Math - 4th Grade. Skills needed & Sequencing of Skills

Transcription

1 Number and Operations ontent Vocabulary Understand and use number notation and N.M Read and write numbers to 1,000,000; relate them to the quantities they represent; compare and order. Generalize place value understanding for multi-digit whole numbers. 4.NBT.2. Read and write multi-digit whole numbers using base-ten numerals, number nam Read write relate compare order Synthesis number model, standard form compare order greater than less than equal not equal least/greatest recognize numbers up to 1, 000,000 understand and use a number model understand and use a number model understands the value of each digit by position recognize greater than/less than/equal/not equal symbols I can read numbers up to 1, 000,000 I can write numbers up to 1,000,000 I can show numbers up to 1,000,000 with a model or picture I can compare numbers up to 1,000,000 I can put numbers in order up to 1,000,000 I can use greater than/less than symbols N.M ompose and decompose numbers using place value to 1,000,000's, e.g., 25,068 is 2 ten thousands, 5 thousands, 0 hundreds, 6 tens, and 8 ones. Generalize place value understanding for multi-digit whole numbers. 4.NBT.2 See Above compose decompose convert standard notation/form; expanded notation; place value; digit; value value of each digit based on its position know how to read/write expanded notation know how to read/write a number in standard number I can identify the value of a digit based its position in a number I can write a number (up to 1,000,000) in its expanded form I can write the standard form of a number when given its expanded form. N.M Understand the magnitude of numbers up to 1,000,000; recognize the place values of numbers and the relationship of each place value to the place to its right, e.g., 1,000 is 10 hundreds. Generalize place value understanding for multi-digit whole numbers. Recognize Understand place value equals relative size of a digit based on its place value (eg. 10 tens equals 100) I can explain or show how many groups of ten it takes to move from one place value to another. factors and multiples N.M Find all factors of any whole number Find through 50, list factor pairs, and List determine if a one-digit number is a factor Determine of a given whole number. factor factor pairs whole number digit product factor tree prime factorization prime composite know the meaning of factor know the meaning of factor pair know which numbers are prime know multiplication facts I can list all the factors of a number up to 50. I can list the factor pairs of a number up to 100. I can tell if a one-digit number is a factor of a whole number. N.M List the first ten multiples of a given onedigit whole number; determine if a whole number is a multiple of a given one-digit whole number. : the four operation with whole numbers to solve problems. 4.OA.1. Interpret a multiplication equation as a List Determine multiples know how to do count-bys or skip counting know the meaning of multiples know multiplication facts I can list the first ten multiples of a one-digit whole number. I can tell if a whole number is a multiple of a one-digit number. I can make "times as many comparison statements" using multiplication facts.

2 ontent Vocabulary N.MR Know that some numbers including 2, 3, 5, 7, and 11 have exactly two factors (1 and the number itself) and are called prime numbers. Define prime numbers factors break apart know multiplication facts thru 12 know how to break apart a number into factors I can tell if a number is a prime number. I can define prime number. N.MR factors and multiples to compose and decompose whole numbers. Gain familiarity with factors and multiples. 4.OA.4. Find all factor pairs for a whole number in the range Recognize that a whole number is a multiple of each of its factors. Determi compose decompose compose decompose factors multiples whole numbers factor trees factor pair prime composite know multiplication facts thru 12 know how to break apart a number into factors know how to create factor trees/fireworks I can find all the factor pairs of a whole number. I can determine whether a whole number less than 100 is prime or composite. Add and subtract whole numbers N.FL Add and subtract whole numbers fluently. place value understanding and properties of operations to perform multi-digit arithmetic. 4.NBT.4. Fluently add and subtract multidigit whole numbers using the standard algorithm. Add Subtract addition subtraction regrouping whole number know basic addition and subtraction facts to 20 know how to regroup know how to borrow or "ungroup" know place value and a number's value I can add and subtract whole numbers fluently. and divide whole numbers N.M two-digit numbers by 2, 3, 4, and 5 using the distributive property, e.g., 21 x 3 = (1 + 20) x 3 = (1 x 3) + (20 x 3) = = 63. multiplication distributive property digit parentheses place value * (multiplication sign) area models know multiplication facts through 10 know how to break apart a 2 digit number into expanded form (eg. 21 = ) know area models for multiplication know how to use the distributive property multiply I can use the area model to multiple a twodigit by one digit number. I can use the distributive property to multiple a two-digit by one digit number. N.FL fluently any whole number by a one-digit number and a three-digit number by a two-digit number; for a twodigit by one-digit multiplication use distributive property to develop meaning for the algorithm. place value understanding and properti multiplication distributive property digit parentheses place value * (multiplication sign) area models know multiplication facts through 10 know area models for multiplication know how to multiple 2-digit by 1-digit up to 3-digit by 2-digit I can fluently multiple any size number by a 1-digit number. I can fluently multiple a 3-digit number by a 2-digit number.

