related facts distinguish between regular and irregular polygons based on reasoning about equal sides and angles. identify, describe and represent the position of a shape following a reflection or translation, using the appropriate language, solve comparison, sum and difference problems using information presented in line graphs complete, read and interpret information in tables, including timetables Resources measuring equipment multilink real life objects protractors mirrors polydron Core pedagogy Recognise 2d and 2d Identify, describe and Identify turns that Discuss and compare Visualise shape representations of represent shapes after are multiples of 90 acute. Obtuse, reflex and manipulate shape. Use properties a reflection or and write angles. them mentally of shape to identify translation (have Then use a protractor regular and irregular patterns inside shape) to measure and draw

57 All data explored through data Continue to practise Children begin to Practise solving (at Link the concepts of cycle- specify range of charts decide on the most least 2 steps) coordinates and scales problem, plan, introduced in year 4. appropriate comparison, addition to the interpretation collect data, Ensure a variety of representation of data and subtraction data of time graphs represent, interpret timetable formats are and discuss why. presented in line and discuss explored. graphs. findings Thinking pedagogy What could it be? ASN Turn clockwise Draw 2 acute angles I m looking at a 3d Translated shapes are through 720 degrees. that add to 120 shape from above and congruent Would I be in the degrees. How many I see a square, from same position if I different angles could the side I see a turn anticlockwise? you have? triangle etc LINKS Multiplication and division, addition and subtraction. Link to real life problems and cross cur

58 Year 6 Number and place Fractions, decimals Ratio and Algebra M value and addition and percentages proportion and subtraction and multiplication and division Year 6 number and place value and addition and subtraction and multiplicati Statutory read, write, order and compare numbers up to and determine the value of each digit requirements round any whole number to a required degree of accuracy use negative numbers in context, and calculate intervals across zero solve number problems and practical problems that involve all of the above. multiply multi-digit numbers up to 4 digits by a two-digit whole number using the efficient written method of long multiplication divide numbers up to 4 digits by a two-digit whole number using the efficient written method of long division, and interpret remain as appropriate for the context perform mental calculations, including with mixed operations and large numbers identify common factors, common multiples and prim use their knowledge of the order of operations to carry out calculations involving the four operations solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why solve problems involving addition, subtraction, multiplication and division

59 multilink real life objects counting sticks number cards Cuisenaire rods dienes Core pedagogy Read, write and order Explore negative numbers in Understand decimals and numbers up to context and calculate intervals across 0 value of Calculate mentally with large Solve problems involving 4 Use estimation before Confidently and fluently use numbers numbers. Children choose operations using calculating. Use understanding formal methods for all 4 method of calculation by BODMAS. of place value, rounding and operations, must be aware of Develop property of numbers- factors, comparing known facts to when these methods are mental common multiples, primes etc. ensure their answer is suitable. flexibility and reasonable. fluency Thinking Place blank cards on number Investigate effect of not using Is my estimation reasonable? What would we use? - pedagogy line and ask what number could this be? BODMAS on outcome of an operation. children explain their reasoning with verbal and written

60 Statutory use common factors to simplify fractions; use common multiples to express fractions in the same denomination requirements compare and order fractions, including fractions >1 associate a fraction with division to calculate decimal fraction equivalents (e.g ) for a simple fraction (e.g. 3 /8 ) add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions multiply simple pairs of proper fractions, writing the answer in its simplest form (e.g. 1 /4 1 /2 = 1 /8 ) divide proper fractions by whole numbers (e.g. 1 /3 2 = 1 /6 ). identify the value of each digit to three decimal places and multiply and divide numbers by 10, 100 and 1000 where the answers multiply one-digit numbers with up to two decimal places by whole numbers use written division methods in cases where the answer has up to two decimal places solve problems which require answers to be rounded to specified degrees of accuracy solve problems involving the calculation of percentages of whole numbers or measures such as 15% of 360 and the use of percentage recall and use equivalences between simple fractions, decimals and percentages, including in different contexts. Resources measuring equipment multilink Websites Division real life objects counting sticks multiplication number cards addition Cuisenaire rods subtraction Core pedagogy Using understanding Use understanding of Use the array model Recall common C

61 fractions using understand value up to express with common fractions by whole and percentages and rec visual 3 decimal places then denominations, they numbers and multiply use this knowledge to usi representations x by 10,100,1000. can then compare and pairs of proper solve problems. Be fra Children multiply 1 order. fractions. They must able to calculate an and 2 digit numbers Use array models to express their answer in fractions, decimal by whole numbers.. use add and subtract the simplest form. fractions and understanding to solve fractions with percentages of amounts puzzles and problems. different and use these to denominators. compare information. Thinking Show me children Ordering of fractions using Agree/disagree Choose and explain the correct If I pedagogy demonstrate effect of multiplying by proportional representations When I multiply by fractions the answer should be bigger. method to solve a problem wha

