KINDERGARTEN Counting and Cardinality K n o w n u m b e r n a m e s a n d t h e c o u n t s e q u e n c e Count to 100 by ones. Count to 100 by tens. Count starting at a number other than 1. Write numbers from 0 to 20. Pick a written number that goes with a group of objects. Tell that 0 is the number that tells there are no objects. C o u n t t o t e l l t h e n u m b e r o f o b j e c t s Say the numbers out loud, in order, as I count the objects in a group. Use each number only once. Count each object only once. Explain that the number of objects in a group is the same as the last number I use to count the objects in order in a group. Show that the number of objects in a group is the same no matter what order I count them. Show that the number of objects in a group is the same no matter how they are arranged. Explain that each number I say when counting by ones is one more that the last number I said. Tell how many objects (up to 20) are in a group if the objects are in a line. Tell how many objects (up to 20) are in a group if the objects are in a rectangular array. Tell how many objects (up to 20) are in a group if the objects are in a circle. Tell how many objects (up to 10) are in a group if the objects are not in any pattern. Take as many objects from a group as you ask me to (up to 20). C o m p a r e n u m b e r s Tell and show if two groups (up to 10 objects) have the same number of objects. Tell and show which of two groups (up to 10 objects) of objects is the larger. Tell which of two numerals is greater than the other. 1 From Common Core Standards 2010
KINDERGARTEN Operations and Algebraic Thinking U n d e r s t a n d a d d i t i o n a s p u t t i n g t o g e t h e r a n d a d d i n g t o, a n d u n d e r s t a n d s u b t r a c t i o n a s t a k i n g a p a r t a n d t a k i n g f r o m Show addition as combining two groups with objects and fingers. Picture addition as combining two groups in my head and explain what I see. Show addition as combining two groups with drawings. Show addition as combining two groups with sounds (claps) and motions. Show addition as combining two groups by writing expressions. Show addition as combining two groups by writing equations. Show addition as one group making another group larger with objects and fingers. Picture addition as one group making another group larger in my head and explain what I see. Show addition as one group making another group larger with drawings. Show addition as one group making another group larger with sounds (claps) and motions. Show addition as one group making another group larger by writing expressions. Show addition as one group making another group larger by writing equations. Show subtraction as taking a group apart with objects and fingers. Picture subtraction as combining two groups in my head and explain what I see. Show subtraction as taking a group apart with drawings. Show subtraction as taking a group apart by writing expressions. Show subtraction as taking a group apart by writing equations. Show subtraction as taking objects from a group with objects and fingers. Picture subtraction as taking objects from a group in my head and explain what I see. Show subtraction as taking objects from a group with drawings. Show subtraction as taking objects from a group by writing expressions. Show subtraction as taking objects from a group by writing equations. Solve addition word problems with an answer within 10, using objects or drawings. Solve subtraction word problems with an answer within 10, using objects or drawings. Use objects or drawings to break apart (decompose) a number less than 11 into two parts in several ways such as 8 is 5 and 3 OR 7 and 1 OR 4 and 4. Record my decompositions in drawings or equations. Use objects and drawings to find the number that adds to 10 with a number I start with such as start with 7 and add 3 to get 10 OR start with 1 and add 9 to get 10. Add any two numbers up to 5 quickly, from memory or using objects, such as 2 and 3 Or 5 and 0. 2 From Common Core Standards 2010
KINDERGARTEN Subtract any two numbers starting with up to 10 and with an answer less than 6 quickly, from memory or using objects,. Number and Operations in Base Ten W o r k w i t h n u m b e r s 1 1 1 9 t o g a i n f o u n d a t i o n s f o r p l a c e v a l u e Describe and show with objects or drawings the numbers from 11 to 19 as one group of ten ones and some other ones such as 18 is one group of ten and 8 ones. Record the result of grouping 11 to 19 as an equation such as 12 = 10+2. Generalize that numbers from 11 to 19 are always one ten and one, two, three, four, five, six, seven. eight, or nine ones. Measurement and Data D e s c r i b e a n d c o m p a r e m e a s u r a b l e a t t r i b u t e s Tell and show which attributes of an object can be measured such as length and weight. Tell about several measurable attributes for a single object. Compare two objects with the same measurable attribute and describe which is longer/shorter or lighter/heavier. C l a s s i f y o b j e c t s a n d c o u n t t h e n u m b e r o f o b j e c t s i n e a c h c a t e g o r y Sort objects into given categories. Tell how many objects are in each category. Sort the categories from smallest to largest. Geometry I d e n t i f y a n d d e s c r i b e s h a p e s ( s q u a r e s, c i r c l e s, t r i a n g l e s, r e c t a n g l e s, h e x a g o n s, c u b e s, c o n e s, c y l i n d e r s, a n d s p h e r e s ) Find and tell about shapes I see around me. Tell where to find these shapes by using words like above, below, in front of, behind, and next to. Name shapes correctly no matter how they are lying or drawn such as a square is always a square and not a diamond if it is turned a certain way. Classify shapes as two-dimensional or three-dimensional. 3 From Common Core Standards 2010
KINDERGARTEN A n a l y z e, c o m p a r e, c r e a t e, a n d c o m p o s e s h a p e s Tell, using informal language, how two shapes are alike and how they are different. Tell, using informal language, about the number of sides and vertices (corners) that a shape has. Tell about other attributes of shapes such as having equal sides or square corners. Draw models of shapes I see around me. Build models of shapes I see around me using sticks, clay, and other things. Put two or more shapes together to make larger shapes such as two triangles with full sides together can make a rectangle. 4 From Common Core Standards 2010
