Grade 4 Bar Models: Multi-Step Problems

Worked examples

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

1. Example 1

   Lisa has 63 apples. Jack has 2 times as many apples as Lisa. How many apples do they have altogether?

   1. Draw Lisa's bar as 1 unit of 63 and Jack's bar as 2 units of 63.
   2. Step 1: find Jack's amount. 2 × 63 = 60 × 2 + 3 × 2 = 120 + 6 = 126.
   3. Step 2: put both bars together. 63 + 126: add the hundreds and tens, then the ones. 63 + 120 = 183, then 183 + 6 = 189.
   4. Check: that is 3 units of 63, and 3 × 63 = 189.
   5. They have 189 apples altogether.

   Answer: 189

2. Example 2

   Max had 483 pencils. Max sold 83 of them and packed the rest equally into 8 boxes. How many pencils are in each box?

   1. Step 1: take the 83 sold off the bar. 483 − 83: take away the tens, then the ones. 483 − 80 = 403, then 403 − 3 = 400.
   2. Step 2: cut the rest into 8 equal units, one for each box, so divide. 400 ÷ 8: take away 8 × 50 = 400 (0 left). 400 ÷ 8 = 50.
   3. There are 50 pencils in each box.

   Answer: 50

3. Example 3

   Jack buys 3 packs of marbles. Each pack has 37 marbles. Jack gives away 39 marbles. How many marbles does Jack have left?

   1. Draw a bar of 3 equal units, one for each pack, each worth 37.
   2. Step 1: find how many marbles in all. 3 × 37 = 30 × 3 + 7 × 3 = 90 + 21 = 111.
   3. Step 2: take away the 39 given away. 111 − 39: take away the tens, then the ones. 111 − 30 = 81, then 81 − 9 = 72.
   4. Jack has 72 marbles left.

   Answer: 72