62 Year 6- ratio and proportion Statutory solve problems involving the relative sizes of two quantities, including similarity requirements solve problems involving unequal sharing and grouping. Resources measuring equipment multilink real life objects counting sticks number cards Cuisenaire rods Core pedagogy Children study Use ratio to Children solve Children make links U Link ratio proportionality using calculate scales in problems with unequal between ratio and rat and proportion scaling drawings. scales. proportion and art- com to all areas of (multiplication and golden ratio sha mathematics division facts and and explore in recipes) and real life representation

63 Thinking This rod is x what are Produce own blue Hard and easy ratio What do you notice is By pedagogy the other rods? prints of the school For one egg use 3 the effect on the shape ha spoons so if we distort the inc

64 Year 6- algebra Statutory express missing number problems algebraically requirements use simple formulae expressed in words generate and describe linear number sequences find pairs of numbers that satisfy number sentences involving two unknowns Resources measuring equipment multilink real life objects counting sticks number cards Cuisenaire rods Core pedagogy Introduce symbols and Learn to interpret Learn to enumerate all Generate and describe Le letters to represent missing number possibilities of linier number sequences num Exploring variables and problems and express combinations of 2 algebraically equ general unknowns in algebraically variables. unk structures and mathematical

65 Thinking Making Making word stories Here are 5 cards The nth term for the M pedagogy generalisations A clown is carrying A A B B B sequence 2,4,6,8 is A Equivalent expressions balloons and he lets 7 They stand for 2 2n num a+b=b+a go and he is left with different whole the Angles a+b+c=180 9 how many did he numbers. The sum of of start with? the 5 numbers is the 9= y what could be the the values of a and b an In bou X

National Curriculum 2014 Numeracy Objectives Number Number and Place Value Year 1 Year 2 Year 3 Year 4 Year 5 Year 6

National Curriculum 2014 Numeracy Objectives Number Number and Place Value Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Number Number and Place Value Pupils should be taught to and backwards, beginning with 0 or 1, or from any given number 0, and in tens from any number, forward and backward 50 and 100; find 10 or 100 more

More information

1. Number 2. Addition and Subtraction 3. Multiplication and Division 4. Fractions

1. Number 2. Addition and Subtraction 3. Multiplication and Division 4. Fractions Numeracy assessment guidelines: 1 Name 1. Number 2. Addition and Subtraction 3. Multiplication and Division 4. Fractions 1 Count to and across 100, forwards and backwards, beginning with 0 or 1, or from

More information

Charlesworth School Year Group Maths Targets

Charlesworth School Year Group Maths Targets Charlesworth School Year Group Maths Targets Year One Maths Target Sheet Key Statement KS1 Maths Targets (Expected) These skills must be secure to move beyond expected. I can compare, describe and solve

More information

My Year 1 Maths Targets

My Year 1 Maths Targets My Year 1 Maths Targets Number number and place value I can count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number. I can count in multiples of twos, fives and

More information

Year 1 maths expectations (New Curriculum)

Year 1 maths expectations (New Curriculum) Year 1 maths expectations Counts to and across 100, forwards and backwards, beginning with 0 or one, or from any given number Counts, reads and writes numbers to 100 in numerals; counts in multiples of

More information

Primary Curriculum 2014

Primary Curriculum 2014 Primary Curriculum 2014 Suggested Key Objectives for Mathematics at Key Stages 1 and 2 Year 1 Maths Key Objectives Taken from the National Curriculum 1 Count to and across 100, forwards and backwards,

More information

Maths Targets Year 1 Addition and Subtraction Measures. N / A in year 1.

Maths Targets Year 1 Addition and Subtraction Measures. N / A in year 1. Number and place value Maths Targets Year 1 Addition and Subtraction Count to and across 100, forwards and backwards beginning with 0 or 1 or from any given number. Count, read and write numbers to 100

More information

The National Curriculum 2014 Programmes of Study for Mathematics

The National Curriculum 2014 Programmes of Study for Mathematics The National Curriculum 2014 Programmes of Study for Mathematics Information inserted by the Lancashire Mathematics Team to support schools and teachers in identifying elements of the curriculum that have

More information

MATHEMATICS LOWER KS2

MATHEMATICS LOWER KS2 MATHEMATICS LOWER KS2 The principal focus of mathematics teaching in lower key stage 2 is to ensure that pupils become increasingly fluent with whole numbers and the four operations, including number facts

More information

Year R Maths Objectives

Year R Maths Objectives Year R Maths Objectives In order to meet the Early Learning Goals at the end of Year R children must be able to: Numbers Count reliably with numbers from -0, place them in order and say which number is

More information

Year 2 Maths Objectives

Year 2 Maths Objectives Year 2 Maths Objectives Counting Number - number and place value Count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backward Place Value Comparing and Ordering Read and write

More information

National Curriculum for England 2014 Abacus Year 4 Medium Term Plan

National Curriculum for England 2014 Abacus Year 4 Medium Term Plan National Curriculum for England 2014 Year 4 always covers the content of the National Curriculum within the paired age range (i.e. Y1/2, Y3/4, 5/6). Very occasionally postpones something from the first

More information

Numeracy Targets. I can count at least 20 objects

Numeracy Targets. I can count at least 20 objects Targets 1c I can read numbers up to 10 I can count up to 10 objects I can say the number names in order up to 20 I can write at least 4 numbers up to 10. When someone gives me a small number of objects