FIRST GRADE Operations and Algebraic Thinking R e p r e s e n t a n d s o l v e p r o b l e m s i n v o l v i n g a d d i t i o n a n d s u b t r a c t i o n Solve word problems using adding to involving numbers within 20 with unknowns in all three positions by using objects or drawings or equations such as 13 + 5 =?; 14 +? = 19; and? + 5 = 18 Solve word problems using taking from involving numbers within 20 with unknowns in all three positions by using objects or drawings or equations such as 13-5 =?; 14 +? = 19; and? + 5 = 18 Solve word problems using putting together involving numbers within 20 with unknowns in all three positions by using objects or drawings or equations such as 13 + 5 =?; 14 +? = 19; and? + 5 = 18 Solve word problems using taking apart involving numbers within 20 with unknowns in all three positions by using objects or drawings or equations such as 13 + 5 =?; 14 +? = 19; and? + 5 = 18 Solve word problems using comparing involving numbers within 20 with unknowns in all three positions by using objects or drawings or equations such as 13 + 5 =?; 14 +? = 19; and? + 5 = 18 Solve word problems by adding three whole numbers whose sum is less than 20 by using objects and drawings. Solve word problems by adding three whole numbers whose sum is less than 20 by using equations with a symbol for the unknown number such as 4+7+5 =? or 4 +? + 3 = 15 U n d e r s t a n d a n d a p p l y p r o p e r t i e s o f o p e r a t i o n s a n d t h e r e l a t i o n s h i p b e t w e e n a d d i t i o n a n d s u b t r a c t i o n Use the turn-around property to help me add. Take numbers apart and move them around to make number sentences easier for me. Turn a subtraction sentence into a missing addend sentence to help me find the answer such as subtract 10 8 by finding the number that makes 10 when added to 8. A d d a n d s u b t r a c t w i t h i n 2 0 Count on as one way to add. Count backwards as one way to subtract. Use the counting on strategy to help me add. Use the making ten strategy to help me add such as thinking 8+6=8+2+4=10+4=14 Take apart a number (to make 10) to help e subtract such as 13-4=13-3-1=9. 1 from Common Core Standards 2010
FIRST GRADE Use the relationship between addition and subtraction to help me subtract such as 8+4=12 so 12-4=8. Take apart numbers to help me add by going to some fact that I already know such as 6+7=6+6+1=12+1=13 Add, using strategies, within 20. Add quickly and accurately within 10. Subtract, using strategies, within 20. Subtract quickly and accurately within 10. W o r k w i t h a d d i t i o n a n d s u b t r a c t i o n e q u a t i o n s Explain the meaning of the equal sign. Determine if equations involving addition are true or false such as 6=6; 2=2+5; 9=9-0; 6+3=1+8. Determine if equations involving subtraction are true of false such as 7=8-1; 7=7-3; 8-0=10-2 Find the answer to whole number addition equations wherever there is a missing number such as 3+5 =?; 8+?=11;?+4=9. Find the answer to whole number subtraction equations wherever there is a missing number such as 9-5 =?; 8-?=3;?-4=4. Number and Operations in Base Ten E x t e n d t h e c o u n t i n g s e q u e n c e Count to 120 starting at 1. Count to 120 starting at any number less than 120. Read all the numerals to 120. Write all the numerals to 120. Find out how many objects are in a group (up to 120) and write that numeral. U n d e r s t a n d p l a c e v a l u e Explain what the two numbers mean in a two-digit number. Show how and tell why ten ones becomes a bundle. Show how and tell why the numbers 11-19 have one bundle of tens and some ones left over. Show and tell why 10, 20, 30, 40, 50, 60, 70, 80, and 90 have only bundles and no left over ones. 2 from Common Core Standards 2010
FIRST GRADE Compare two-digit numbers and tell which is larger, smaller, or if they are equal by telling about their tens and ones. Record if one number is larger than another using the > sign. Record if one number is less than another using the < sign. Record if one number is the same as another using the = sign. U s e p l a c e v a l u e u n d e r s t a n d i n g a n d p r o p e r t i e s o f o p e r a t i o n s t o a d d a n d s u b t r a c t Use objects and drawings to add a two-digit and a one-digit number within 100. Use strategies to add a two-digit and a one-digit number within 100. Use objects and drawings to add a two-digit number and 10, 20, 30, 40, 50, 60, 70, or 80. Use strategies to add a two-digit number and 10, 20, 30, 40, 50, 60, 70, or 80. Explain that when I add two-digit numbers, I add the tens to tens and the ones to ones. Show how and tell why I sometimes need to make a new bundle when I am adding oneand two-digit numbers. Write equations to show my thinking for adding one- and two-digit numbers together. Add 10 to a two-digit number that I am given, quickly and accurately, in my mind. Explain my thinking about how I found the number that was 10 more than the number given to me. Subtract 10 from a two-digit number given to me, quickly and accurately, in my mind, Explain my thinking about how I found the number that was 10 less than the number given to me. Use objects and drawings to subtract 10, 20, 30, 40, 50, 60, 70, 80, or 90 from 90, 80, 70, 10 (getting positive or zero differences). Use strategies to subtract 10, 20, 30, 40, 50, 60, 70, 80, or 90 from 90, 80, 70, 10 (getting positive or zero differences). Record my thinking about subtracting 10, 20, 30, 40, 50, 60, 70, 80, or 90 from 90, 80, 70, 10 Measurement and Data M e a s u r e l e n g t h s i n d i r e c t l y a n d b y i t e r a t i n g l e n g t h u n i t s Order three objects from shortest to longest. Decide if an object is longer or shorter than an object that I can just look at. Describe how an object can be measured by laying shorter objects end to end beside it and deciding how many of the shorter objects are as long as the original object. 3 from Common Core Standards 2010
