Common Core Learning Standards s1

Common Core Learning Standards GRADE 1 Mathematics OPERATIONS & ALGEBRAIC THINKING Common Core Learning Concepts Embedded Skills Vocabulary Standards Represent and solve problems Addition & Solve addition and subtraction word problems within 20 . Add (+) involving addition and subtraction. Subtraction . Addend Read addition and subtraction word problems to select the . Sum operation needed for solving . Equal (=) 1. OA.1. Draw visual representations of addition and subtraction . Difference Use addition and subtraction within 20 to word problems within 20 . Subtract (-) solve word problems involving situations of Manipulate object to explain what operations is needed to . Part adding to, taking from, putting together, taking solve addition and subtraction word problems within 20 . Whole apart, and comparing, with unknowns in all Write an addition or subtraction equation to match a word . Altogether positions, e.g., by using objects, drawings, and problem . Unknown equations with a symbol for the unknown Explain the meaning of the symbols in an addition and . Symbol 2 number to represent the problem . subtraction equation . Equation Read an equation (number sentence), using the term ‘plus’ . Solve for (+), ‘minus’ for (-) and ‘equals’ for (=) . Represent Create word problem (number stories) that match a given . Compare number sentence 2 See Glossary for Common Addition & Solve a word problem for an unknown in all positions of Subtraction Situations with Unknowns addition and subtraction equations (by writing an equation with a symbol for the unknown)2 SAMPLE TASKS

I. Sam has 6 fish. Tim has 5. How many fish do they have altogether? Show your work.

II. Jenny has 12 pennies. She lost 4 on her way home. How many does she have left? Show your work.

Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. III. There are 8 students at the park. Then 7 more showed up. How many students are there now? Write a number sentence to represent the problem.

IV. There are 8 students at the park. Some more students show up. There are now 15 students. How many students came? Write an equation to solve the problem.

V. There are some students at the park. Then 8 more students came. There are now 15 students. How many students were at the park in the beginning? Explain how you know your answer is correct.

VI. Create a number story to match this equation. 6+9 = 15

VII. Number Stories Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. i. Draw a picture of a group of things, such as animals, toys, or flowers.

ii. Tell a number story about your picture to a partner.

VIII. There are nine birds on a tree. Some birds flew away. If there are only three birds left, how many birds flew away? Draw a picture and write an equation to show your work.

Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. Common Core Learning Concepts Embedded Skills Vocabulary Standards Represent and solve problems involving Addition Solve addition word problems with three addends, for . Add (+) addition and subtraction. sums up to 20. . Addend Read addition word problems to select the operation . Sum needed for solving . Equal 1. OA.2. Draw visual representations of addition word problems . Part Solve word problems that call for addition of three addends, for sums up to 20 . Whole three whole numbers whose sum is less than or Manipulate objects to explain what operations is needed . Altogether equal to 20, e.g., by using objects, drawings, and to solve addition word problems with three addends, for . Unknown equations with a symbol for the unknown number sums up to 20 . Symbol to represent the problem. Write an addition equation to match a word problem . Equation . Solve Explain the meaning of the symbols in an addition . Represent equation Read an addition equation (number sentence), using the term ‘plus’ for (+) and ‘equals’ for (=) Create word problem (number stories) that match a given addition equation with three addends Solve a word problem for an unknown in all positions of an addition equations (by writing an equation with a symbol for the unknown) SAMPLE TASKS

I. Ben has 3 pencils. Pat has 2 pencils. Beth has 3 pencils. How many pencils do they have altogether? Write a number sentence to solve.

Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. II. Create a number story to match this equation: 8+3+2 = 13

III. There are 6 students at the zoo. Then 4 more showed up. Another group of 5 students joined them. How many students are there now? Show your work.

IV. There are 6 boys at the zoo. Some girls join the group. Then another 5 boys joined them. There are now 15 students. How many girls were in the group? Explain how you know your answer is correct.

V. There are some students at the zoo. Then 4 more students came. Another group of 5 students joined them. There are now 15 students. How many students were at the park in the beginning? Write an equation to represent the problem.

