Grade 5 Bar Models: Multi-Step Problems

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   Amy has 10 cards. Tom has 22 cards. Amy gives 7 to Tom. How many cards do they have altogether now?

   1. Draw a bar for Amy (10) and a bar for Tom (22). When Amy gives 7 to Tom, Amy's bar gets 7 shorter and Tom's bar gets 7 longer.
   2. After the gift: Amy has 10 − 7 = 3 and Tom has 22 + 7 = 29.
   3. Put the two bars together. 29 + 3: make a ten first. 29 + 1 = 30, then 30 + 2 = 32.
   4. Shortcut: the cards only moved from one person to the other, so the total is the same as before: 10 + 22 = 32.
   5. They have 32 cards altogether now.

   Answer: 32

2. Example 2

   Tom has 22 cookies. Lisa has 24 cookies. Tom gives 5 to Lisa. How many cookies do they have altogether now?

   1. Draw a bar for Tom (22) and a bar for Lisa (24). When Tom gives 5 to Lisa, Tom's bar gets 5 shorter and Lisa's bar gets 5 longer.
   2. After the gift: Tom has 22 − 5 = 17 and Lisa has 24 + 5 = 29.
   3. Put the two bars together. 17 + 29: add the tens, then the ones. 17 + 20 = 37, then 37 + 9 = 46.
   4. Shortcut: the cookies only moved from one person to the other, so the total is the same as before: 22 + 24 = 46.
   5. They have 46 cookies altogether now.

   Answer: 46

3. Example 3

   Sam has 17 books. Amy has 21 books. Sam gives 10 to Amy. How many books do they have altogether now?

   1. Draw a bar for Sam (17) and a bar for Amy (21). When Sam gives 10 to Amy, Sam's bar gets 10 shorter and Amy's bar gets 10 longer.
   2. After the gift: Sam has 17 − 10 = 7 and Amy has 21 + 10 = 31.
   3. Put the two bars together. 31 + 7 = 38.
   4. Shortcut: the books only moved from one person to the other, so the total is the same as before: 17 + 21 = 38.
   5. They have 38 books altogether now.

   Answer: 38