Grade 4 Bar Models: Challenge Problems

Worked examples

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

1. Example 1

   Amy has 14 marbles. Lisa has 16 marbles. Amy gives 7 to Lisa. How many marbles do they have altogether now?

   1. Draw a bar for Amy (14) and a bar for Lisa (16). When Amy gives 7 to Lisa, Amy's bar gets 7 shorter and Lisa's bar gets 7 longer.
   2. After the gift: Amy has 14 − 7 = 7 and Lisa has 16 + 7 = 23.
   3. Put the two bars together. 23 + 7 = 30.
   4. Shortcut: the marbles only moved from one person to the other, so the total is the same as before: 14 + 16 = 30.
   5. They have 30 marbles altogether now.

   Answer: 30

2. Example 2

   Jack has 11 apples. Amy has 12 apples. Jack gives 7 to Amy. How many apples do they have altogether now?

   1. Draw a bar for Jack (11) and a bar for Amy (12). When Jack gives 7 to Amy, Jack's bar gets 7 shorter and Amy's bar gets 7 longer.
   2. After the gift: Jack has 11 − 7 = 4 and Amy has 12 + 7 = 19.
   3. Put the two bars together. 19 + 4: make a ten first. 19 + 1 = 20, then 20 + 3 = 23.
   4. Shortcut: the apples only moved from one person to the other, so the total is the same as before: 11 + 12 = 23.
   5. They have 23 apples altogether now.

   Answer: 23

3. Example 3

   Mia has 16 apples. Amy has 14 apples. Mia gives 6 to Amy. How many apples do they have altogether now?

   1. Draw a bar for Mia (16) and a bar for Amy (14). When Mia gives 6 to Amy, Mia's bar gets 6 shorter and Amy's bar gets 6 longer.
   2. After the gift: Mia has 16 − 6 = 10 and Amy has 14 + 6 = 20.
   3. Put the two bars together. 10 + 20 = 30.
   4. Shortcut: the apples only moved from one person to the other, so the total is the same as before: 16 + 14 = 30.
   5. They have 30 apples altogether now.

   Answer: 30