More information

Knowing and Using Number Facts

Knowing and Using Number Facts Knowing and Using Number Facts Use knowledge of place value and Use knowledge of place value and addition and subtraction of two-digit multiplication facts to 10 10 to numbers to derive sums and derive

More information

Year 2 Maths Objectives

Year 2 Maths Objectives Year 2 Maths Objectives Place Value COUNTING COMPARING NUMBERS IDENTIFYING, REPRESENTING & ESTIMATING NUMBERS count in steps of 1, 2, 3, and 5 from 0, and in tens from any two-digit number, forward or

More information

Maths Year 2 Step 1 Targets Number and place value count in steps of 2 and 5 from 0; forwards and backwards. use number facts to solve problems

Maths Year 2 Step 1 Targets Number and place value count in steps of 2 and 5 from 0; forwards and backwards. use number facts to solve problems Maths Year 2 Step 1 Targets Number and place value count in steps of 2 and 5 from 0; forwards and backwards. Begin to use the term multiple identify and represent numbers using different representations

More information

Oral and Mental calculation

Oral and Mental calculation Oral and Mental calculation Read and write any integer and know what each digit represents. Read and write decimal notation for tenths and hundredths and know what each digit represents. Order and compare

More information

Maths Level Targets. This booklet outlines the maths targets for each sub-level in maths from Level 1 to Level 5.

Maths Level Targets. This booklet outlines the maths targets for each sub-level in maths from Level 1 to Level 5. Maths Level Targets This booklet outlines the maths targets for each sub-level in maths from Level 1 to Level 5. Expected National Curriculum levels for the end of each year group are: Year 1 Year 2 Year

More information

Unit 9. Unit 10. Unit 11. Unit 12. Introduction Busy Ant Maths Year 2 Medium-Term Plans. Number - Geometry - Position & direction

Unit 9. Unit 10. Unit 11. Unit 12. Introduction Busy Ant Maths Year 2 Medium-Term Plans. Number - Geometry - Position & direction Busy Ant Maths Year Medium-Term Plans Unit 9 Geometry - Position & direction Unit 0 ( Temperature) Unit Statistics Unit Fractions (time) 8 Busy Ant Maths Year Medium-Term Plans Introduction Unit Geometry

More information

Level 1 - Maths Targets TARGETS. With support, I can show my work using objects or pictures 12. I can order numbers to 10 3

Level 1 - Maths Targets TARGETS. With support, I can show my work using objects or pictures 12. I can order numbers to 10 3 Ma Data Hling: Interpreting Processing representing Ma Shape, space measures: position shape Written Mental method s Operations relationship s between them Fractio ns Number s the Ma1 Using Str Levels

More information

Scope and Sequence KA KB 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B

Scope and Sequence KA KB 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B Scope and Sequence Earlybird Kindergarten, Standards Edition Primary Mathematics, Standards Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced

More information

Year 1. Use numbered number lines to add, by counting on in ones. Encourage children to start with the larger number and count on.

Year 1. Use numbered number lines to add, by counting on in ones. Encourage children to start with the larger number and count on. Year 1 Add with numbers up to 20 Use numbered number lines to add, by counting on in ones. Encourage children to start with the larger number and count on. +1 +1 +1 Children should: Have access to a wide

More information

MATHEMATICS - SCHEMES OF WORK

MATHEMATICS - SCHEMES OF WORK MATHEMATICS - SCHEMES OF WORK For Children Aged 7 to 12 Mathematics Lessons Structure Time Approx. 90 minutes 1. Remind class of last topic area explored and relate to current topic. 2. Discuss and explore

More information

National Curriculum for England 2014 Abacus Year 2 Medium Term Plan

National Curriculum for England 2014 Abacus Year 2 Medium Term Plan National Curriculum for Engl 2014 Year 2 always covers the content of the National Curriculum within the paired age range (i.e. Y1/2, Y3/4, 5/6). Very occasionally postpones something from the first year

More information

Mathematics K 6 continuum of key ideas

Mathematics K 6 continuum of key ideas Mathematics K 6 continuum of key ideas Number and Algebra Count forwards to 30 from a given number Count backwards from a given number in the range 0 to 20 Compare, order, read and represent to at least

More information

CALCULATION POLICY NEW CURRICULUM 2014 MENTAL AND WRITTEN CALCULATIONS

CALCULATION POLICY NEW CURRICULUM 2014 MENTAL AND WRITTEN CALCULATIONS CALCULATION POLICY NEW CURRICULUM 2014 MENTAL AND WRITTEN CALCULATIONS 1 This policy outlines both the mental and written methods that should be taught from Year 1 to Year 6. The policy has been written

More information

Math syllabus Kindergarten 1

Math syllabus Kindergarten 1 Math syllabus Kindergarten 1 Number strand: Count forward and backwards to 10 Identify numbers to 10 on a number line Use ordinal numbers first (1 st ) to fifth (5 th ) correctly Recognize and play with

More information

INFORMATION FOR PARENTS AND CARERS TARGETS IN MATHEMATICS

INFORMATION FOR PARENTS AND CARERS TARGETS IN MATHEMATICS Emerging towards the expected Year 1 level I can share 6 objects between 2 children. I can write and use numbers (less than 10) in role play. I can compare bigger than and smaller than in role play. I

More information

Year 3 Year 4 Year 5 Year 6. Strand 1 Number

Year 3 Year 4 Year 5 Year 6. Strand 1 Number NRICH http://nrich.maths.org problems linked to the primary national curriculum for mathematics in Years 3, 4, 5 and 6 The stars indicate the level of confidence and competence needed to begin the activity.

