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Common Core Learning StandardsGRADE 1 Mathematics

OPERATIONS & ALGEBRAIC THINKING

Common Core Learning Standards Concepts Embedded Skills Vocabulary

Represent and solve problems involving addition and subtraction.

Addition & Subtraction

Solve addition and subtraction word problems within 20 Add (+) Addend Sum Equal (=) Difference Subtract (-) Part Whole Altogether Unknown Symbol Equation Solve Represent Compare

Read addition and subtraction word problems to select the operation needed for solving

1. OA.1. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem2.

2See Glossary for Common Addition & Subtraction Situations with Unknowns

Draw visual representations of addition and subtraction word problems within 20Manipulate object to explain what operations is needed to solve addition and subtraction word problems within 20Write an addition or subtraction equation to match a word problemExplain the meaning of the symbols in an addition and subtraction equationRead an equation (number sentence), using the term ‘plus’ for (+), ‘minus’ for (-) and ‘equals’ for (=)Create word problem (number stories) that match a given number sentenceSolve a word problem for an unknown in all positions of addition and subtraction equations (by writing an equation with a symbol for the unknown)2

SAMPLE TASKSI. Sam has 6 fish. Tim has 5. How many fish do they have altogether? 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.

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

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 Storiesi. 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.



Represent and solve problems involving addition and subtraction.

Addition Solve addition word problems with three addends, for sums up to 20.

Add (+) Addend Sum Equal Part Whole Altogether Unknown Symbol Equation Solve Represent

Read addition word problems to select the operation needed for solving

1. OA.2. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Draw visual representations of addition word problems three addends, for sums up to 20Manipulate objects to explain what operations is needed to solve addition word problems with three addends, for sums up to 20Write an addition equation to match a word problem

Explain the meaning of the symbols in an addition equationRead 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 addendsSolve a word problem for an unknown in all positions of an addition equations (by writing an equation with a symbol for the unknown)

SAMPLE TASKSI. 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.


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.


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?



Understand and apply properties of operations and the relationship between addition and subtraction.

Properties Explain or show the commutative property of addition (by switching the addends to get the same sum)

Addend(s) Sum Difference Commutative

Property Associative

Property Symbol Equation Relationship

Explain or show the associative property of addition with three addends (by grouping any two addends then adding the third to get the same sum)

1. OA.3. Apply properties of operations as strategies to add and subtract.3 Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

3Students need not use formal terms for these properties

Explain the meaning of the symbols in an addition equationRead an addition equation (number sentence), using the term ‘plus’ for (+) and ‘equals’ for (=)Create different addition equations for the same sum

Add and subtract, using properties of operations

SAMPLE TASKSI. 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 = ____ + = ____


III. Add 2 addends together first. Write the sum. Then add the 3 rd 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.



Understand and apply properties of operations and the relationship between addition and subtraction.

Properties Describe addition and subtraction relationships Addend Unknown Equation Fact family Addition Subtraction Related fact Solve Property

Write a fact family given 3 different numbers and explain how they are related

1. OA.4. Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that make 10 when added to 8. Add and subtract within 20.

Read an equation (number sentence), using the term ‘plus’ for (+), ‘minus’ for (-) and ‘equals’ for (=)

Solve for an unknown addend using subtraction

SAMPLE TASKSI. 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.

______ _______ ________ _________

____________________________________________________

____________________________________________________



Add and Subtract within 20. Addition & Subtraction

Add within 20 using counting or counting on to solve Add Subtract Sum Difference Count on Count back Solve Equation Relate

Subtract within 20 using count back or counting on (addition) to solve

1. OA.5. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

Explain the effect of addition and subtraction (subtraction will result in a smaller number & addition will result in a larger number)


Write an addition or subtraction equation

Add and subtract using number patterns (skip counting, doubles)

SAMPLE TASKSI. 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=____


Addition Subtraction


Add and Subtract within 20. Addition & Subtraction

Add and subtract fluently within 10 (with quick recall and without any visual aids)

Count on Count back Add Subtract Double Group of 5 Group of 10 Related fact Equivalent Decompose

Show and explain related addition and subtraction facts

1. OA.6. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 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).

Create a known fact to help with another fact (i.e. composing a five, composing a ten, doubles, etc.)

Explain addition and subtraction strategies used

SAMPLE TASKSI. 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 = ______


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.



Work with addition and subtraction equations.


Explain the meaning of the symbols in an addition and subtraction equation

True False Equation Equal Balanced Addition Subtraction


1. OA.7. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

Evaluate an equation for a given value (Example: 3 + ⃝ = 8. Is this equation true if ⃝=6? Why or why not?)Manipulate objects, draw pictures or balance a scale to prove an equation (number sentence) true or false for different values.

SAMPLE TASKSI. 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

____________________________________________________________________________________

___________________________________________________________________________________



Work with addition and subtraction equations.


Explain the meaning of the symbols in an addition and subtraction equation

True False Equation Equal Balanced Addition Subtraction Whole Part


1. OA.8. Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 +? = 11, 5 = _ – 3, 6 + 6 = _.

Calculate the missing value in a given equation.(Example: 3 + ⃝ = 8. What value of ⃝ will make this equation true?)Manipulate objects, draw pictures or balance a scale to prove an equation (number sentence) true for a value found.

SAMPLE TASKS

See Sample Tasks Below


I. Complete the table below using manipulatives to help you solve for the unknown value.

Counter In a Cup

Total Number of Counters

11

Counters Out of the Cup

Counters In the Cup

6

3

7

8

1


II. Solve for the unknown number in each equation.

9 + = 14

- 7 = 4

6 + 9 =

10 - = 8

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

15 = 7 + 8

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


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