GRADE 3 OVERALL EXPECTATIONS. Subject: Mathematics


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1 GRADE 3 OVERALL EXPECTATIONS Subject: Mathematics The mathematics expectations are arranged in five interwoven strands of knowledge: number, data handling, shape and space, pattern and function and measurement. In number and pattern and function, students inquire into our number system, and its operations, patterns and functions. This is where students acquire the language of arithmetic. These two strands are usually taught as stand alone mathematical topics, if they are not included in the units of inquiry. Data handling, measurement, and shape and space, are the areas of mathematics that other disciplines use to research, describe, represent and understand aspects of their domain, therefore, topics in these strands are studied also in authentic contexts of the units of inquiry. The students will have the opportunity to identify and reflect upon big ideas by making connections between the questions asked and the concepts that drive the inquiry. (Adopted from the IB PYP Mathematics scope and sequence 2003) These are the target skills and expectations for Grade 3. Number Whole Numbers representing numbers up to 10,000 place using numerals, words, objects and digital displays identifying the number before and after a given two, three or fourdigit number applying an understanding of place value and the role of zero to read, write and order numbers up to four digits stating the place value of digits in two, three or fourdigit numbers eg in the number 3426, the 3 represents 3000 or 3 thousands ordering a set of fourdigit numbers in ascending or descending order using the symbols for is less than (<) and is greater than (>) to show the relationship between two numbers counting forwards and backwards by tens or hundreds, on and off the decade eg 1220, 1230, 1240 (on the decade); 423, 323, 223 (off the decade) Estimation/Rounding Reasonably estimate answers by rounding and approximation. Make reasonable estimates of sums, differences and products. Round 3 digit numbers to the nearest thousand. Be introduced to a four function calculator to check computation. Calculations Select, demonstrate, and explain multiple strategies for solving multipledigit addition, subtraction, multiplication, and division equations. Continue to select, solve, and explain equations using a variety of methods (words, pictures, symbols, charts, graphs, etc). Addition and Subtraction Continue to model addition and subtraction equations to with and without regrouping.
2 Use mathematical vocabulary and symbols of addition and subtraction: add, subtract, difference, sum ( +,  ). using mental strategies for addition and subtraction involving two, three and fourdigit numbers, including o the jump strategy eg ; = 53, = 58 o the split strategy eg ; is 58 o the compensation strategy eg ; is 93, subtract 1, to obtain 92 o using patterns to extend number facts eg 5 2 = 3, so is 300 o bridging the decades eg ; is 44, = 51 o changing the order of addends to form multiples of 10 eg ; add 16 and 4 first o recording mental strategies eg ; I added 20 to 159 to get 179, then I added 2 more to get 181. or, on an empty number line adding and subtracting two or more numbers, with and without trading, using concrete materials and recording their method using a formal written algorithm and applying place value to solve addition and subtraction problems, involving two, three and fourdigit numbers Introduced to reading, writing, and modelling addition and subtraction of integers. Multiplication and Division counting by threes, fours, sixes, sevens, eights or nines using skip counting linking multiplication and division facts using groups or arrays using mental strategies to recall multiplication facts up to 10 x 10, including  the commutative property of multiplication eg 7 x 9 = 9 x 7  using known facts to work out unknown facts eg 5 x 5 = 25 so 5 x 6 = (5 x 5) the relationship between multiplication facts eg the multiplication facts for 6 are double the multiplication facts for 3 recognising and using and / to indicate division using mental strategies to divide by a onedigit number, including  the inverse relationship of multiplication and division eg 63 9 = 7 because 7 x 9 = 63  relating to known division facts eg 36 4; halve 36 and halve again using mental strategies to multiply a onedigit number by a multiple of 10 (eg 3 x 20) by  repeated addition ( = 60)  using place value concepts (3 x 2 tens = 6 tens = 60)  factoring (3 x 2 x 10 = 6 x 10 = 60)