3 N.FL Divide numbers up to four-digits by onedigit numbers and by 10. place value understanding and properties of operations to perform multi-digit arithmetic. 4.NBT.6. Find whole-number quotients and remainders with up to four-digit dividends and one-digi Divide ontent Vocabulary division divide / or -- (division sign on computer) remainder equal shares (division sign) fact family dividend factor division quotient divisor R (remainder symbol) number sentence know basic division facts to 100 I can divide a 4-digit number by a 1-digit use manipulatives to divide a total up to 4- number. digits into equal shares with/without I can divide a 4-digit number by 10. remainders use a algorithm to divide a 4-digit into equal groups of 10 use an algorithm to divide a 4-digit number by a 1-digit number. N.FL Find the value of the unknowns in equations such as a 10 = 25; 125 b = 25. : the four operation with whole numbers to solve problems. 4.OA.2. or divide to solve word problems involving multiplicative comparison, e.g., by using drawings Find Determine variable unknown inverse operation equation know basic math facts understand and use inverse operations know that a variable takes the place of a number in an equation I can find the value of an unknown number in an equation. N.MR the relationship between multiplication and division to simplify computations and check results. Simplifiy heck multiplication division check product quotient know basic math facts I can use multiplication to check a division understand and use inverse operations to answer. check answers I can use division to check a multiplication answer. N.MR contextual problems involving whole number multiplication and division. : the four operation with whole numbers to solve problems. 4.OA.3: multistep word problems posed with whole numbers and having whole-number answers using the four o valuation product quotient number sentence all together times equal shares equal groups divide know how to multiply a 3-digit number by a 2-digit number. know how to divide numbers (4-digit by 1 digit) know how to read a word problem for needed information I can read a word problem and determine if I need to use multiplication or division. I can use multiplication and division to solve word problems.

4 Read, interpret and compare decimal fractions ontent Vocabulary.N.M Read and interpret decimals up to two decimal places; relate to money and place value decomposition. Read Interpret Relate valuation decimals tenths hundredths $ (dollar sign) base ten equivalent fraction penny. (decimal symbol) decimal point fourths place value < (less than sign) halfdollar quarter = (equal to sign) dime halves > (greater than sign) dollar Read whole numbers Read decimals up to hundredths place Understand place value up to hundredths place Relate place value to money Understand fractions I can read a decimal up to the hundredths place. N.M Know that terminating decimals represents fractions whose denominators are 10, 10 x 10, 10 x 10 x 10, etc., e.g., powers of 10. Know terminating decimal fraction tenths hundredths base ten denominator Read and write fractions as tenths and hundredths Read decimals Write decimals I know that the place value of the last digit of a decimal is the denominator of a fraction. I can write a decimal as a fraction over 10 or 100. N.M Locate tenths and hundredths on a number line. Locate number line fractional part whole number Recognize that decimals are fractional parts of a whole number Read a number line divided into tenths I can read a number line divided into tenths. I can identify a decimal on a number line. I can place a decimal on a number line. N.M Read, write, interpret, and compare decimals up to two decimal places. Read Write Interpret ompare compare greater than> less than< equal = Read decimals up to hundredths Write decimals up to hundredths Understand the value of a decimal ompare decimals I can compare decimals. I can explain what a decimal means in a given situation or problem (xample: $0.23 is 23 cents and can be modeled as 23 pennies or two dimes and 3 pennies). N.MR Write tenths and hundredths in decimal and fraction forms, and know the decimal equivalents for halves and fourths. Write Know fraction tenths hundredths base ten denominator Read and write fractions as tenths and hundredths Read decimals Write decimals Know the decimal equivalents for halves and fourths. I know the decimal equivalents for halves and fourths.

