Dear Parents and Caregivers, We appreciate the support you give to your child’s education. You are a vital partner in this learning. We would like to share some information to help you better understand Arizona’s College and Career Ready Standards. The purpose of these letters is to clarify vocabulary and strategies that your child may use to make sense of numbers and develop underlying mathematical ideas. We do not expect you to teach these methods but want to help you understand the work your child will be bringing home. The topic of this letter is strategies for addition and subtraction within 20 in first grade. End-­‐of-­‐year goals In Kindergarten, students learned strategies for addition and subtraction within 10. In first grade, students are expected to demonstrate fluency for addition and subtraction within 10 using a variety of strategies, and then use these strategies to add and subtract within 20. Students are developing strategies for adding and subtracting whole numbers based on their prior work with small numbers. They use a variety of strategies to model add-­‐to, take-­‐from, put-­‐together, take-­‐apart, and compare situations to deepen their understanding of and develop the meaning behind and relationship between addition and subtraction. Counting on Counting on is starting at a number and counting up from that number. •
For an addition problem, children can remember the bigger number in their head and show the smaller number on their fingers to count on. For each number they count on, they should put a finger down. When they have no more fingers, this is their sum. For example, if the equation is 7 + 5, the children say “7” and put five fingers up and count on 8, 9, 10, 11, 12, putting a finger down with each count. The last number they say is the sum. •
Children might use a number path or number line to show counting on in addition, starting at one addend and counting on the amount of the second addend to reach their sum. Students might use the number path or number line for counting back in subtraction. •
1 2 3 4 5 6 7 8 9 10 number path subtraction Students also use counters (beans, buttons, cereal) to demonstrate counting on by putting down the amount of the first addend and counting on the amount of the second addend as they put additional counters down Counters can be used for taking away in subtraction. Making a 10 One foundation for addition and subtraction is composing (making), or decomposing (taking apart) a 10. Understanding how numbers relate to 10 is critical for fluent computation. Making a ten is an important strategy because it is easy to add a number to 10 (or to a multiple of 10). This is an important feature of our base-­‐10 number system. •
To solve an addition problem using the making a 10 strategy, students might use blocks or cubes to model the problem. They will show the 2 addends on the blocks, split one of the addends apart to add on to the other number to make a ten and then add the ten and the other addend together to get their sum. Mesa Public Schools/Grade 1/Add & Subtract within 20/2013 Authorization to reprint or disseminate must be granted by Mesa Public Schools (February-­‐2014). For example to solve 6 + 8 = ?, think, “How can I make a ten?” Decompose the 6 to make the problem 4 + 2 + 8 or decompose the 8 to make the problem 6 + 4 + 4 6 + 8 = 4 + 2 + 8 = 4 + 10 = 14 6 + 8 = 6 + 4 + 4 = 10 + 4 = 14 Children might use ten frames to solve addition problems by making a ten. o
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For example, for 9 + 5: Decomposing a number leading to a 10 A related approach to that practiced above for addition can be used for subtraction, decomposing (taking apart) a number leading to a 10. •
Students may use blocks or cubes to show a subtraction problem where they decompose a number leading to a 10. For 13 – 4, think, “How can I make a ten?” Decompose the 4 to make the problem 13 – 3 – 1. 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9 Using the relationship between addition and subtraction This concept shows how addition and subtraction are related. For example, 12 – 7 = 5, but 7 and 5 can be added together again to end up with 12, 7 + 5 = 12. What this means for children is if they have trouble with subtraction, they can use addition to help solve the problem. Children see this relationship when they study fact families (e.g., for the fact family 12, 7, 5: 7 + 5 = 12, 5 + 7 = 12, 12 – 5 = 7, 12 – 7 = 5). •
To solve 11 – 5 = ?, a child can think 5 + ? = 11 and get the correct answer: 6, by relating the addition and the subtraction. Children demonstrate this relationship between addition and subtraction by using blocks, cubes, beans, and cereal. Student may use number cards to show related facts. Using known facts to create equivalent sums If children can add by using the facts they already know, they will have another effective strategy use when adding. •
Children can use numbers or blocks to show or explain the easier facts they see within other equations. They solve equations using known facts. For example when adding 6 + 7, they can think, “6 + 6 + 1 = 12 + 1= 13.” How t o help at home •
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Ask your child to use objects/counters to solve math problems and to show addition and subtraction math concepts (beans, buttons, clothespins, cereal). Encourage your child to draw a picture to solve addition and subtraction problems and explain his/her thinking. Practice fact families to show the relationship between addition and subtraction. Make up addition and subtraction stories about daily events and ask your child to use different strategies to solve the problem. Ask your child to explain his/her thinking. Practice addition and subtraction math facts for fluency within 10. Use sites such as http://www.softschools.com/math/games to practice addition and subtraction. Remember, making mistakes is a part of learning. Mesa Public Schools/Grade 1/Add & Subtract within 20/2013 Authorization to reprint or disseminate must be granted by Mesa Public Schools (February-­‐2014).