Grade 5 Bar Models: Unit Review

Worked examples

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

1. Example 1

   Max has 77 cards. Sam has 4 times as many cards as Max. How many cards do they have altogether?

   1. Draw Max's bar as 1 unit of 77 and Sam's bar as 4 units of 77.
   2. Step 1: find Sam's amount. 4 × 77 = 70 × 4 + 7 × 4 = 280 + 28 = 308.
   3. Step 2: put both bars together. 77 + 308: add the hundreds, then the ones. 77 + 300 = 377, then 377 + 8 = 385.
   4. Check: that is 5 units of 77, and 5 × 77 = 385.
   5. They have 385 cards altogether.

   Answer: 385

2. Example 2

   Lisa has 70 stickers. Max has 6 times as many stickers as Lisa. How many stickers do they have altogether?

   1. Draw Lisa's bar as 1 unit of 70 and Max's bar as 6 units of 70.
   2. Step 1: find Max's amount. 6 × 70 = 420.
   3. Step 2: put both bars together. 70 + 420 = 490.
   4. Check: that is 7 units of 70, and 7 × 70 = 490.
   5. They have 490 stickers altogether.

   Answer: 490

3. Example 3

   Lisa has 72 marbles. Mia has 5 times as many marbles as Lisa. How many marbles do they have altogether?

   1. Draw Lisa's bar as 1 unit of 72 and Mia's bar as 5 units of 72.
   2. Step 1: find Mia's amount. 5 × 72 = 70 × 5 + 2 × 5 = 350 + 10 = 360.
   3. Step 2: put both bars together. 72 + 360 = 432.
   4. Check: that is 6 units of 72, and 6 × 72 = 432.
   5. They have 432 marbles altogether.

   Answer: 432