FIRST GRADE Tell why there cannot be any overlap or gaps in the smaller objects. T e l l a n d w r i t e t i m e Use an analog clock to tell time in hours and half-hours. R e p r e s e n t a n d i n t e r p r e t d a t a Organize data with two or three categories. Create a graph with data in two or three categories. Interpret a graph with two or three categories by answering questions such as what is the total number of data points? Interpret a graph with two or three categories by answering questions such as how many are in each category? and how many more or less in one category than in another? Create questions, then answers about graphs with two or three categories. Geometry R e a s o n w i t h s h a p e s a n d t h e i r a t t r i b u t e s Distinguish between defining and non-defining attributes of shapes such as defining would be number of sides in polygon, non-defining would be orientation, size, color. Build shapes to possess defining attributes. Draw shapes to possess defining attributes. Use two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) to create composite shapes. Use three-dimensional shapes (cubes, right rectangular prisms, right cones, right cylinders) to create composite shapes. [Students do not need to learn formal names.] Use two- and three- dimensional composite shapes to create larger composite shapes. Divide circles and rectangles into two equal shares and describe the shares using halves, and half of. Divide circles and rectangles into four equal shares and describe the shares As fourths, quarters, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Explore and generalize that decomposing the whole into more equal shares creates smaller shares. 4 from Common Core Standards 2010
SECOND GRADE Operations and Algebraic Thinking R e p r e s e n t a n d s o l v e p r o b l e m s i n v o l v i n g a d d i t i o n a n d s u b t r a c t i o n. Solve one- and two-step word problems using numbers within 100 involving adding to with the unknown number in all positions. Solve one- and two-step word problems using numbers within 100 involving taking from with the unknown number in all positions. Solve one- and two-step word problems using numbers within 100 involving putting together with the unknown number in all positions. Solve one- and two-step word problems using numbers within 100 involving taking apart with the unknown number in all positions. Solve one- and two-step word problems using numbers within 100 involving comparing with the unknown number in all positions. Solve one- and two-step word problems using numbers within 100 involving addition and subtraction with the unknown number in all positions by using drawings. Solve one- and two-step word problems using numbers within 100 involving addition and subtraction with the unknown number in all positions by using equations with a symbol for the unknown number. A d d a n d s u b t r a c t w i t h i n 2 0. Add within 20 using a mental strategy such as counting on. Add within 20 using a mental strategy such as making ten. Add within 20 using a mental strategy such as decomposing a number leading to ten. Add within 20 using a mental strategy such as using the relationship between addition and subtraction. Add within 20 using a mental strategy such as creating equivalent but easier or known sums. For example adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). State from memory quickly and accurately the sums of any two one-digit numbers. W o r k w i t h e q u a l g r o u p s o f o b j e c t s t o g a i n f o u n d a t i o n s f o r m u l t i p l i c a t i o n. Decide if a group of up to 20 objects has an even or odd number such as by pairing them or counting by 2s. Write an equation for an even number expressing it as the sum of two equal addends. Find the total number of objects in a rectangular array with up to 5 rows and 5 columns by adding. 1 from Common Core Standards 2010
SECOND GRADE Write an equation to show the total number of objects in an array expressing it as the sum of equal addends. Number and Operations in Base Ten U n d e r s t a n d p l a c e v a l u e. Show and tell the meaning of each of the three digits in a three-digit number in terms of hundreds, tens, and ones. Show and tell the meaning of a hundred as a bundle of ten tens. Show and tell that 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds with 0 tens and 0 ones. Count within 1000. Skip-count within 1000 by 5s. Skip-count within 1000 by 10s. Skip-count within 1000 by 100s. Read numbers to 1000 from numerals. Read numbers to 1000 from number names. Read numbers to 1000 in expanded form. Write numbers to 1000 using numerals. Write numbers to 1000 using number names. Write numbers to 1000 in expanded form. Compare two three-digit numbers based on the meanings of hundreds, tens, and ones. Use >, =, and < symbols to record the results of the comparison. U s e p l a c e v a l u e u n d e r s t a n d i n g a n d p r o p e r t i e s o f o p e r a t i o n s t o a d d a n d s u b t r a c t. Add, quickly and accurately, within 100 using strategies based on place value. Add, quickly and accurately, within 100 using properties of operations. Subtract, quickly and accurately, within 100 using strategies based on place value. Subtract, quickly and accurately, within 100 using properties of operations. Add and subtract using the relationship between addition and subtraction. Add up to four two-digit numbers using strategies based on place balue and properties of operations. Add within 1000 using concrete models or drawings. Add within 1000 using strategies based on place value. Add within 1000 using properties of operations. Add within 1000 using concrete models or drawings and relate the strategy to a written method. 2 from Common Core Standards 2010
SECOND GRADE Add within 1000 using strategies based on place value and relate the strategy to a written method. Add within 1000 using properties of operations and relate the strategy to a written method. Subtract within 1000 using concrete models or drawings. Subtract within 1000 using strategies based on place value. Subtract within 1000 using properties of operations. Subtract within 1000 using concrete models or drawings and relate the strategy to a written method. Subtract within 1000 using strategies based on place value and relate the strategy to a written method. Subtract within 1000 using properties of operations and relate the strategy to a written method. Add or subtract within 1000 using the relationship between addition and subtraction. Show and tell about the process of adding three-digit numbers in that one adds hundreds and hundreds, tens and tens, ones and ones and sometimes finds it necessary to change ones into tens and tens into ones. Show and tell about the process of subtracting