3 using mental strategies to divide by a onedigit number, in problems for which answers include a remainder eg 29 6; if 4 x 6 = 24 and 5 x 6 = 30 the answer is 4 remainder 5 recording remainders to division problems eg 17 4 = 4 remainder 1 recording answers, which include a remainder, to division problems to show the connection with multiplication eg 17 = 4 x Fractions/Decimals Use mathematical vocabulary and symbols of fractions: numerator, denominator, equivalence. Add and subtract fractions with the same denominator. Understand and model the concept of equivalence to 1: two halves = 1, three thirds = 1 Understand addition and subtraction of decimals to the 100 th place. Modelling, comparing and representing fractions with denominators 5, 10 and 100 by extending the knowledge and skills covered above to fifths, tenths and hundredths Applying an understanding of place value to express whole numbers, tenths and hundredths as decimals Modelling, comparing and representing fractions with denominators 2, 4 and 8 by o finding equivalence between halves, quarters and eighths using concrete materials and diagrams, by redividing the unit o placing halves, quarters and eighths on a number line between 0 and 1 to further develop equivalence Modelling, comparing and representing fractions with denominators 5, 10 and 100 by extending the knowledge and skills covered above to fifths, tenths and hundredths Pattern and Function Physical Patterns Model with manipulatives the relationship between division and subtraction. Model with manipulatives the relationship between division and multiplication. Model with manipulatives the relationship between multiplication and addition. Numerical Patterns Continue to analyse patterns in number systems to 100. Begin to understand and use the relationship between addition and subtraction: 4+3 = 7, 73 = 4. Understand and use number patterns to solve problems (missing numbers). Continue to identify patterns for multiplication and division: 4x3 =12, 3x4 = 12, 12 3 = 4, 12 4=3 (number families). Recognize, describe, and extend more complex patterns in numbers Use multiplication equations to find unknown quantities (how many rows of two make six). Form and apply a generalisation for a given multiplication problem. Graphical Patterns Model multiplication as an array. Data Handling Sorting Discuss, compare and create sets from data that has subsets using different diagrams.
4 Data Processing Design a survey, process and interpret the data. Understand the purpose of a database by manipulating the data to answer questions and solve problems. Graphing Use the scale on the vertical axis of a bar graph to represent large quantities. Collect and display data in a bar graph and interpret results. Use a tally chart to create a frequency table. Construct a database. Data Analysis Find, describe, and explain the mode in a set of data and its use. Make informed guesses and justify them. Identify the data necessary to solve a given problem. Interpret a database. Shape and Space Shapes Identify, describe and model congruency in 2D shapes. Combine and transform 2D shapes to make other shapes. Describe, sort and model triangles, quadrilaterals and other polygons. Relate solid faces to 2D shapes. Begin to understand that closed figures are polygons having straight sides. Begin to understand perimeter and area in relation to shapes. Understand closed figures with curved lines: circles and ovals. Angles and Lines Understand angle formation, including right angles. Understand an angle as a measure of rotation. Symmetry Create symmetrical patterns, including tessellation. Understand that regular shapes have lines of symmetry. Position Describe position by naming a region in a grid. Continue using four main compass points on a grid. Understand and describe rotations: whole turns, half turns, quarter turns for example north, south, east, and west on a compass, or on an analogue clock. Measurement Time Identify and be able to write time using intervals of 1, 5 and 10 minutes, on 12 hour and 24 hour clocks. Understand the difference between digital and analogue time. Continue to use calendar days, months, seasons. Mass and Capacity Begin to understand and use measures of capacity, and weight measures. Begin to understand and use milligrams in comparison to grams and kilograms. Begin to understand decimal notation and fractional notation in recording mass and capacity. Size and Distance
5 Begin to understand and use linear measures. Begin to understand and use millimetres in comparison to centimetres and kilometres. Begin to understand decimal notation and fractional notation in recording size and distance. Temperature Continue to understand and use the Celsius and Fahrenheit temperature scales. Begin to understand negative and positive temperature in Celsius and Fahrenheit temperature scales. Money Model addition and subtraction using money. Understand decimal notation in relationship to money. Vocabulary and Tools Select appropriate tools and units of measurement. Continue to use measuring tools.
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