More information

Assessment for Learning Explain how you solved this problem. equipment to show your solution? STRAND CODE Year 2 Objectives Year 2 Year 2

Assessment for Learning Explain how you solved this problem. equipment to show your solution? STRAND CODE Year 2 Objectives Year 2 Year 2 BLOCK A Speaking and listening objectives for the block Explain how you solved this problem. Speak with clarity and Does everyone understand how the problem was Unit 1 intonation when reading and reciting

More information

Teaching programme: Reception

Teaching programme: Reception Teaching programme: Reception Counting and recognising numbers 2 8 2 2, 3 4, 5 5 6 7 7 8 Counting Say and use the number names in order In familiar contexts such as number rhymes, songs, stories, counting

More information

SIL Maths Plans Year 3_Layout 1 06/05/2014 13:48 Page 2 Maths Plans Year 3

SIL Maths Plans Year 3_Layout 1 06/05/2014 13:48 Page 2 Maths Plans Year 3 Maths Plans Year 3 Contents Introduction Introduction 1 Using the Plans 2 Autumn 1 7 Autumn 2 21 Spring 1 43 Spring 2 59 Summer 1 75 Basic Skills 89 Progression 97 The Liverpool Maths team have developed

More information

I know when I have written a number backwards and can correct it when it is pointed out to me I can arrange numbers in order from 1 to 10

I know when I have written a number backwards and can correct it when it is pointed out to me I can arrange numbers in order from 1 to 10 Mathematics Targets Moving from Level W and working towards level 1c I can count from 1 to 10 I know and write all my numbers to 10 I know when I have written a number backwards and can correct it when

More information

Number: Multiplication and Division

Number: Multiplication and Division MULTIPLICATION & DIVISION FACTS count in steps of 2, 3, and 5 count from 0 in multiples of 4, 8, 50 count in multiples of 6, count forwards or backwards from 0, and in tens from any and 100 7, 9, 25 and

More information

BRIEF ON THE CHANGES TO THE NEW NATIONAL MATHS CURRICULUM FROM SEPTEMBER 2014

BRIEF ON THE CHANGES TO THE NEW NATIONAL MATHS CURRICULUM FROM SEPTEMBER 2014 BRIEF ON THE CHANGES TO THE NEW NATIONAL MATHS CURRICULUM FROM SEPTEMBER 2014 Page 0 of 84 Table of Contents TIMELINE TIMELINE FOR IMPLEMENTATION OF NEW NATIONAL MATHS CURRICULUM... 4 KEY TIMELINE FOR

More information

MATHS LEVEL DESCRIPTORS

MATHS LEVEL DESCRIPTORS MATHS LEVEL DESCRIPTORS Number Level 3 Understand the place value of numbers up to thousands. Order numbers up to 9999. Round numbers to the nearest 10 or 100. Understand the number line below zero, and

More information

Cambridge Primary Mathematics Curriculum Framework (with codes)

Cambridge Primary Mathematics Curriculum Framework (with codes) Cambridge Primary Mathematics Curriculum Framework (with codes) Contents Introduction Stage 1...1 Stage 2...5 Stage 3...9 Stage 4...14 Stage 5...18 Stage 6...24 Note on codes Each learning objective has

More information

Subtraction. Year 1 subtract from numbers up to 20

Subtraction. Year 1 subtract from numbers up to 20 Year 1 subtract from up to 20 Children are encouraged to develop a mental picture of the number system in their heads to use for calculation. They develop ways of recording calculations using pictures,

More information

Addition and subtraction

Addition and subtraction Addition and subtraction numbers using concrete objects, pictorial representations. All number facts 10 are secure by the end of Year 1 in order to progress and consolidate decimal numbers in KS2. From

More information

EVERY DAY COUNTS CALENDAR MATH 2005 correlated to

EVERY DAY COUNTS CALENDAR MATH 2005 correlated to EVERY DAY COUNTS CALENDAR MATH 2005 correlated to Illinois Mathematics Assessment Framework Grades 3-5 E D U C A T I O N G R O U P A Houghton Mifflin Company YOUR ILLINOIS GREAT SOURCE REPRESENTATIVES:

More information

Measurement with Reasoning

Measurement with Reasoning compare, describe and solve practical problems for: * lengths and heights [e.g. long/short, longer/shorter, tall/short, double/half] * mass/weight [e.g. heavy/light, heavier than, lighter than] * capacity

More information

National curriculum tests. Key stage 2. Mathematics test framework. National curriculum tests from 2016. For test developers