three-digit numbers in that one subtracts hundreds from hundreds, tens from tens, ones from ones and sometimes finds it necessary to decompose hundreds and/or tens. Mentally add 10 or 100 to a given number from 100 to 900. Mentally subtract 10 or 100 from a given number from 100 to 900. Explain, using drawings or objects if desired, why addition strategies work using place value and the properties of operations. Explain, using drawings or objects if desired, why subtraction strategies work using place value and the properties of operations. Measurement and Data M e a s u r e a n d e s t i m a t e l e n g t h s i n s t a n d a r d u n i t s. Select the appropriate tool such as a ruler, yardstick, measuring tape, to find the length of an object. Measure the length of an object using an appropriate tool. Measure the length of an object twice, using different units each time. Describe how the two measurements relate to the size of the unit chosen such as an object measured in both inches and centimeters would have a larger number for the centimeters because the unit is smaller. Estimate the length of objects using inches. Estimate the length of objects using feet. 3 from Common Core Standards 2010
SECOND GRADE Estimate the length of objects using centimeters. Estimate the length of objects using meters. Measure two objects to determine how much longer one is than the other. Express the difference in length between two objects using a standard unit. R e l a t e a d d i t i o n a n d s u b t r a c t i o n t o l e n g t h Solve addition word problems involving lengths that are in the same units using drawings. Solve addition word problems involving lengths that are in the same units using equations with a symbol for the unknown number. Solve subtraction word problems involving lengths that are in the same units using drawings. Solve subtraction word problems involving lengths that are in the same units using equations with a symbol for the unknown number. Represent whole numbers as lengths from 0 on a number line with equally spaced points for 0, 1, 2, Represent whole-number sums within 100 on a number line. Represent whole-number differences within 100 on a number line. W o r k w i t h t i m e a n d m o n e y. Tell time from an analog clock to the nearest five minutes using a.m. and p.m. Tell time from an digital clock to the nearest five minutes using a.m. and p.m. Solve word problems involving dollar bills, quarters, dimes nickels, and pennies such as: if you have 2 dimes and 3 pennies, how many cents do you have? Use $ and symbols correctly. R e p r e s e n t a n d i n t e r p r e t d a t a. Gather measurement data by measuring lengths to the nearest whole unit, of several objects or by making repeated measurements of the same object. Create a line plot of measurements of length where the horizontal scale is marked off in whole-number units. Draw a picture graph to use for data with up to four categories. Draw a bar graph to use for data with up to four categories. Solve simple put-together problems using information from a bar graph. Solve simple take-apart problems using information from a bar graph. Solve simple comparison problems using information from a bar graph. 4 from Common Core Standards 2010
SECOND GRADE Geometry R e a s o n w i t h s h a p e s a n d t h e i r a t t r i b u t e s. Identify shapes having special attributes such as a given number of angles or a given number of equal faces. Draw shapes having special attributes such as a given number of angles or a given number of equal faces. Identify triangles. Identify quadrilaterals. Identify pentagons. Identify triangles, hexagons. Identify cubes. Divide a rectangle into rows and columns of same-size squares. Count the total number of same-size squares within a rectangle. Divide circles into two, three, and four equal shares. Divide rectangles into two, three, and four equal shares. Describe a portioned circle or rectangle using the words halves, thirds, half of, and so forth. Describe the whole as two halves, three thirds, four fourths. Show and tell about equal shares of identical wholes need not have the same shape. 5 from Common Core Standards 2010
M ATHEMATICS COMMON CORE LEARNING TARGETS THIRD GRADE Operation and Algebraic Thinking R e p r e s e n t a n d s o l v e p r o b l e m s i n v o l v i n g m u l t i p l i c a t i o n a n d d i v i s i o n. Explain what the product of two numbers means such as 5 x 7 is the number of objects in 5 groups of 7 objects each OR 5 jumps on the number line of 7 spaces each. Crete a real life situation for an expression such as 4 x 3 means four rows of cans with three cans in each row. Explain that a division expression like 56 8 could mean that 56 objects have been partitioned equally into 8 parts OR 56 objects have been partitioned into equal parts with 8 objects in each part. Create a real life situation for an expression such as 32 8 showing that 32 children have been placed in 8 groups for a game OR 32 8 might mean that 32 children have been placed in teams of 8 children for a game. Solve multiplication word problems involving equal groups using drawings. Solve multiplication word problems involving equal groups using equations with a symbol for the unknown number. Solve multiplication word problems involving arrays using drawings. Solve multiplication word problems involving arrays using equations with a symbol for the unknown number. Solve multiplication word problems involving measurement quantities using drawings. Solve multiplication word problems involving measurement quantities using equations with a symbol for the unknown number. Solve division word problems involving equal groups using drawings. Solve division word problems involving equal groups using equations with a symbol for the unknown number. Solve division word problems involving arrays using drawings. Solve division word problems involving arrays using equations with a symbol for the unknown number. Solve division word problems involving measurement quantities using drawings. Solve division word problems involving measurement quantities using equations with a symbol for the unknown number. Find the unknown whole number in an equation such as 8 x? = 48. Find the unknown whole number in an equation such as? x 6 = 42. Find the unknown whole number in an equation such as 8 x 9 =?. Find the unknown whole number in an equation such as 56? = 7. Find the unknown whole number in an equation such as 54 9 =?. find the unknown whole number in an equation such as 8 =? 9. 1 From Common Core Standards 2010
