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