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Structures of Addition and Subtraction

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... relevant addition, subtraction, multiplication, and division problems involving decimals ... Hundreds grids / thousand grids. Number lines. Fraction blocks ... – PowerPoint PPT presentation

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Title: Structures of Addition and Subtraction


1
Structures of Addition and Subtraction
  • See Chapter 7, Van de Walle (2005)

2
Helping students to Understand
  • Two basic tools for developing understanding
  • Word Problems
  • Concrete Models

3
Join Problems
  • Join Result Unknown
  • Dylan had 3 pennies and his mother gave him 2
    more pennies. How many pennies does he have in
    all?
  • Join Change Unknown
  • Dylan had 3 pennies and his mother gives him some
    more pennies. Now he has 5 pennies. How many
    pennies did his mother give him?
  • Join Initial Unknown
  • Dylan had some pennies and his mother gave him 2
    more pennies. Now he has 5 pennies. How many
    pennies did he have to start?

4
Separate Problems
  • Separate Result Unknown
  • Gillian had 10 shells in her bucket. She gave
    her brother 3 shells. How many does she have
    left?
  • Separate Change Unknown
  • Gillian had 10 shells in her bucket. She gave
    some to her brother. Now she has 7 shells left.
    How many did she give to her brother?
  • Separate Initial Unknown
  • Gillian had some shells in her bucket. She gave
    3 to her brother. Now she has 7 shells left.
    How many did she start with?

5
Part-Part-Whole Problems
  • Part-Part-Whole Whole Unknown
  • There were 7 boys and 6 girls at a party. How
    many children in all were at the party?
  • Part-Part-Whole Part Unknown
  • There were 13 children at a party. If 7 of them
    were boys, how many were girls?

6
Compare Problems
  • Compare Difference Unknown
  • Angela has 35 and Kelly has 42. How much more
    money does Kelly have?
  • Compare Larger Unknown
  • Angela has 35. Kelly has 7 more than her. How
    much money does Kelly have?
  • Compare Smaller Unknown
  • Kelly has 7 more than Angela. If Kelly has 42,
    how much does Angela have?

7
Grade 5 6 Addition and Subtraction Outcomes
  • Grade 5
  • B1 find sums and differences involving decimals
    to thousandths
  • B8 solve and create addition and subtraction
    problems involving whole numbers and/or decimals
  • B10 estimate sums and differences involving
    decimals to thousandths

8
Grade 5 6 Addition and Subtraction Outcomes
  • Grade 6
  • B5 add and subtract simple fractions using models
  • B7 solve and create relevant addition,
    subtraction, multiplication, and division
    problems involving whole numbers
  • B8 solve and create relevant addition,
    subtraction, multiplication, and division
    problems involving decimals

9
Modeling with manipulatives and pictorial
representations
  • Base-ten Materials
  • Hundreds grids / thousand grids
  • Number lines
  • Fraction blocks
  • Fraction circles
  • Fraction Strips
  • Fraction Squares
  • Two-Colour Counters
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