National curriculum tests. Key stage 2. Mathematics test framework. National curriculum tests from 2016. For test developers National curriculum tests Key stage 2 Mathematics test framework National curriculum tests from 2016 For test developers Crown copyright 2015 2016 key stage 2 mathematics test framework: national curriculum

More information

Autumn - 12 Weeks. Spring 11 Weeks. Summer 12 Weeks. Not As We Know It Limited 2014

Autumn - 12 Weeks. Spring 11 Weeks. Summer 12 Weeks. Not As We Know It Limited 2014 A Year 5 Mathematician Planning of coverage and resources. Autumn - 12 Weeks Spring 11 Weeks Summer 12 Weeks TARGETS NHM YR 5 Collins 5 Abacus 5 Abacus 6 LA Prior Step NHM 4 CPM 4 Ginn 4 Number, place

More information

Number and Place Value. September 2014 1. Year 3 Year 4 Year 5 Year 6

Number and Place Value. September 2014 1. Year 3 Year 4 Year 5 Year 6 NRICH http://nrich.maths.org problems linked to the primary national curriculum for mathematics in Years 3, 4, 5 and 6 The stars indicate the level of confidence and competence needed to begin the activity.

More information

Primary Years Programme Mathematics Curriculum

Primary Years Programme Mathematics Curriculum Primary Years Programme Mathematics Curriculum The following document seeks to lay out the minimum requirement to be taught in Mathematics for each grade level in each of the areas of Number, Pattern and

More information

Illinois State Standards Alignments Grades Three through Eleven

Illinois State Standards Alignments Grades Three through Eleven Illinois State Standards Alignments Grades Three through Eleven Trademark of Renaissance Learning, Inc., and its subsidiaries, registered, common law, or pending registration in the United States and other

More information

In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data.

In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data. MATHEMATICS: THE LEVEL DESCRIPTIONS In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data. Attainment target

More information

Multiplication. Year 1 multiply with concrete objects, arrays and pictorial representations

Multiplication. Year 1 multiply with concrete objects, arrays and pictorial representations Year 1 multiply with concrete objects, arrays and pictorial representations Children will experience equal groups of objects and will count in 2s and 10s and begin to count in 5s. They will work on practical

More information

Addition. They use numbered number lines to add, by counting on in ones. Children are encouraged to start with the larger number and count on.

Addition. They use numbered number lines to add, by counting on in ones. Children are encouraged to start with the larger number and count on. Year 1 add with numbers up to 20 Children are encouraged to develop a mental picture of the number system in their heads to use for calculation. They develop ways of recording calculations using pictures,

More information

ISAT Mathematics Performance Definitions Grade 4

ISAT Mathematics Performance Definitions Grade 4 ISAT Mathematics Performance Definitions Grade 4 EXCEEDS STANDARDS Fourth-grade students whose measured performance exceeds standards are able to identify, read, write, represent, and model whole numbers

More information

Everyday Mathematics CCSS EDITION CCSS EDITION. Content Strand: Number and Numeration

Everyday Mathematics CCSS EDITION CCSS EDITION. Content Strand: Number and Numeration CCSS EDITION Overview of -6 Grade-Level Goals CCSS EDITION Content Strand: Number and Numeration Program Goal: Understand the Meanings, Uses, and Representations of Numbers Content Thread: Rote Counting

More information

Everyday Mathematics GOALS

Everyday Mathematics GOALS Copyright Wright Group/McGraw-Hill GOALS The following tables list the Grade-Level Goals organized by Content Strand and Program Goal. Content Strand: NUMBER AND NUMERATION Program Goal: Understand the

More information

Mathematics Scope and Sequence, K-8

Mathematics Scope and Sequence, K-8 Standard 1: Number and Operation Goal 1.1: Understands and uses numbers (number sense) Mathematics Scope and Sequence, K-8 Grade Counting Read, Write, Order, Compare Place Value Money Number Theory K Count

More information

Number: Multiplication and Division with Reasoning

Number: Multiplication and Division with Reasoning count in multiples of twos, fives and tens (copied from Number and Number: Multiplication and Division with Reasoning MULTIPLICATION & DIVISION FACTS Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 count in

More information

Maths Vocabulary for the New National Curriculum

Maths Vocabulary for the New National Curriculum Maths Vocabulary for the New National Curriculum This document sets out Key Stage 1 (KS1) and Key Stage 2 (KS2) maths vocabulary under the new National Curriculum. The tables can be used to check pupils

More information

The Crescent Primary School Calculation Policy

The Crescent Primary School Calculation Policy The Crescent Primary School Calculation Policy Examples of calculation methods for each year group and the progression between each method. January 2015 Our Calculation Policy This calculation policy has

More information

Swavesey Primary School Calculation Policy. Addition and Subtraction

Swavesey Primary School Calculation Policy. Addition and Subtraction Addition and Subtraction Key Objectives KS1 Foundation Stage Say and use number names in order in familiar contexts Know that a number identifies how many objects in a set Count reliably up to 10 everyday