M ATHEMATICS COMMON CORE LEARNING TARGETS THIRD GRADE U n d e r s t a n d p r o p e r t i e s o f m u l t i p l i c a t i o n a n d t h e r e l a t i o n s h i p b e t we e n m u l t i p l i c a t i o n a n d d i v i s i o n. Apply and explain in informal language the commutative property of multiplication and how it helps with learning multiplication. Apply and explain in informal language the associative property of multiplication and how it helps with learning multiplication. Apply and explain in informal language the distributive property and how it helps with learning multiplication. Use multiplication to help with division such as finding, in 36 9, what number makes 36 when multiplied by 9. M u l t i p l y a n d d i v i d e wi t h i n 1 0 0. Use strategies such as the relationship of multiplication and division to help do and learn multiplication. Use strategies such as the relationship of multiplication and division to help do and learn division. Quickly and accurately state from memory the product of any two whole numbers less than 10 (by the end of grade 3). So l v e p r o b l e m s i n v o l v i n g t h e f o u r o p e r a t i o n s, a n d i d e n t i f y a n d e xp l a i n p a t t e r n s i n a r i t h m e t i c. Write equations (using a letter for the unknown quantity) for two-step word problems using any combination of the four operations. Perform operations using Order of Operations without parentheses. Perform operations using Order of Operations with parentheses. Solve two-step word problems using the four operations. Use mental computation to decide about the reasonableness of answers to two-step word problems. Use estimation strategies, including rounding, to decide about the reasonableness of answers to two-step word problems. Identify arithmetic patterns. Identify arithmetic patterns in the addition table. Identify arithmetic patterns in the multiplication table. Identify the patterns using properties of the operations such as the commutative property. Explain patterns such as 4 times a number is always even or why 4 times a number can be decomposed into two equal addends. 2 From Common Core Standards 2010
M ATHEMATICS COMMON CORE LEARNING TARGETS THIRD GRADE Number and Operations in Base Ten Us e p l a c e v a l u e u n d e r s t a n d i n g a n d p r o p e r t i e s o f o p e r a t i o n s t o p e r f o r m m u l t i - d i g i t a r i t h m e t i c. A range of algorithms may be used. Use what I know about place value to round numbers to the nearest 10. Use what I know about place value to round numbers to the nearest 100. Quickly and accurately add numbers within 1000 using strategies, algorithms based on place value, properties of operations, or the relationship between addition and subtraction. Quickly and accurately subtract numbers within 1000 using strategies, algorithms based on place value, properties of operations, or the relationship between addition and subtraction. Use strategies based on place value to multiply one-digit while numbers by multiples of 10 (up to 90). Number and Operations-Fractions De v e l o p u n d e r s t a n d i n g o f f r a c t i o n s a s n u m b e r s. Explain that a fraction 1/some number (b) means that one whole is divided into an equal number(b) of parts. Explain that a fraction a/b is a parts of the size 1/b. Divide the part of a number line between 0 and 1 into b equal parts and know that each part is a segment with a value of 1/b. Locate the place on a number line between 0 and 1 that represents 1/b. Locate the place on a number line between 0 and 1 that is equal to a/b because it has a segments of length 1/b. Measurement and Data So l v e p r o b l e m s i n v o l v i n g m e a s u r e m e n t a n d e s t i m a t i o n o f i n t e r v a l s o f t i m e, l i q u i d v o l u m e s, a n d m a s s e s o f o b j e c t s. Tell time to the nearest minute. Write time to the nearest minute. Measure time intervals in minutes. Represent word problems with addition and subtraction of time intervals in minutes on a number line. Solve word problems with addition and subtraction of time intervals in minutes possibly using a number line. 3 From Common Core Standards 2010
M ATHEMATICS COMMON CORE LEARNING TARGETS THIRD GRADE Measure liquid volumes (capacity) using standard units such as liters (l). Estimate liquid volumes in liters. Measure the mass of an object by using standard units such as grams (g) and kilograms (kg). Estimate the mass of an object by using standard units such as grams (g) and kilograms (kg). Re p r e s e n t a n d i n t e r p r e t d a t a. Draw a scaled picture graph with several categories. Draw a picture graph so that each picture represents several objects such as one banana in the graph might represent 5 bananas in the data. Draw a scaled bar graph with several categories. Draw a bar graph so that each square represents several objects such as one square in the graph might represent 4 girls in the data. Solve one and two-step problems using the information in picture and bar graphs such as how many less. Measure lengths using rulers marked with halves and fourths of an inch. Use several such measurements as a set of data. Make a line plot of the measurement data making the horizontal scale is marked off in appropriate units such as whole numbers, halves, or quarters. G e o m e t r i c m e a s u r e m e n t : u n d e r s t a n d c o n c e p t s o f a r e a a n d r e l a t e a r e a t o m u l t i p l i c a t i o n a n d t o a d d i t i o n. Explain why area is an attribute of plane figures. Show and tell about the meaning and connection of a unit square and one square unit Explain how to find area by covering up a plane figure with unit squares and having no gaps or overlaps. Measure area by counting unit squares such as square cm, square m, square in, square ft, and improvised units. Find the area of a rectangle with whole-number side lengths by tiling it. Show that the area would be the same if the side lengths were multiplied together. Find the area of rectangles in real world situations with whole-number side lengths by multiplying. Use rectangular areas in mathematical reasoning such as if a rectangle had an area twice as large, what could be the side lengths? Use tiling in a rectangle with one side length a and the other b+c to represent the distributive property. Divide the area of a figure (having all right angles) into non-overlapping rectangles. 4 From Common Core Standards 2010