5 Understand fractions ontent Vocabulary N.M Understand fractions as parts of a set of objects. Understand fraction numerator denominator equal parts whole/total set fractured whole compare Understand that a whole set can be I can use fractions to compare the number divided into equal parts of parts to the whole onceptual understanding of fractions using basic facts Understand numerators and denominators in terms of parts of a whole N.MR xplain why equivalent fractions are equal, using models such as fraction strips or the number line for fractions with denominators of 12 or less, or equal to 100. xtend understanding of fraction equivalence and ordering. 4.NF.1. xplain why a fraction a xplain equivalent fractions models fraction strips number line denominators equal to manipulatives to explain equivalent fractions Read and write fractions with denominators of 12 or less, or equal to 100 I can use a model to explain why equivalent fractions are equal. N.MR Locate fractions with denominators of 12 or less on the number line; include mixed numbers. Locate number line fractional part whole number mixed number Read a number line divided into fractional parts Read and write mixed numbers Understand that a mixed number = whole(s) + fractional part I can read a number line divided into fractional parts. I can identify a fraction (and mixed number) on a number line. I can place a fraction (and mixed number) on a number line. N.MR Understand the relationships among halves, fourths, and eighths and among thirds, sixths, and twelfths. Understand halves fourths eighths thirds sixths twelfths relationship Understand these fractions: halves, fourths, and eighths and thirds, sixths, and twelfths. I understand the relationship between halves, fourths, and eighths. I understand the relationship between thirds, sixths, and twelfths. N.M Know that fractions of the form m/n where m is greater than n, are greater than 1 and are called improper fractions; locate improper fractions on the number line. Know Locate fraction numerator denominator greater than improper fraction Know fractions How to use a number line with fractions Know equal numerator and denominators = 1 whole Fractions with numerators larger than the denominator are called improper fractions I know fractions with numerators larger than the denominator are called improper fractions. I can locate improper fractions on a number line. N.MR Write improper fractions as mixed numbers, and understand that a mixed number represents the number of "wholes" and the part of a whole remaining, e.g., 5/4 = 1 + 1/4 = 1 1/4. Write Understand fraction numerator denominator mixed number improper fraction whole part Know the difference between a whole number and a fraction Know the difference between an improper fraction and a mixed number I can write improper fraction as a mixed number.

