Grade 3 Bar Models: Multi-Step Problems

Worked examples

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

1. Example 1

   Jack had 28 cards. Jack got 49 more and then gave away 52. How many cards does Jack have now?

   1. Step 1: Jack got 49 more, so the bar gets longer. 28 + 49: add the tens, then the ones. 28 + 40 = 68, then 68 + 9 = 77.
   2. Step 2: Jack gave away 52, so take that piece off the bar. 77 − 52: take away the tens, then the ones. 77 − 50 = 27, then 27 − 2 = 25.
   3. Jack has 25 cards now.

   Answer: 25

2. Example 2

   Max has 24 pencils. Jack has 5 more pencils than Max. How many pencils do they have altogether?

   1. Draw Max's bar for 24. Jack's bar is the same length plus an extra piece of 5.
   2. Step 1: find Jack's amount. 24 + 5 = 29.
   3. Step 2: put both bars together. 24 + 29: add the tens, then the ones. 24 + 20 = 44, then 44 + 9 = 53.
   4. They have 53 pencils altogether.

   Answer: 53

3. Example 3

   Max buys 9 packs of pencils. Each pack has 8 pencils. Max gives away 37 pencils. How many pencils does Max have left?

   1. Draw a bar of 9 equal units, one for each pack, each worth 8.
   2. Step 1: find how many pencils in all. 9 × 8 = 72.
   3. Step 2: take away the 37 given away. 72 − 37: take away the tens, then the ones. 72 − 30 = 42, then 42 − 7 = 35.
   4. Max has 35 pencils left.

   Answer: 35