More information

PROGRESSION MAP Multiplication This must be viewed alongside the division map so that connections can be made. YR Y1 Y2 Y3 Y4 Y5 Y6

PROGRESSION MAP Multiplication This must be viewed alongside the division map so that connections can be made. YR Y1 Y2 Y3 Y4 Y5 Y6 PROGRESSION MAP Multiplication This must be viewed alongside the division map so that connections can be made. YR Y1 Y2 Y3 Y4 Y5 Y6 Begin to understand multiplication by using concrete objects, pictorial

More information

ASSESSMENT FOCUS APP MATHS NUMBER TRACKER LEVEL 1 1c 1b 1a Using and Applying. * I am beginning to represent my maths work with objects and pictures

ASSESSMENT FOCUS APP MATHS NUMBER TRACKER LEVEL 1 1c 1b 1a Using and Applying. * I am beginning to represent my maths work with objects and pictures ASSESSMENT FOCUS APP MATHS NUMBER TRACKER LEVEL 1 1c 1b 1a Using and Applying Problem solving *I am beginning to understand maths ideas in everyday situations by using them in role play *I am beginning

More information

Ingleby Manor Scheme of Work : Year 7. Objectives Support L3/4 Core L4/5/6 Extension L6/7

Ingleby Manor Scheme of Work : Year 7. Objectives Support L3/4 Core L4/5/6 Extension L6/7 Autumn 1 Mathematics Objectives Support L3/4 Core L4/5/6 Extension L6/7 Week 1: Algebra 1 (6 hours) Sequences and functions - Recognize and extend number sequences - Identify the term to term rule - Know

More information

Calculation Policy Version 1 January 2015

Calculation Policy Version 1 January 2015 2015 Calculation Policy Version 1 January 2015 NATIONAL CURRICULUM 2014 ABBOTSMEDE PRIMARY SCHOOL CASTOR C OF E PRIMARY SCHOOL DISCOVERY PRIMARY SCHOOL DOGSTHORPE INFANTS EYE C OF E PRIMARY SCHOOOL NENE

More information

Count back in ones on a numbered number line to take away, with numbers up to 20

Count back in ones on a numbered number line to take away, with numbers up to 20 SUBTRACTION Stage 1 Subtract from numbers up to 20 Children consolidate understanding of subtraction practically, showing subtraction on bead strings, using cubes etc. and in familiar contexts, and are

More information

PROGRESSION THROUGH CALCULATIONS FOR SUBTRACTION

PROGRESSION THROUGH CALCULATIONS FOR SUBTRACTION PROGRESSION THROUGH CALCULATIONS FOR SUBTRACTION By the end of year 6, children will have a range of calculation methods, mental and written. Selection will depend upon the numbers involved. Children should

More information

Minnesota Academic Standards

Minnesota Academic Standards A Correlation of to the Minnesota Academic Standards Grades K-6 G/M-204 Introduction This document demonstrates the high degree of success students will achieve when using Scott Foresman Addison Wesley

More information

Mathematics standards

Mathematics standards Mathematics standards Grade 6 Summary of students performance by the end of Grade 6 Reasoning and problem solving Students represent and interpret routine and non-routine mathematical problems in a range

More information

Subtraction Year 1 6 2 = 4

Subtraction Year 1 6 2 = 4 Subtraction Year 1 Key Vocabulary Key skills for subtraction at Y1: Given a number, say one more or one less. Count to and over 100, forward and back, from any number. Represent and use subtraction facts

More information

Key Stage 2 Mathematics Programme of Study

Key Stage 2 Mathematics Programme of Study Deeloping numerical reasoning Identify processes and connections Represent and communicate Reiew transfer mathematical to a ariety of contexts and eeryday situations identify the appropriate steps and

More information

PUTTERIDGE PRIMARY SCHOOL

PUTTERIDGE PRIMARY SCHOOL Calculations policy Version 3 PUTTERIDGE PRIMARY SCHOOL Autumn 2015 Authored by: Rob Weightman Written Methods& Mental Methods & A D D I T I O N FOUNDATION STAGE YEAR 1 YEAR 2 Count with 1:1 correspondence

More information

Bridging Documents for Mathematics

Bridging Documents for Mathematics Bridging Documents for Mathematics 5 th /6 th Class, Primary Junior Cycle, Post-Primary Primary Post-Primary Card # Strand(s): Number, Measure Number (Strand 3) 2-5 Strand: Shape and Space Geometry and

More information

Number: Fractions (including Decimals and Percentages) Reasoning

Number: Fractions (including Decimals and Percentages) Reasoning Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 COUNTING IN FRACTIONAL STEPS Pupils should count in fractions up to 10, starting from any number and using the1/2 and 2/4 equivalence on the number line (Non Statutory

More information

KS3 Maths Learning Objectives (excludes Year 9 extension objectives)

KS3 Maths Learning Objectives (excludes Year 9 extension objectives) KS3 Maths Learning Objectives (excludes Year 9 extension objectives) blue Year 7 black Year 8 green Year 9 NUMBER N1 Place value and standard form N1.1 Place value N1.2 Powers of ten Framework Objectives

