Introduction to Addition and Subtraction

Presented byFrank H. Osborne, Ph. D.

© 2015

EMSE 3123Math and Science in Education

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Introduction to Addition and SubtractionWe use manipulatives to illustrate addition and

subtraction in early grades.•Addition is the union of two sets. •We start with numbers less than ten.

•This is followed by grouping by tens when working with numbers over ten.

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Introduction to Addition and SubtractionWe use manipulatives to illustrate addition

and subtraction in early grades.•Addition is the union of two sets.

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Introduction to Addition and SubtractionWe use manipulatives to illustrate addition

and subtraction in early grades.•Subtraction begins with a set and we "take away" a sub-set.

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Introduction to Addition and Subtraction• Sums of 10. Done by coloring circles.

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Introduction to Addition and Subtraction• Decomposing: Sums of 10.

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Introduction to Addition and Subtraction• How many more do you need to make 10?

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Introduction to Addition and Subtraction• How many more do you need to make 10?

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Introduction to Addition and Subtraction• Fluently add and subtract within five.

• Children need to practice math skills all the time. Your job as their teacher is to make it interesting and enjoyable to them so that they show positive affective behavior.

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Introduction to Addition and SubtractionDecomposing numbers:

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Introduction to Addition and SubtractionDecomposing numbers:

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Introduction to Addition and SubtractionAddition using word problems. “Mary has

3 apples and John has 2 apples. How many apples do they have in all?”

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Introduction to Addition and SubtractionSubtraction using word problems. “They give

one apple to the teacher. How many do they have left over?”

Word problems are very, very important. This is how math gets related to the real world. It also helps to reinforce ties to language arts skills.

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Introduction to Addition and SubtractionWe transition into first grade•Addition and subtraction within 20•Word problems involving 3 numbers•Properties of operations•Working with equations

– Understand the meaning of the equals sign. It means that both sides are the same. That is why it is made up of two lines that are the same. (=)

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Introduction to Addition and Subtraction• Combine the two sets of objects and express the

result by grouping accordingly.

• This introduces the concept of grouping by tens.

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Introduction to Addition and SubtractionRepeat the above example to demonstrate

the following additions. In each case draw a diagram showing the manipulatives.a. 5 + 6b. 8 + 9

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Introduction to Addition and Subtraction5 + 6

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Introduction to Addition and Subtraction8 + 9

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How Many Tens, How Many Ones• We see how many tens and ones result from each

addition.

Note that a. and d. already contain a ten. In b. and c. one number has to be decomposed to make ten by addition to the other.

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How Many Tens, How Many Ones• We see how many tens and ones result from each

addition.

• In b. the green 6 was decomposed into 1 + 5• The 1 was added to the blue 9 to make a 10.• In c. the brown 8 was decomposed into 4 + 4• One 4 was added to the 6 to make a 10.

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Introduction to Addition and SubtractionDecomposing numbers:

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Introduction to Addition and SubtractionDecomposing numbers:

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Introduction to Addition and SubtractionCounting ladybugs.

Continue up to 10 + 9 = 19. Remember groups of 10 and ones.

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Introduction to Addition and SubtractionWord problems involving three numbers.“Claudia has 8 pencils, Juan has 2 pencils

and Ana has 6 pencils. How many pencils are there in all?

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Introduction to Addition and Subtraction“Claudia has 8 pencils, Juan has 2 pencils and

Ana has 6 pencils. How many pencils are there in all?

Strategy: We observe that 8 + 2 = 10 so the equation 8 + 2 + 6 becomes 10 + 6 = 16.

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Introduction to Addition and SubtractionCommutative Property of Addition• If we know that 4 + 7 = 11, then we also

know that 7 + 4 = 11.

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Introduction to Addition and SubtractionAssociative Property of Addition• Add: 3+ 8 + 7• Method: We see that 3 + 7 = 10 so the

problem now becomes

3 + 8 + 7 = 10 + 8 = 18

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Introduction to Addition and SubtractionSubtraction as an unknown-addend problem.• Subtract: 10 – 7 = ?• Method: We ask what number when added to

7 makes 10?

• Since we know that you need to have add 3 to 7 in order to make 10, we conclude that

10 – 7 = 3

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Introduction to Addition and SubtractionCounting is related to addition and subtraction.• Add: 3 + 8

• We count 3 hops followed by 8 hops for a total of 11, so 3 + 8 = 11. Note that with addition we count to the right.

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Introduction to Addition and SubtractionCounting is related to addition and subtraction.• We think of subtraction the same way.• Subtract 7 from 16.

• We start at 16, and hop back 7, so 16 – 7 = 9.• Note that in subtraction we count back to the left while

in addition we count on to the right.

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Introduction to Addition and SubtractionChildren must practice and become fluent in addition and

subtraction within 20. Strategies:•Counting on

•see Van De Walle, page 133ff)

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Introduction to Addition and SubtractionChildren must practice and become fluent in

addition and subtraction within 20. Strategies:•Skip counting (at least with 2, 3, 4 and 5)

•Making ten – (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14)

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Introduction to Addition and SubtractionChildren must practice and become fluent in

addition and subtraction within 20. Strategies:•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 that 12 - 8 = 4);

•Creating equivalent but easier or known sums– (e.g., adding 6 + 7 by creating the known

equivalent 6 + 6 + 1 = 12 + 1 = 13).

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Introduction to Addition and Subtraction• 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?– A) 6 = 6– B) 7 = 8 – 1– C) 5 + 2 = 2 + 5– D) 4 + 1 = 5 + 2.

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Introduction to Addition and Subtraction• 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?– A) 6 = 6 True– B) 7 = 8 – 1 True– C) 5 + 2 = 2 + 5 True– D) 4 + 1 = 5 + 2. False

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Introduction to Addition and Subtraction• 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.– A) 8 + ? = 11 8 + 3 = 11– B) 5 = [] – 3 5 = 8 - 3– C) 6 + 6 = 6 + 6 = 12

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The End

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