🧪 Math Lab 🔢 Unit 1 ✕ Unit 2 ÷ Unit 3 📊 Bar Models

🧮 Bar Model Explorer

Turn word problems into pictures — see exactly what to do!

🔷 Model 1: Part-Part-Whole
Addition & Subtraction

Parts add up to make a Whole. If you know all the parts, add to find the whole. If you know the whole and one part, subtract to find the missing part.

👉 When to use: "How many altogether?", "How many are left?", "What's the total?"
Part 1
5
Part 2
3
⎩ ⎰ ⎱ ⎭
Whole
8
Either: Whole unknown → + add parts | Part unknown → subtract from whole
🟩 Model 2: Equal Parts (× & ÷)
Multiplication & Division

A whole split into equal-sized groups. If you know groups × size, multiply. If you know the total and either the groups or size, divide.

👉 When to use: "How many in each?", "Shared equally", "___ times as many", "How many altogether?" (with identical groups)
Each
4
× 3 groups
4
4
4
⎩ ⎰ ⎱ ⎭
Total
12
Either: Total unknown → × multiply | Per-group unknown → ÷ divide
🟨 Model 3: Comparison
Comparing Amounts

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?
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?
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?
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?
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?
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?
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
  • For equal parts, draw all parts the same width
  • Draw a big bracket { } around the whole