Two bars stacked to compare. The longer bar = the bigger number. Find the difference or add/subtract to find the other amount.
👉 When to use: "How many more?", "How many fewer?", "___ more than ___", "___ times as many"
A
10
B
10
Diff
0
Key:"6 more than ___" → +"8 fewer than ___" → −
🌟 The 5-Step Method
1
Read twice — underline what it's asking
2
Pick the model type (adding? comparing? equal groups?)
3
Draw bars with labels and "?" for unknowns
4
Choose operation — whole missing? add/multiply. Part missing? subtract/divide
5
Solve and check — does the answer make sense?
🧐 Common Oops Moments
Bars not proportional — if one number is 5 and another is 10, the bar for 5 should be about half as wide. Use graph paper or keep it rough-but-close.
Adding when you should subtract — the model actually fixes this! If you drew a "part" bar inside a "whole" bar, you can see it's a missing piece → subtraction.
Not labeling — always write the number ON the bar and put "?" where it's unknown. Labels = clarity.
Mixing up who has more — in comparison models, draw the person with MORE as the longer bar. Always.
📊 Grade-Level Guide
🌱 3rd Grade
Part-Whole with +/− up to 1,000
Simple comparison (more/less)
Equal groups ×/÷ with 1-digit numbers
One-step problems
🌿 4th Grade
All 3rd grade models with bigger numbers (10,000+)
2-step problems combining model types
Multiplicative comparison ("4 times as many")
2-digit × 2-digit with area models
Long division with remainders
Fractions on a bar model
✏️ Try These!
Read each problem, think which model fits, solve it, then check your answer.
1Charlotte has 24 stickers. She gives 9 to her friend. How many stickers does Charlotte have left?
🤔 Which model? Part-Part-Whole, Comparison, or Equal Parts?
Model: Part-Part-Whole. Whole = 24, Part 1 = 9, Part 2 = ? → 24 − 9 = ?
Answer: 24 − 9 = 15 stickers
2There are 45 books on a shelf. There are 12 more books on another shelf. How many books are on the second shelf?
🤔 Which model?
Model: Comparison. Shelf A = 45, Difference = 12 more → 45 + 12 = ?
Answer: 45 + 12 = 57 books
3Tom has 6 toy cars. Sam has 3 times as many as Tom. How many cars does Sam have?
🤔 Which model?
Model: Equal Parts (or Comparison with multiplication). 3 groups of 6 → 3 × 6 = ?
Answer: 6 × 3 = 18 cars
4A baker has 36 cookies. She puts them into 4 boxes equally. How many cookies in each box?
🤔 Which model?
Model: Equal Parts. Total = 36, # of groups = 4, per-group unknown → 36 ÷ 4 = ?
Answer: 36 ÷ 4 = 9 cookies each box
5Ella has 28 beads. Mia has 9 beads. How many more beads does Ella have than Mia?
🤔 Which model?
Model: Comparison. Ella = 28, Mia = 9, find difference → 28 − 9 = ?
Answer: 28 − 9 = 19 more beads
6Max read 15 pages on Monday and 27 pages on Tuesday. How many pages did he read in total?
🤔 Which model?
Model: Part-Part-Whole. Part 1 = 15, Part 2 = 27, whole unknown → 15 + 27 = ?
Answer: 15 + 27 = 42 pages
🗺️ Which Model To Pick?
"How many altogether?"
→
Part-Whole +
"How many left / remain?"
→
Part-Whole −
"How many more/less?"
→
Comparison −
"___ more than ___"
→
Comparison +
"___ fewer than ___"
→
Comparison −
"Shared equally"
→
Equal Parts ÷
"Times as many"
→
Equal Parts ×
"How many in each?"
→
Equal Parts ÷
"How many groups?"
→
Equal Parts ÷
"At first… then…"
→
Before-After
📐 Drawing Tips
Draw bars going across (left to right)
Make the bar size match the number size — rough is fine, just not wildly off
Write the number inside each bar section, put ? where it's unknown
For comparison, stack bars on top of each other — bigger bar on top or bottom, doesn't matter