VI. There are 6 students at the zoo. Then 4 students joined them. Another group of students joined them. There are 15 students at the zoo. How many students joined them? Draw a picture to show your work.

VII. Use objects to solve the following word problem: Ann has 4 red balls, 2 green balls, and 5 yellow balls. How many balls does she have in all? Explain how you solved the problem.

Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. VIII. Draw a picture to solve. Dave has 3 crayons. He finds 9 more crayons. Then 2 more crayons are given to him. How many total crayons does he have?

Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. Common Core Learning Concepts Embedded Skills Vocabulary Standards Understand and apply properties of Properties Explain or show the commutative property of addition (by . Addend(s) operations and the relationship switching the addends to get the same sum) . Sum Explain or show the associative property of addition with . Difference between addition and subtraction. three addends (by grouping any two addends then adding . Commutative the third to get the same sum) Property 1. OA.3. Explain the meaning of the symbols in an addition . Associative Apply properties of operations as strategies to equation Property add and subtract.3 Examples: If 8 + 3 = 11 is Read an addition equation (number sentence), using the . Symbol known, then 3 + 8 = 11 is also known. term ‘plus’ for (+) and ‘equals’ for (=) . Equation (Commutative property of addition.) To add 2 + 6 Create different addition equations for the same sum . Relationship + 4, the second two numbers can be added to Add and subtract, using properties of operations make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

3Students need not use formal terms for these properties SAMPLE TASKS

I. Write 7+8= 15 another way. Show how both sums are the same.

II. Add. Change the order of the addends. Add again. Compare and contrast the two problems.

5 + 2 = ____

+ = ____

Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. III. Add 2 addends together first. Write the sum. Then add the 3rd addend to find the final sum.

7 + 2 + 4 = _____ 7 + 2 + 4=______

⃝ + 4 = _____ 7 + ⃝ =______

8 Show 5 + 3 + 8 = ____ using cubes. Write the steps for how you solved this problem. Compare your steps with your partner.

Common Core Learning Concepts Embedded Skills Vocabulary Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. Standards Understand and apply properties of Properties Describe addition and subtraction relationships . Addend operations and the relationship . Unknown Write a fact family given 3 different numbers and explain . Equation between addition and subtraction. how they are related . Fact family 1. OA.4. Read an equation (number sentence), using the term . Addition Understand subtraction as an unknown-addend ‘plus’ for (+), ‘minus’ for (-) and ‘equals’ for (=) . Subtraction problem. For example, subtract 10 – 8 by finding Solve for an unknown addend using subtraction . Related fact the number that make 10 when added to 8. Add . Solve and subtract within 20. . Property

SAMPLE TASKS

I. Solve 10 – 6.

THINK 6 + ___ = 10

SO 10 – 6 = ____

II. Write an addition sentence you can use to help you solve 17-8.

III. Explain how addition & subtraction are related.

IV. Write an addition fact family for 12. Explain how the addends are related.

______

Common Core Learning Concepts Embedded Skills Vocabulary Standards Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. Add and Subtract within 20. Addition & Add within 20 using counting or counting on to solve . Add Subtraction . Subtract Subtract within 20 using count back or counting on . Sum (addition) to solve . Difference 1. OA.5. Explain the effect of addition and subtraction (subtraction . Count on Relate counting to addition and subtraction (e.g., will result in a smaller number & addition will result in a . Count back by counting on 2 to add 2). larger number) . Solve Read an equation (number sentence), using the term . Equation ‘plus’ for (+), ‘minus’ for (-) and ‘equals’ for (=) . Relate Write an addition or subtraction equation Add and subtract using number patterns (skip counting, doubles) SAMPLE TASKS

Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. I. Circle the greater addend. Then count on to find the sum.

9 + 3 =____

II. Use the number line to solve the following addition and subtraction problems.

17 - 8 = _____ 5 + 9 = _____ 12 – 4 = _____

III. Compare and contrast addition and subtraction. Use numbers pictures and words to show how they are similar and different.