M ATHEMATICS COMMON CORE LEARNING TARGETS THIRD GRADE Solve real life situations by finding the areas of non-overlapping rectangles and adding them together such as finding the area of a box before it has been folded. G e o m e t r i c m e a s u r e m e n t : r e c o g n i z e p e r i m e t e r a s a n a t t r i b u t e o f p l a n e f i g u r e s a n d d i s t i n g u i s h b e t we e n l i n e a r a n d a r e a m e a s u r e s. Find the perimeter of a polygon if I am given the side lengths. Find the perimeter of a polygon if I first need to find the side length of an unknown side. Exhibit rectangles with the same perimeter, but different areas. Exhibit rectangles with different perimeters, but the same area. Solve real life situations involving perimeters of polygons. Solve mathematical problems involving the perimeters of polygons. Geometry Re a s o n wi t h s h a p e s a n d t h e i r a t t r i b u t e s. Classify polygons into categories with common attributes. Explain why different categories may share an attribute such as rhombuses and rectangle share the attribute of four sides. Place categories with shared attributes into a larger category such as rhombuses, trapezoids, and squares are all quadrilaterals. Recognize shapes that belong in a certain category. Draw examples of shapes that do not belong in a certain category. Divide a shape into parts with equal areas. Name each part of the shape as a unit fraction of the whole such as a shape divided into 4 parts with equal areas has each part named 1/4. 5 From Common Core Standards 2010
M ATHEMATICS COMMON CORE LEARNING TARGETS FOURTH GRADE Operations and Algebraic Thinking Us e t h e f o u r o p e r a t i o n s wi t h wh o l e n u m b e r s t o s o l v e p r o b l e m s. Show and tell about a multiplication equation as a comparison such as 35=5x7 means that 35 is seven times as many as 5. Write an equation for a statement such as 45 is five times as many as nine. Solve word problems involving comparing through multiplication by using drawings. Solve word problems involving comparing through multiplication by using equations with a symbol for the unknown. Solve word problems involving comparing through division by using drawings. Solve word problems involving comparing through division by using equations with a symbol for the unknown. Tell about the difference between comparison for addition and for multiplication. Represent multi-step addition and subtraction word problems that contain whole numbers with an equation that includes a letter standing for the unknown quantity. Represent multi-step multiplication word problems that contain whole numbers with an equation that includes a letter standing for the unknown quantity. Represent multi-step division word problems that contain whole numbers and will have a whole number answer with an equation that includes a letter standing for the unknown quantity. Solve multi-step addition and subtraction word problems that contain whole numbers with an equation that includes a letter standing for the unknown quantity. Solve multi-step multiplication word problems that contain whole numbers with an equation that includes a letter standing for the unknown quantity. Solve multi-step division word problems that contain whole numbers and will have a whole number answer with an equation that includes a letter standing for the unknown quantity. Use mental computation and estimation strategies to decide if an answer to multi-step addition and/or subtraction word problem is reasonable. Use mental computation and estimation strategies to decide if an answer to multi-step multiplication and addition or subtraction word problem is reasonable. Use mental computation and estimation strategies to decide if an answer to multi-step division and addition or subtraction word problem is reasonable. G a i n f a m i l i a r i t y wi t h f a c t o r s a n d m u l t i p l e s. Find all the factor pairs for whole numbers less than 100. Explain that multiples less than 100 are products of the number s factors. Determine whether a whole number less than 100 is a multiple of a one-digit number. 1 from Common Core Standards 2010
M ATHEMATICS COMMON CORE LEARNING TARGETS FOURTH GRADE Determine if a whole number less than 100 is prime or composite. G e n e r a t e a n d a n a l y z e p a t t e r n s. Create a number pattern given a rule such as add 7 or divide by 3. Create a pattern of shapes given a rule. Find characteristics of patterns such as for the pattern that starts and 1 and has a rule of add 3, the numbers 1, 4, 7, 10, 13, 16 alternate odd, even. Describe characteristics of a pattern and explain informally why the characteristic will continue. Number and Operations in Base Ten G e n e r a l i z e p l a c e v a l u e u n d e r s t a n d i n g f o r m u l t i - d i g i t wh o l e n u m b e r s. Use the concept for two or more digit numbers, that a digit in one place is 10 times as large as the digit on its right such as recognizing that 700 70 = 10. Read and write multi-digit numbers using base 10 numerals. Read and write multi-digit numbers using number names. Read and write multi-digit numbers in expanded form. Compare two multi-digit numbers and record the results using > and < signs. Round multi-digit numbers to any place. Us e p l a c e v a l u e u n d e r s t a n d i n g a n d p r o p e r t i e s o f o p e r a t i o n s t o p e r f o r m m u l t i - d i g i t a r i t h m e t i c. Add multi-digit whole numbers using the standard algorithm. Subtract multi-digit whole numbers using the standard algorithm. Multiply two two-digit numbers using place value strategies and the properties of operations. Multiply a number with up to four digits by a one-digit number. Show and tell about multiplication of multi-digit numbers by using equations. Show and tell about multiplication of multi-digit numbers by using rectangular arrays and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and onedigit divisors using place value strategies, properties of operations, and/or the relationship between multiplication and division. Show and tell about division of multi-digit numbers producing whole number quotients and remainders by using equations. Show and tell about division of multi-digit numbers producing whole number quotients and remainders by using rectangular arrays and/or area models. 2 from Common Core Standards 2010