More information

Standards and progression point examples

Standards and progression point examples Mathematics Progressing towards Foundation Progression Point 0.5 At 0.5, a student progressing towards the standard at Foundation may, for example: connect number names and numerals with sets of up to

More information

Calculation strategies for subtraction

Calculation strategies for subtraction Calculation strategies for subtraction 1 Year 1 Subtract numbers up to 20. Children are encouraged to develop a mental picture of the number system in their heads to use for calculation. They develop ways

More information

PROGRESSION THROUGH CALCULATIONS FOR MULTIPLICATION

PROGRESSION THROUGH CALCULATIONS FOR MULTIPLICATION PROGRESSION THROUGH CALCULATIONS FOR MULTIPLICATION THE FOLLOWING ARE STANDARDS THAT WE EXPECT THE MAJORITY OF CHILDREN TO ACHIEVE BY THE END OF THE YEAR. YR Related objectives: Count repeated groups of

More information

Excel Math Fourth Grade Standards for Mathematical Practice

Excel Math Fourth Grade Standards for Mathematical Practice Excel Math Fourth Grade Standards for Mathematical Practice The Common Core State Standards for Mathematical Practice are integrated into Excel Math lessons. Below are some examples of how we include these

More information

1A: Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

1A: Understand numbers, ways of representing numbers, relationships among numbers, and number systems. NCTM STANDARD 1: Numbers and Operations Kindergarten Grade 2 1A: Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Kindergarten Grade One Grade Two 1. Count

More information

MULTIPLICATION. Present practical problem solving activities involving counting equal sets or groups, as above.

MULTIPLICATION. Present practical problem solving activities involving counting equal sets or groups, as above. MULTIPLICATION Stage 1 Multiply with concrete objects, arrays and pictorial representations How many legs will 3 teddies have? 2 + 2 + 2 = 6 There are 3 sweets in one bag. How many sweets are in 5 bags

More information

COMMON CORE STATE STANDARDS FOR MATHEMATICS 3-5 DOMAIN PROGRESSIONS

COMMON CORE STATE STANDARDS FOR MATHEMATICS 3-5 DOMAIN PROGRESSIONS COMMON CORE STATE STANDARDS FOR MATHEMATICS 3-5 DOMAIN PROGRESSIONS Compiled by Dewey Gottlieb, Hawaii Department of Education June 2010 Operations and Algebraic Thinking Represent and solve problems involving

More information

Summary Of Mental Maths Targets EYFS Yr 6. Year 3. Count from 0 in multiples of 4 & 8, 50 & 100. Count back in 100s, 10s, 1s eg.

Summary Of Mental Maths Targets EYFS Yr 6. Year 3. Count from 0 in multiples of 4 & 8, 50 & 100. Count back in 100s, 10s, 1s eg. Autumn 1 Say the number names in order to 10. Read and write from 1 to 20 in numerals and words. Count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backward. Count from 0 in

More information

Simonside Primary School Progression in Multiplication

Simonside Primary School Progression in Multiplication Simonside Primary School Progression in Multiplication Year Objective Method Pictorial/ EYFS Chanting of counting in 2s Repeated ing Counting in pairs Doubling / recorded using ICT (eg digital photos /

More information

A level is a level. Compiled for 2008

A level is a level. Compiled for  2008 Level5opaedia A level is a level Compiled for www.glosmaths.org, 2008 Please note that Using and Applying assessment criteria are not included within the Levelopaedia Numbers and the Number System Use

More information

Vocabulary, Signs, & Symbols product dividend divisor quotient fact family inverse. Assessment. Envision Math Topic 1

Vocabulary, Signs, & Symbols product dividend divisor quotient fact family inverse. Assessment. Envision Math Topic 1 1st 9 Weeks Pacing Guide Fourth Grade Math Common Core State Standards Objective/Skill (DOK) I Can Statements (Knowledge & Skills) Curriculum Materials & Resources/Comments 4.OA.1 4.1i Interpret a multiplication

More information

Glencoe. correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 3-3, 5-8 8-4, 8-7 1-6, 4-9

Glencoe. correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 3-3, 5-8 8-4, 8-7 1-6, 4-9 Glencoe correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 STANDARDS 6-8 Number and Operations (NO) Standard I. Understand numbers, ways of representing numbers, relationships among numbers,

More information

Voyager Sopris Learning Vmath, Levels C-I, correlated to the South Carolina College- and Career-Ready Standards for Mathematics, Grades 2-8

Voyager Sopris Learning Vmath, Levels C-I, correlated to the South Carolina College- and Career-Ready Standards for Mathematics, Grades 2-8 Page 1 of 35 VMath, Level C Grade 2 Mathematical Process Standards 1. Make sense of problems and persevere in solving them. Module 3: Lesson 4: 156-159 Module 4: Lesson 7: 220-223 2. Reason both contextually

More information

Geometry Progress Ladder

Geometry Progress Ladder Geometry Progress Ladder Maths Makes Sense Foundation End-of-year objectives page 2 Maths Makes Sense 1 2 End-of-block objectives page 3 Maths Makes Sense 3 4 End-of-block objectives page 4 Maths Makes

More information

Grade 5 Math Content 1

Grade 5 Math Content 1 Grade 5 Math Content 1 Number and Operations: Whole Numbers Multiplication and Division In Grade 5, students consolidate their understanding of the computational strategies they use for multiplication.

