Word Problem Schemas Anchor Chart
Part 1 Additive Word Problem Schemas
Tape Diagram Schema Guide
Visual bar models to identify structure, select operations, and solve addition & subtraction problems.
Add & Subtract
1
Combine Schema (Part-Part-Whole)
Static Sets • No Action
Problem: Maya has 7 blue marbles and 5 red marbles. How many marbles does Maya have in all?
Think: Are two distinct groups being joined into one total without any time passage or change?
Part + Part = Total | 7 + 5 = [ ? ]
Tape Diagram (Total Unknown)
Total = ?
Part 1 7 (Blue)
Part 2 5 (Red)
Known: Part A & Part B Find: Whole
2
Change Schema (Join or Separate)
Dynamic • Action over Time
Problem: Leo had 14 toy cars. He gave some to his brother. Now Leo has 9 toy cars left. How many did he give away?
Think: Was there an initial quantity that increased (+) or decreased (−) through an event?
Start − Change = End | 14 − [ ? ] = 9
Tape Diagram (Change Unknown)
Start Amount: 14 cars
Result (Left) 9
Change ? (Gave Away)
Solve: 14 − 9 = 5
3
Compare Schema (More or Fewer)
Relational • Two Quantities
Problem: Nora read 16 books this month. Sam read 9 books. How many more books did Nora read than Sam?
Think: Are two distinct sets being measured against each other to find the difference or gap?
Larger − Smaller = Difference | 16 − 9 = [ ? ]
Tape Diagram (Two Comparison Bars)
Nora
Larger Quantity 16
Sam
9 (Smaller)
? (Diff)
Difference = Larger − Smaller
Schema Clue: Look at the relationship between quantities, not just isolated keywords like "more" or "less."
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Part 2 Multiplicative Word Problem Schemas
Tape Diagram Schema Guide
Visual bar models to identify structure, select operations, and solve multiplication & division problems.
Multiply & Divide
4
Equal Groups Schema
Repeated Sets • Equal Size
Problem: A bakery packs 6 cookies into each box. How many cookies are packed in 4 boxes?
Think: Do you have multiple groups containing the exact same number of items?
# Groups × Group Size = Total | 4 × 6 = [ ? ]
Tape Diagram (Total Unknown)
Total = ? cookies
Box 1 6
Box 2 6
Box 3 6
Box 4 6
4 groups (boxes) 6 items per group
5
Array & Area Schema
Rows × Columns • Dimension
Problem: Chairs in an auditorium are arranged in 5 rows with 8 chairs in each row. How many chairs are in the room?
Think: Are objects organized in an ordered grid or rectangular spatial dimension?
Rows × Items/Row = Total | 5 × 8 = [ ? ]
Area / 2D Tape Representation
5 rows
8 chairs per row
Total Area = ? 5 rows of 8 = 40 chairs
If Total is known: Total ÷ Rows = Columns (Chairs/Row)
6
Sharing & Partitioning Schema
Partitive Division • Fair Distribution
Problem: Carlos has 24 stickers to share equally among 3 friends. How many stickers does each friend receive?
Think: Is a known total being distributed evenly among a specific number of groups?
Total ÷ # of Groups = Group Size | 24 ÷ 3 = [ ? ]
Tape Diagram (Partition Unknown)
Total = 24 stickers
Friend 1 ?
Friend 2 ?
Friend 3 ?
Known: Total & 3 Equal Shares Each share = 8
Equation Checklist: Does my tape diagram show equal parts? Equal parts signal multiplication or division!
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