M ATHEMATICS COMMON CORE LEARNING TARGETS FOURTH GRADE Number and Operations-Fractions E xt e n d u n d e r s t a n d i n g o f f r a c t i o n e q u i v a l e n c e a n d o r d e r i n g. Show with models and tell why some equivalent fractions are of the form a/b = (nxa)/(nxb). Generate equivalent fractions using the definition of a/b = (nxa)/(nxb). Compare fractions with different denominators by creating common denominators. Compare fractions with different denominators by comparing both of them to a benchmark such as 1/2. Compare fractions with different numerators by creating common numerators or denominators. Compare fractions with different numerators by comparing both of them to a benchmark such as 1/2. Recognize the importance of a common whole when comparing two fractions. Record the results of comparisons of fractions using >,=,<. Justify the comparison of fraction results using objects or drawings. B u i l d f r a c t i o n s f r o m u n i t f r a c t i o n s b y a p p l y i n g a n d e xt e n d i n g p r e v i o u s u n d e r s t a n d i n g s o f o p e r a t i o n s o n wh o l e n u m b e r s. Explain that a fraction a/b is the sum of fractions 1/b such as 3/4 is the sum of 1/4 + 1/4 + 1/4. Show and tell that addition of fractions is the joining of parts of the same whole. Show and tell that subtraction of fractions is the separating of parts of the same whole. Decompose a fraction in several ways into a sum of fractions with the same denominator and write the results in equations such as 3/8=1/8+1/8+1/8; 3/8=1/8+2/8; 21/8=1+1+4/8+1/8 = 8/8 + 8/8+ 4/8 + 1/8 Use an object or drawing to explain the decompositions. Write a fraction equivalent to a mixed number. Add mixed numbers with like denominators using equivalent (improper) fractions with the properties of operations. Subtract mixed numbers with like denominators using equivalent (improper) fractions with the properties of operations and/or the relationship between addition and subtractions. Use objects, drawings, and equations to solve word problems involving addition of fractions with like denominators that use the same whole. Use objects, drawings, and equations to solve word problems involving subtraction of fractions with like denominators that use the same whole. 3 from Common Core Standards 2010
M ATHEMATICS COMMON CORE LEARNING TARGETS FOURTH GRADE Extend multiplication knowledge of whole numbers to multiplying a whole number and a fraction such as showing with objects or drawings that 5/4 = 5 x 1/4 recording the equation in this way. Use that idea that a/b is a multiple of 1/b to multiply any fraction by a while number using objects and/or drawings such as 3 x 2/5 is 6 x 1/5 = 6/5. Generalize all multiplication of fractions to be n x a/b = (nxa)/b. Use objects or drawings to solve word problems involving multiplication of a fraction by a while number such as 5 people at a party will each eat a sandwich with 3/8 of a pound of meat. How many pounds of meat will be needed? Place the answer to multiplication word problems between whole numbers such as if the answer is 15/8, that lies between 1 and 2 pounds, but much closer to 2. U n d e r s t a n d d e c i m a l n o t a t i o n f o r f r a c t i o n s, a n d c o m p a r e d e c i m a l f r a c t i o n s Find equivalent fractions with a denominator of 100 for fractions with a denominator of 10 such as 6/10 = 60/100. Add two fractions with denominators of 10 and 100 such as 3/10 and 4/100 = 34/100. Change fractions with denominators of 10 and 100 into decimals such as 4/10 = 0.4 and 62/100 = 0.62. Use decimals with labels such as 0.62 meters for the length of a box. Locate decimals such as 0.62 on a number line. Use reasoning to compare the size of two decimals to hundredths such as find the larger of 0.47 and 0.4. Use the same whole to compare decimals. Record the results of comparing two decimals using >,=, or <. Use objects and/or drawings to justify the results of a comparison by reasoning. Measurement and Data So l v e p r o b l e m s i n v o l v i n g m e a s u r e m e n t a n d c o n v e r s i o n o f m e a s u r e m e n t s f r o m a l a r g e r u n i t t o a s m a l l e r u n i t. State and use the relative sizes of measurement units with a system such as km,m,cm; kg,g; lb,oz; hr, min, sec. Express measurements in a larger unit in terms of a smaller unit such as 3 pounds = 48 ounces and 2 m = 200 cm. Record measurement equivalents in a two-column table such as 1 ft. is 12 times as long as 1 in and 1 kg is 1000 times as heavy as 1 g. Express measurements in terms of two units such as a 4 ft. snake is 48 in. long. Generate a conversion table for feet and inches listing the numbered pairs (1,12), (2,24), (3,36),... 4 from Common Core Standards 2010
M ATHEMATICS COMMON CORE LEARNING TARGETS FOURTH GRADE Solve word problems involving distances using the four operations with whole numbers, simple fractions and decimals. Solve word problems involving intervals of time using the four operations with whole numbers, simple fractions and decimals. Solve word problems involving liquid volumes (capacity) using the four operations with whole numbers, simple fractions and decimals. Solve word problems involving masses of objects using the four operations with whole numbers, simple fractions and decimals. Solve word problems involving money using the four operations with whole numbers, simple fractions and decimals. Solve word problems involving measurements with different sizes of units using the four operations with whole numbers, simple fractions and decimals. Represent measurement quantities with diagrams such as the number line or cylinders with measurement scales. Solve real world problems by applying the area formula for rectangles such as finding the width of a rectangular room given the area of the flooring and the length of the room. Solve mathematical problems by applying the area formula for rectangles. Solve real world problems by applying the perimeter formula for rectangles. Solve mathematical problems by applying the area formula for rectangles. Re p r e s e n t a n d i n t e r p r e t d a t a. Create a line plot for a set of data that contains measurements in using unit fractions. Solve addition and subtraction problems based on the fractional data in a line plot such as finding the difference between the length of the longest and shortest specimens in an insect collection. G e o m e t r i c m e a s u r e m e n t : u n d e r s t a n d c o n c e p t s o f a n g l e a n d m e a s u r e a n g l e s. Recognize angles as geometric shapes that are formed where two rays share a common endpoint. Show and tell about how an angle is measured using a circle with the center being the common endpoint of the rays. Show and tell about how the angle is measured through the size of the arc (part of the circle) which is included between the two rays. Show and tell about an angle that turns through 1/360 of the circle is called a onedegree angle Show and tell about an angle with n one-degree angles has a measurement of n degrees. Measure angles in whole-degrees using a protractor. 5 from Common Core Standards 2010
