Grade: Grade 2 Subject: SAT/ACT Skills Unit: Word Problems with Diagrams Lesson: 3 of 6 SAT: ProblemSolving+DataAnalysis ACT: Math

Question Types

Learn

Word problems with diagrams come in different types. Learning to recognize each type helps you solve them faster!

Type 1: Counting Problems

These problems ask "How many?" Look at the picture and count carefully.

Example: Look at the picture of apples in a basket. How many apples are there?

Strategy: Count each apple one by one. Touch or point to each one as you count.

Type 2: Comparison Problems

These problems ask "How many more?" or "How many fewer?" You compare two groups.

Example: Sam has 8 stickers. Mia has 5 stickers. How many more stickers does Sam have?

Strategy: Draw both groups. Line them up. Count the extra ones.

Type 3: Part-Part-Whole Problems

These problems give you parts and ask for the whole, OR give you the whole and one part.

Example: There are 6 red cars and 4 blue cars. How many cars in all?

Strategy: Draw a box split into parts. Fill in what you know. Find what's missing.

Type 4: Picture Graph Problems

These problems use pictures arranged in rows or columns to show information.

Example: The graph shows favorite fruits. Each picture = 1 student. How many students like bananas?

Strategy: Find the right row or column. Count the pictures.

Examples

Example 1: Counting Problem

Problem: Look at the fish tank diagram. Count all the fish.

    🐟 🐟 🐟
  🐟 🐟 🐟 🐟
    🐟 🐟

Solution:

  1. Count the top row: 3 fish
  2. Count the middle row: 4 fish
  3. Count the bottom row: 2 fish
  4. Add them up: 3 + 4 + 2 = 9 fish

Answer: There are 9 fish in the tank.

Example 2: Comparison Problem

Problem: Emma has 7 buttons. Jake has 4 buttons. How many more buttons does Emma have?

Emma: O O O O O O O
Jake:  O O O O

Solution:

  1. Line up the buttons in the diagram
  2. Match Jake's buttons to Emma's: 4 match up
  3. Count Emma's extra buttons: 3 buttons
  4. Or subtract: 7 - 4 = 3

Answer: Emma has 3 more buttons than Jake.

Example 3: Part-Part-Whole Problem

Problem: There are 12 birds. Some are on the tree and 5 are flying. How many are on the tree?

+------------------+
|  Total: 12 birds |
+--------+---------+
| On tree|  Flying |
|   ?    |    5    |
+--------+---------+

Solution:

  1. The whole is 12 birds
  2. One part is 5 birds flying
  3. Find the other part: 12 - 5 = 7

Answer: 7 birds are on the tree.

Practice

Identify the question type first, then solve each problem.

Problem 1

Look at the stars below. How many stars are there?

  * * * * *
  * * * *
  * * *

Question Type: _____________

Answer: _____________

Problem 2

Lily picked 9 flowers. Rosa picked 6 flowers. How many more flowers did Lily pick?

Question Type: _____________

Answer: _____________

Problem 3

There are 15 books total. 8 books are on the shelf. The rest are on the table. How many books are on the table?

Question Type: _____________

Answer: _____________

Problem 4

The picture graph shows pets students have:

Dogs:    [pet][pet][pet][pet][pet][pet]
Cats:    [pet][pet][pet][pet]
Fish:    [pet][pet][pet][pet][pet]
Birds:   [pet][pet]

How many students have cats?

Question Type: _____________

Answer: _____________

Problem 5

Tom has 11 marbles. He gives some to his friend. Now he has 4 marbles. How many did he give away?

Question Type: _____________

Answer: _____________

Problem 6

Count the shapes in this pattern:

  [] [] []
  O  O  O  O
  [] [] [] []

How many squares (boxes) are there?

Question Type: _____________

Answer: _____________

Problem 7

Class 2A has 14 students. Class 2B has 11 students. How many fewer students does Class 2B have?

Question Type: _____________

Answer: _____________

Problem 8

Maya has 7 red crayons and 6 blue crayons. How many crayons does she have in all?

Question Type: _____________

Answer: _____________

Problem 9

Look at the picture graph of snacks eaten:

Monday:    [snack][snack][snack]
Tuesday:   [snack][snack][snack][snack][snack]
Wednesday: [snack][snack]
Thursday:  [snack][snack][snack][snack]

On which day were the most snacks eaten? How many?

Question Type: _____________

Answer: _____________

Problem 10

A bus has 20 seats. 13 people are sitting. How many seats are empty?

Question Type: _____________

Answer: _____________

Check Your Understanding

1. What is the first thing you should do when you see a word problem with a diagram?

A) Start adding numbers right away
B) Identify the question type
C) Draw your own picture
D) Skip to the next problem

2. "How many more" and "How many fewer" are clue words for which type of problem?

A) Counting problems
B) Comparison problems
C) Part-Part-Whole problems
D) Picture graph problems

3. In a part-part-whole problem, if you know the whole and one part, what do you do to find the other part?

Answer Key

Practice Problems:

  1. Counting Problem; 12 stars (5 + 4 + 3)
  2. Comparison Problem; 3 more flowers
  3. Part-Part-Whole Problem; 7 books
  4. Picture Graph Problem; 4 students
  5. Part-Part-Whole Problem; 7 marbles
  6. Counting Problem; 7 squares
  7. Comparison Problem; 3 fewer students
  8. Part-Part-Whole Problem; 13 crayons
  9. Picture Graph Problem; Tuesday, 5 snacks
  10. Part-Part-Whole Problem; 7 empty seats

Check Your Understanding:

  1. B) Identify the question type
  2. B) Comparison problems
  3. Subtract the part you know from the whole

Next Steps

  • Practice identifying question types before solving
  • Create your own diagram for each problem type
  • Move on to the Timed Drill lesson to build speed