______

IV. Explain how counting back can help you solve the following subtraction problem: 12-7=____

Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. Common Core Learning Concepts Embedded Skills Vocabulary Standards Add and Subtract within 20. Addition & Add and subtract fluently within 10 (with quick recall and . Count on Subtraction without any visual aids) . Count back Show and explain related addition and subtraction facts . Add . Subtract 1. OA.6. Create a known fact to help with another fact (i.e. . Double Add and subtract within 20, demonstrating composing a five, composing a ten, doubles, etc.) . Group of 5 fluency for addition and subtraction within 10. Explain addition and subtraction strategies used . Group of 10 Use strategies such as counting on; making ten . Related fact (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing . Equivalent a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 . Decompose = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). SAMPLE TASKS

I. Show and explain what it means to double a number.

II. Solve and explain why these are double facts.

4 + 4 =______

2 +2 = ______

3 + 3 = ______

1 + 1 = ______

Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. III. Use a doubles fact to solve 6 + 5. Explain how you got your answer.

IV. There are 14 markers in the box. Some are red and some are blue. The number of red crayons is the same as the number of blue crayons. Write a doubles fact to solve.

______= ______+ ______

V. How are the following facts related?

6 + 5 = 11 11 – 6 = 5

VI. Solve the following by making a ten: 5+8=_____. Explain how you got your answer.

VII. Solve the following: 19- 8=______. Explain the strategy you used to solve the problem.

Common Core Learning Concepts Embedded Skills Vocabulary Standards Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. Work with addition and subtraction Addition & Explain the meaning of the symbols in an addition and . True equations. Subtraction subtraction equation . False Read an equation (number sentence), using the term . Equation ‘plus’ for (+), ‘minus’ for (-) and ‘equals’ for (=) . Equal 1. OA.7. Evaluate an equation for a given value . Balanced Understand the meaning of the equal sign, and (Example: 3 + ⃝ = 8. Is this equation true if ⃝=6? Why . Addition determine if equations involving addition and or why not?) . Subtraction subtraction are true or false. For example, which Manipulate objects, draw pictures or balance a scale to of the following equations are true and which are prove an equation (number sentence) true or false for false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. different values. SAMPLE TASKS

I. 7 + n = 12. Is this equation true if n = 5? Why or why not?

______

II. Circle the equation that is true. Cross out the equation that is false.

7 – 5 = 5 – 2

8 – 8 = 6 – 6

Draw a picture to prove your answer.

III. Use counters to show if this equation is true or false. Explain your reasoning.

5 + 6 = 11 – 6

______

Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. Common Core Learning Concepts Embedded Skills Vocabulary Standards Work with addition and subtraction Addition & Explain the meaning of the symbols in an addition and . True equations. Subtraction subtraction equation . False Read an equation (number sentence), using the term . Equation ‘plus’ for (+), ‘minus’ for (-) and ‘equals’ for (=) . Equal 1. OA.8. Calculate the missing value in a given equation. . Balanced Determine the unknown whole number in an (Example: 3 + ⃝ = 8. What value of ⃝ will make this . Addition addition or subtraction equation relating three equation true?) . Subtraction whole numbers. For example, determine the Manipulate objects, draw pictures or balance a scale to . Whole unknown number that makes the equation true in prove an equation (number sentence) true for a value . Part each of the equations 8 +? = 11, 5 = _ – 3, 6 + 6 = _. found. SAMPLE TASKS

See Sample Tasks Below

Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. I. Complete the table below using manipulatives to help you solve for the unknown value.

Counter In a Cup

Total Number of Counters

Counters Out of Counters In the the Cup Cup

Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. II. Solve for the unknown number in each equation.

9 +  = 14

- 7 = 4

6 + 9 =

10 - = 8

Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. III. Explain what the = symbol tells us in the number sentence below.

8 + 7 = 10 + 5

IV. Verbally read the following equations.

8 + 3 = 11

13 – 6 = 7

2 + 3 + 5 = 12 – 2

V. Solve for the unknown number. Prove how you know your answer is correct. **Note to teacher: students can prove their answer verbally, with the use of pictures (pre-made or student drawn), using manipulatives, etc.**

+ 9 = 18