M ATHEMATICS COMMON CORE LEARNING TARGETS FOURTH GRADE Sketch an angle when given the number of degrees. Show and tell about adding angles together when they share a side. Show and tell about taking an angle apart into smaller angles. Solve addition and subtraction problems to find unknown angles in a diagram by using an equation with a symbol for the unknown number. Geometry Draw a n d Id e n t i f y l i n e s a n d a n g l e s, a n d c l a s s i f y s h a p e s b y p r o p e r t i e s o f t h e i r l i n e s a n d a n g l e s. Identify points in a two-dimensional figure. Identify lines in a two-dimensional figure. Identify line segments in a two-dimensional figure. Identify rays in a two-dimensional figure. Identify right angles in a two-dimensional figure. Identify acute angles in a two-dimensional figure. Identify obtuse angles in a two-dimensional figure. Identify perpendicular lines in a two-dimensional figure. Identify parallel lines in a two-dimensional figure. Draw examples of points. Draw examples of lines. Draw examples of line segments. Draw examples of rays.. Draw examples of right angles. Draw examples of acute angles. Draw examples of obtuse angles. Draw examples of perpendicular lines. Draw examples of parallel lines. Identify right triangles. Classify two-dimensional figures based on whether or not they have parallel lines. Classify two-dimensional figures based on whether or not they have perpendicular lines. Show and tell about a two-dimensional figure that can be folded on a line across it so that it forms matching parts. Identify line-symmetric figures. Draw a line of symmetry on a figure. 6 from Common Core Standards 2010
FIFTH GRADE Operations and Algebraic Thinking W r i t e a n d i n t e r p r e t n u m e r i c a l e x p r e s s i o n s. Use parentheses in number expressions. Use brackets and/or braces in number expressions. Evaluate number expressions that contain parentheses. Evaluate number expressions that contain parentheses, brackets and braces. Write simple number expressions that record calculations, without evaluating them such as add 8 and 7, then multiply by 2 as 2 x (8 + 7). Interpret number expressions without evaluating them such as recognizing that 3 x (18932 + 921) is three times as large as 18932 + 921 without having to calculate. A n a l y z e p a t t e r n s a n d r e l a t i o n s h i p s. Generate two (similar) number patterns using two given rules such as add 3 starting at 0 and add 6 starting at 0. Recognize and discuss relationships between terms in each sequence such as the term from the second sequence are twice as large as the terms in the first sequence. Form ordered pairs from the corresponding terms of two sequences. Graph the ordered pairs from the corresponding terms of two sequences on a coordinate plane. Explain, using informal language, why the graph looks as it does. Number and Operations in Base Ten U n d e r s t a n d t h e p l a c e v a l u e s y s t e m. Use the concept for multi-digit numbers, that a digit in one place is 10 times as large as the digit on its right such as recognizing that 700 70 = 10. Use the concept for multi-digit numbers that a digit in one place is 1/10 as large as the digit on its left. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10. Explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to indicate powers of 10. Read decimals to thousandths using base 10 numerals. 1 from Common Core Standards 2010
FIFTH GRADE Read decimals to thousandths using number names. Read decimals to thousandths in expanded form such as 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Write decimals to thousandths using base 10 numerals. Write decimals to thousandths using number names. Write decimals to thousandths in expanded form such as 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Compare two decimals to thousandths based on meanings of the digits in each place. Compare two decimals to thousandths using >, =, and < symbols to record the results of comparisons. Round decimals to any place using place value understandings. P e r f o r m o p e r a t i o n s w i t h m u l t i - d i g i t w h o l e n u m b e r s a n d w i t h d e c i m a l s t o h u n d r e d t h s. Quickly and accurately multiply multi-digit whole numbers using the standard algorithm. Divide to find whole-number quotients of whole numbers with up to four-digits and two-digit divisors using place value strategies, properties of operations, and/or the relationship between multiplication and division. Show and explain calculations of up to four-digit numbers divided by up to two-digit numbers by using equations. Show and explain calculations of up to four-digit numbers divided by up to two-digit numbers by using rectangular arrays. Show and explain calculations of up to four-digit numbers divided by up to two-digit numbers by using area models. Add and subtract decimals to hundredths using concrete models or drawings based upon place value, properties of operations, and/or the relationship between addition and subtraction. Record and explain the strategy and reasoning used for adding and subtracting decimals to hundredths. Multiply and divide decimals to hundredths using concrete models or drawings based upon place value, properties of operations, and/or the relationship between multiplication and division. Record and explain the strategy and reasoning used for multiplying and dividing decimals to hundredths. 2 from Common Core Standards 2010