6 Understand fractions ontent Vocabulary N.MR ompare and order up to three fractions with denominators 2, 4, and 8, and 3, 6, and 12, including improper fractions and mixed numbers. xtend understanding of fraction equivalence and ordering. 4.NF.2. ompare two fractions with different numerators and Add and subtract fractions ompare Order compare greater than> less than< equal = numerator denominator mixed number improper fraction ompare and order whole numbers Understand these fractions: halves, fourths, and eighths and thirds, sixths, and twelfths I compare all types of fractions. I can put different types of fractions in order. N.MR Add and subtract fractions less than 1 with denominators through 12 and/or 100, in cases where the denominators are equal or when one denominator is a multiple of the other, e.g., 1/12 + 5/12 = 6/12; 1/6 + 5/12 = 7/12; 3/10-23/100 = 7/100. Build fraction numerator denominator -- like and unlike quivalent common fractions (halves, fourths, and eighths and thirds, sixths, twelfths, tenths, and hundredths) Add and subtract whole numbers (know math facts) Numerator vs. denominator I can add and subtract fractions with like denominators. I can add and subtract fractions with unlike denominators. N.MR contextual problems involving sums and differences for fractions where one denominator is a multiple of the other (denominators 2 through 12, and 100). Build fractions from unit fractions by applying and extending previous understandings of operatio sum difference total all together in all how many more less than great than how many are left quivalent common fractions (halves, fourths, and eighths and thirds, sixths, twelfths, tenths, and hundredths) Add and subtract whole numbers (know math facts) Numerator vs. denominator the correct operation to use in a word problem I can read a word problem and determine if I need to use addition or subtraction. I can add and subtract fractions to solve word problems. N.MR Find the value of an unknown in equations such as 1/8 + x = 5/8 or 3/4 - y = 1/2. Find variable unknown inverse operation equation part whole know basic math facts understand and use inverse operations know that a variable takes the place of a number in an equation how to add and subtract fractions I can find the value of an unknown fraction in an equation. fractions by whole numbers MR fractions by whole numbers, using repeated addition and area or array models. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. 4.NF.4. Apply and extend previous understandings o Add fraction repeat additon area models array know basic multiplication facts know how to do repeat addition use how to use models to represent fractions and multiplication I can use a model and repeat addition to multipy a fraction by a whole number. I can solve word problems with fractions multiplied by a whole number.

7 Add and subtract decimal fractions N.MR For problems that use addition and subtraction of decimals through hundredths, represent with mathematical statements and solve. Write reate ontent Vocabulary decimals hundredths tenths whole numbers Know how to write a number sentence Know how to add and subtract I can write a number sentence with decimals for a given word problem. N.FL Add and subtract decimals through hundredths. Write reate decimals hundredths tenths whole numbers Know basic math facts Know how to add and subtract Know how to regroup and ungroup I can add two or more numbers including decimals through hundredths in real-life situations. I can add two or more numbers including decimals through hundredths in real-life situations. and divide decimal fractions N.FL and divide decimals up to two decimal places by a one-digit whole number where the result is a terminating decimal, e.g., = 0.14, but not 5 3 = 1.6 repeating. Divide ompute decimals hundredths tenths whole numbers know multiplication facts through 10 know area models for multiplication know how to multiple 2-digit by 1-digit up to 3-digit by 2-digit know basic division facts to 100 use manipulatives to divide a total up to 4- digits into equal shares with/without re I can multiply a number with two decimal places by a one-digit whole number in reallife situations. I can divide a number with two decimal places by a one-digit whole number in reallife situations. stimate N.FL stimate the answers to calculations involving addition, subtraction, or multiplication. stimate stimation Add Subtract Place Value know addition, subtraction and multiplication know how to round numbers I can estimate the answers to an addition, subtraction, or multiplication problem. N.FL Know when approximation is appropriate stimate and use it to check the reasonableness of answers; be familiar with common placevalue errors in calculations. valuate valuation stimation Add Subtract Division Place Value know how to estimate I can use estimation to tell if an answer is reasonable. N.FL Make appropriate estimations and calculations fluently with whole numbers using mental math strategies. stimate valuate ompute valuation stimation Add Subtract Division Place Value N know addition, subtraction, multiplication and division know how to estimate I can estimate using mental math.

