Transcript Introduction to Addition and Subtraction

EMSE 3123
Math and Science in Education
Introduction to Addition and
Subtraction
Presented by
Frank H. Osborne, Ph. D.
© 2015
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Introduction to Addition and Subtraction
We 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 Subtraction
We 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 Subtraction
We 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 Subtraction
Decomposing numbers:
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Introduction to Addition and Subtraction
Decomposing numbers:
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Introduction to Addition and Subtraction
Addition 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 Subtraction
Subtraction 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 Subtraction
We 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 Subtraction
Repeat the above example to demonstrate
the following additions. In each case
draw a diagram showing the
manipulatives.
a. 5 + 6
b. 8 + 9
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Introduction to Addition and Subtraction
5+6
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Introduction to Addition and Subtraction
8+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 Subtraction
Decomposing numbers:
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Introduction to Addition and Subtraction
Decomposing numbers:
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Introduction to Addition and Subtraction
Counting ladybugs.
Continue up to 10 + 9 = 19. Remember
groups of 10 and ones.
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Introduction to Addition and Subtraction
Word 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 Subtraction
Commutative 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 Subtraction
Associative 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 Subtraction
Subtraction 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 Subtraction
Counting 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 Subtraction
Counting 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 Subtraction
Children 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 Subtraction
Children 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 Subtraction
Children 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)
B)
C)
D)
6=6
7=8–1
5+2=2+5
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)
B)
C)
D)
6=6
7=8–1
5+2=2+5
4 + 1 = 5 + 2.
True
True
True
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
– B) 5 = [] – 3
– C) 6 + 6 =
8 + 3 = 11
5=8-3
6 + 6 = 12
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The End
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