More information

The Australian Curriculum Mathematics

The Australian Curriculum Mathematics The Australian Curriculum Mathematics Mathematics ACARA The Australian Curriculum Number Algebra Number place value Fractions decimals Real numbers Foundation Year Year 1 Year 2 Year 3 Year 4 Year 5 Year

More information

Addition and subtraction. Key Stage 1:

Addition and subtraction. Key Stage 1: Key Stage 1: The principal focus of mathematics teaching in key stage 1 is to ensure that pupils develop confidence and mental fluency with whole numbers, counting and place value. This should involve

More information

PROGRESSION THROUGH CALCULATIONS FOR MULTIPLICATION

PROGRESSION THROUGH CALCULATIONS FOR MULTIPLICATION PROGRESSION THROUGH CALCULATIONS FOR MULTIPLICATION By the end of year 6, children will have a range of calculation methods, mental and written. Selection will depend upon the numbers involved. Children

More information

Topic: 1 - Understanding Addition and Subtraction

Topic: 1 - Understanding Addition and Subtraction 8 days / September Topic: 1 - Understanding Addition and Subtraction Represent and solve problems involving addition and subtraction. 2.OA.1. Use addition and subtraction within 100 to solve one- and two-step

More information

Math Common Core Standards Fourth Grade

Math Common Core Standards Fourth Grade Operations and Algebraic Thinking (OA) Use the four operations with whole numbers to solve problems. OA.4.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as a statement

More information

1) Make Sense and Persevere in Solving Problems.

1) Make Sense and Persevere in Solving Problems. Standards for Mathematical Practice in Second Grade The Common Core State Standards for Mathematical Practice are practices expected to be integrated into every mathematics lesson for all students Grades

More information

SCOPE & SEQUENCE. Kindergarten, First Grade, and Second Grade. Skills and Activities

SCOPE & SEQUENCE. Kindergarten, First Grade, and Second Grade. Skills and Activities SCOPE & SEQUENCE Kindergarten, First Grade, and Second Grade Skills and Activities INNOVATIVE LEARNING CONCEPTS INC. creators of TOUCHMATH TouchMath materials were first published in 1975. Innovative Learning

More information

numerical place value additional topics rounding off numbers power of numbers negative numbers addition with materials fundamentals

numerical place value additional topics rounding off numbers power of numbers negative numbers addition with materials fundamentals Math Scope & Sequence fundamentals number sense and numeration of the decimal system Count to 10 by units Associate number to numeral (1-10) KN 1 KN 1 KN 2 KN 2 Identify odd and even numbers/numerals and

More information

Teaching Guidance. For. Counting and Partitioning Numbers

Teaching Guidance. For. Counting and Partitioning Numbers Teaching Guidance For Counting and Partitioning Numbers (Overcoming Barriers Moving Levels 1 to 2, 2 to 3, 3 to 4, 4 to 5) 1 of 2 The National Strategies Primary Overcoming barriers in mathematics helping

More information

Step 1 Representations Recordings Number count reliably with numbers from 1 to 20. Bead strings to 20 and 100 5+3=8 15+3=18. What else do you know?

Step 1 Representations Recordings Number count reliably with numbers from 1 to 20. Bead strings to 20 and 100 5+3=8 15+3=18. What else do you know? Progression in calculation: Abbey Park Middle School NH 2013/2014 amended for APMS by IT June 2014, Addition and Subtraction Step 1 Representations Recordings count reliably with from 1 to 20 What number

More information

SUBTRACTION CALCULATION GUIDANCE

SUBTRACTION CALCULATION GUIDANCE SUBTRACTION CALCULATION GUIDANCE Year 1 read, write and interpret mathematical statements involving, subtraction (-) and equals (=) signs represent and use number bonds and related subtraction facts within

More information

Pocantico Hills School District Grade 1 Math Curriculum Draft

Pocantico Hills School District Grade 1 Math Curriculum Draft Pocantico Hills School District Grade 1 Math Curriculum Draft Patterns /Number Sense/Statistics Content Strands: Performance Indicators 1.A.1 Determine and discuss patterns in arithmetic (what comes next

More information

St Ninian s High School. I understand this part of the course = I am unsure of this part of the course =

St Ninian s High School. I understand this part of the course = I am unsure of this part of the course = St Ninian s High School Mathematics Department Curriculum for Excellence TJ Book E Pupil Learning Log I understand this part of the course = I am unsure of this part of the course = I do not understand

More information

Number Sense and Operations

Number Sense and Operations Number Sense and Operations representing as they: 6.N.1 6.N.2 6.N.3 6.N.4 6.N.5 6.N.6 6.N.7 6.N.8 6.N.9 6.N.10 6.N.11 6.N.12 6.N.13. 6.N.14 6.N.15 Demonstrate an understanding of positive integer exponents

More information