8 Measurement Measure using common tools and appropriate units ontent Vocabulary M.UN Measure using common tools and select appropriate units of measure. problems involving measurement and conversion of measurements from a larger unit to a smaller unit. 4.MD.1. Know relative sizes of measurement units within one system of units inc Select hoose Measure Locate Label : (colon sign) day mass º (degree sign) degree meter (m) ruler a.m. duration meter stick second Fahrenheit scale (F) metric measurement system temperature balance foot (ft) midnight thermometer freezing point millilite month volume capacity height night week elsius scale () hour ounce (oz) weight centimeter (cm) Know basic units of measurement for length, weight/mass, volume (capacity), temperature and time. I can use various measurement tools and units of measurement correctly. inch (in.) p.m. width clock interval pint (pt) yard (yd) colon kilogram (kg) pound (lb) yard stick cup (c) leng

9 ontent Vocabulary M.PS Give answers to a reasonable degree of precision in the context of a given problem. Select hoose Measure Locate Label See measurement vocabulary Know basic units of measurement for length, weight/mass, volume (capacity), temperature and time. I can use various measurement tools and units of measurement correctly in a given real-life situation. M.UN Measure and compare integer temperatures in degrees. Measure ompare elsius Farenheit Integer Thermometer Temperature Know Farenheit and elsius temperature. I can measure and compare temperature in degrees. Measure using common tools and appropriate units M.T Measure surface area of cubes and rectangular prisms by covering and counting area of the faces. Measure ompute Surface area ube Rectangular Prism Faces Area N a cube and rectangular prism Know what faces are Know how to measure Know how to compute area Know addition I can measure the surface area of cubes and rectangular prisms onvert measurement units M.T arry out the following conversions from one unit of measure to a larger or smaller unit of measure: meters to centimeters, kilograms to grams, liters to milliliters, hours to minutes, minutes to seconds, years to months, weeks to days, feet to inches, ou onvert meters centimeters kilograms grams liters milliliters hours minutes seconds years months weeks days feet inches ounces pounds convert Know basic units of measurement for length, weight/mass, volume (capacity), temperature and time. Know the relationship between the basic units of measurement for length, weight/mass, volume (capacity), temperature and time. I can convert from one unit of measurement to another unit of measurement (e.g. Meters to centimeters and vice versa). *ach of unit of measure will need it's own learning target

10 perimeter and area formulas ontent Vocabulary M.T Know and understand the formulas for perimeter and area of a square and a rectangle; calculate the perimeters and areas of these shapes and combinations of these shapes using the formulas. problems involving measurement and conversion of measurement know understand calculate combine use Perimeter Area alcuate Height width length base units square units combination formula complex figure compound shape know area and perimeter know how to compute perimeter and area of quadralaterals know to break apart polygons into basic shapes use of variables to represent numbers I know the formulas of area and perimeter I can use the formulas for area and perimeter to measure squares and rectangles. I can find the area and perimeter of a compound shape. M.T Find one dimension of a rectangle given the other dimension and its perimeter or area. calculate solve length width side area perimeter formula know area and perimeter know how to compute perimeter and area of quadralaterals know the formulas for perimeter and area of quadralaterals use of variables to represent numbers I can use the perimeter and/or area formula of a rectangle to find an unknown side. M.T Find the side of a square given its perimeter or area. calculate solve length width side area perimeter formula know area and perimeter know how to compute perimeter and area of quadralaterals know the formulas for perimeter and area of quadralaterals use of variables to represent numbers I can use the perimeter and/or area formula of a square to find an unknown side. M.PS contextual problems about perimeter and area of squares and rectangles in compound shapes. calculate solve determine length width side area perimeter formula compound shape units of measure know area and perimeter know how to compute perimeter and area of quadrilaterals know to break apart compound shapes into basic shapes know how to determine the appropriate formula I can find the area and perimeter of a compound shape in real life situations. Understand right angles M.T right angles and compare angles to right angles. Geometric measurement: understand concepts of angle and measure angles. 4.MD.5. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concep compare right angle angles acute obtuse recognize an angle I can identify right angles. I can compare other angles to a right angle. I can define an angle. I recognize that an angle is a fraction of a circle. I can use a protractor to measure angles.

