Grade: Grade 2 Subject: SAT/ACT Skills Unit: Word Problems with Diagrams Lesson: 5 of 6 SAT: ProblemSolving+DataAnalysis ACT: Math

Review Mistakes

Learn

Everyone makes mistakes! The best learners look at their mistakes and figure out what went wrong. This helps you avoid making the same mistake again.

Why Review Mistakes?

  • Mistakes show us what we need to learn
  • Understanding errors makes us smarter
  • Reviewing helps us remember the right way
  • Top test-takers always review their work

Common Mistake Types

Mistake Type 1: Miscount

What happens: You count too fast and skip items or count some twice.

How to fix: Touch or point to each item. Cross off items as you count. Count twice to check.

Mistake Type 2: Wrong Operation

What happens: You add when you should subtract, or subtract when you should add.

How to fix: Look for clue words. "How many in all?" = add. "How many left?" = subtract. "How many more?" = subtract.

Mistake Type 3: Didn't Read Carefully

What happens: You miss an important word or number in the problem.

How to fix: Read the problem twice. Underline the question. Circle important numbers.

Mistake Type 4: Ignored the Diagram

What happens: The diagram has helpful information you didn't use.

How to fix: Always look at the diagram first. Ask "What does this picture tell me?"

Mistake Type 5: Answered the Wrong Question

What happens: You solved the problem but answered something different than what was asked.

How to fix: Re-read the question after solving. Does your answer match what was asked?

Examples of Mistakes

Let's look at some problems where students made mistakes. Can you spot the error?

Example 1: The Miscount

Problem: Count the dots.

  . . . . .
  . . . .
  . . . . . .
            

Student's answer: 14 dots

What went wrong? The student counted 5 + 4 + 5 = 14, but the bottom row has 6 dots, not 5.

Correct answer: 5 + 4 + 6 = 15 dots

Lesson: Count each row carefully. Point to each dot as you count.

Example 2: Wrong Operation

Problem: Mia has 12 stickers. She gives 5 to her friend. How many does she have left?

Student's answer: 17 stickers (added 12 + 5)

What went wrong? The student added instead of subtracting. "How many left?" means something was taken away.

Correct answer: 12 - 5 = 7 stickers

Lesson: Look for clue words. "Gives away" and "how many left" mean subtract.

Example 3: Didn't Read Carefully

Problem: There are 8 red apples and 6 green apples in a basket. How many red apples are there?

Student's answer: 14 apples (added 8 + 6)

What went wrong? The student added all the apples, but the question only asked about red apples.

Correct answer: 8 red apples (it was given in the problem!)

Lesson: Read the question carefully. Sometimes the answer is already in the problem.

Example 4: Ignored the Diagram

Problem: Look at the picture graph. How many students chose pizza?

Favorite Lunch:
Pizza:    [X][X][X][X][X][X]
Sandwich: [X][X][X][X]
Salad:    [X][X]
            

Student's answer: 12 students (added all rows)

What went wrong? The student counted all the students instead of just the pizza row.

Correct answer: 6 students chose pizza

Lesson: Find the right row or column in the graph. Only count what the question asks about.

Practice

For each problem, a student made a mistake. Find the error and solve it correctly.

Problem 1

Count the stars:

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

Student's answer: 11 stars

What mistake did the student make? _____________

Correct answer: _____________

Problem 2

Jack had 15 marbles. He found 4 more. How many does he have now?

Student's answer: 11 marbles

What mistake did the student make? _____________

Correct answer: _____________

Problem 3

The graph shows favorite colors:

Blue:   [X][X][X][X][X]
Red:    [X][X][X]
Green:  [X][X][X][X]
Yellow: [X][X]
            

How many more students chose blue than red?

Student's answer: 5 students

What mistake did the student make? _____________

Correct answer: _____________

Problem 4

There are 9 birds on a wire. 3 fly away. Then 2 more birds land on the wire. How many birds are on the wire now?

Student's answer: 4 birds

What mistake did the student make? _____________

Correct answer: _____________

Problem 5

Emma has 7 dolls. Her sister has 5 dolls. How many dolls do they have together?

Student's answer: 2 dolls

What mistake did the student make? _____________

Correct answer: _____________

Problem 6

Look at the shapes:

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

How many squares are there?

Student's answer: 8 shapes

What mistake did the student make? _____________

Correct answer: _____________

Problem 7

A box has 20 crayons. Tom takes out 8 crayons to draw. How many crayons are still in the box?

Student's answer: 28 crayons

What mistake did the student make? _____________

Correct answer: _____________

Problem 8

The picture graph shows books read:

Amy:  [book][book][book][book]
Ben:  [book][book][book][book][book][book]
Cara: [book][book][book]
            

Who read the fewest books? How many?

Student's answer: Ben read 6 books

What mistake did the student make? _____________

Correct answer: _____________

Problem 9

There are 14 students in line. 6 students are boys. How many are girls?

Student's answer: 6 girls (said it's the same as boys)

What mistake did the student make? _____________

Correct answer: _____________

Problem 10

Sam has 11 grapes. He eats some. Now he has 4 grapes. How many did he eat?

Student's answer: 4 grapes

What mistake did the student make? _____________

Correct answer: _____________

Check Your Understanding

Answer Key

  1. Student miscounted. Correct: 4 + 5 + 3 = 12 stars
  2. Student subtracted instead of adding ("found more" = add). Correct: 15 + 4 = 19 marbles
  3. Student just counted blue (5) instead of finding the difference. Correct: 5 - 3 = 2 more students
  4. Student forgot to add the 2 birds that landed. Correct: 9 - 3 + 2 = 8 birds
  5. Student subtracted instead of adding ("together" = add). Correct: 7 + 5 = 12 dolls
  6. Student counted all shapes instead of just squares. Correct: 4 squares
  7. Student added instead of subtracting ("takes out" = subtract). Correct: 20 - 8 = 12 crayons
  8. Student answered who read most, not fewest. Correct: Cara read 3 books (fewest)
  9. Student guessed instead of calculating. Correct: 14 - 6 = 8 girls
  10. Student wrote what was left, not what was eaten. Correct: 11 - 4 = 7 grapes eaten

Self-Reflection

1. Which mistake type do YOU make most often?

2. What will you do to avoid that mistake?

3. Why is it helpful to check your work?

Next Steps

  • Keep a "mistake journal" - write down errors you make and how to fix them
  • Before turning in work, always check for the 5 common mistakes
  • Move on to the Mixed Set for final practice