11 Problem-solving ontent Vocabulary M.PS contextual problems about surface area. calculate solve determine Surface area ube Rectangular Prism Faces Area a cube and rectangular prism Know what faces are Know how to measure Know how to compute area Know addition I can calculate the surface area of a shape in real life situations. Geometry Understand perpendicular, parallel, and intersecting lines G.GS and draw perpendicular, parallel, and intersecting lines using a ruler and a tool or object with a square (90º) corner. Draw and identify lines and angles, and classify shapes by properties of their lines and angles. 4.G.1. Draw points, line basic geometric shapes and their components, and solve problems Draw Perpendicular Paralllel Intersecting Lines Line Segments Right Angles lines and line segments a ruler to draw a line or a square corner I can identify perpendicular, parallel and intersecting lines. I can draw perpendicular, parallel and intersecting lines. G.GS basic geometric shapes including isosceles, equilateral, and right triangles, and use their properties to solve problems. Draw and identify lines and angles, and classify shapes by properties of their lines and angles. 4.G.2. lassify two-dimensi Draw Isosceles quilateral Right Triangle ongruent Sides Angles basic geometric shapes congruent line segments right angles I can identify isosceles, equilateral and right triangles. I can compare basic geometric shapes and classify them based on their sides and angles. G.SR and count the faces, edges, and vertices of basic three-dimensional geometric solids including cubes, rectangular prisms, and pyramids; describe the shape of their faces. Draw Surface Faces dges Vertices 3-D geometric solids ubes Rectangular Prisms Pyramids basic geometric shapes congruent line segments right angles I can identify 3-dimensional geometric solids. I can count the faces, edges, and vertices of a geometric solid. I can describe the shape of each face on a geometric solid. Recognize symmetry and transformations G.TR Recognize plane figures that have line symmetry. Draw and identify lines and angles, and classify shapes by properties of their lines and angles. 4.G.3. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the fi Recognize Understand Plane figures Symmetry ongruent ompare two objects for similarities basic geometric shapes I can identify lines of symmetry in a twodimensional shape.

12 ontent Vocabulary G.TR Recognize rigid motion transformations (flips, slides, turns) of a two-dimensional object. Recognize Transformations Flip Reflection Slide Translation Turn Rotation Recognize the a two-dimensional shape keeps it's properties when it has a change in position I can use reflections, translations and rotations to change the position of a shape. Represent and solve problems for given data D.R onstruct tables and bar graphs from given data. onstruct Synthesis Bar graph Double bar graph Data tables Pictographs Tables Data Read bar graphs, data tables, and pictographs onstruct a bar graph from given data I can read and use information from a bar graph. I can create a bar graph from information in a data table. D.R Order a given set of data, find the median, and specify the range of values. Order Find mean median range maximum minimum Put a list of numbers in order from least to greatest the middle number from a list of numbers ordered from least to greatest. I can put data in order from least to greatest. I can use the list to identify the minimum, maximum, range and median. D.R problems using data presented in tables and bar graphs, e.g., compare data represented in two bar graphs and read bar graphs showing two data sets. Interpret Data Tables Bar Graphs Basic addition, subtraction, multiplication and division Interpret information from a bar graph ompare information presented in bar graphs. I can identify and compare information given from a bar graph. Generate and analyze patterns. 4.OA.5. Generate a number or shape pattern that follows a given rule. apparent features of the pattern that were not explicit in the rule itself. For example, given the rule Add 3 and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. xplain informally why the numbers will continue to alternate in this way. Generalize place value understanding for multi-digit whole numbers. 4.NBT.3. place value understanding to round multi-digit whole numbers to any place. Understand decimal notation for fractions, and compare decimal fractions. 4.NF.5. xpress a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/ NF.6. decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. 4.NF.7. ompare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model problems involving measurement and conversion of measurements from a larger unit to a smaller unit. 4.MD.2. the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Represent and interpret data. 4.MD.4. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.