Grade: Grade 5 Subject: Mathematics Unit: Data & Patterns SAT: ProblemSolving+DataAnalysis ACT: Math

Guided Practice

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Building Your Skills Step by Step

This lesson provides guided practice to help you master data and patterns. Each problem includes step-by-step hints you can reveal when needed.

Work through each problem carefully. Click on the steps to reveal guidance when you need help!

Practice Strategy: Try to solve each problem on your own first. Only reveal the steps if you get stuck. This builds stronger problem-solving skills!

Guided Problems

1 Reading a Data Table

The table shows the number of books students read during summer vacation:

Student Books Read
Maya12
James8
Sofia15
Liam10
Emma11

Question: What is the total number of books read by all students?

1 Identify all the values to add ▶
Look at the "Books Read" column. The values are: 12, 8, 15, 10, and 11.
2 Add the numbers strategically ▶
Group numbers that add to 10 or are easy to add:
10 + 15 = 25
12 + 8 = 20
25 + 20 = 45
45 + 11 = 56
3 State the answer ▶
The total number of books read by all students is 56 books.

Your Turn:

What is the mean (average) number of books read per student?

2 Finding a Pattern Rule

Find the rule and the next two terms in this pattern:

7 → 12 → 17 → 22 → ? → ?
1 Find the difference between consecutive terms ▶
12 - 7 = 5
17 - 12 = 5
22 - 17 = 5
The difference is always 5!
2 Write the rule ▶
Rule: Start at 7, add 5 each time.
3 Apply the rule to find the next terms ▶
22 + 5 = 27
27 + 5 = 32

Your Turn:

What is the 10th term in this pattern?

3 Interpreting Graph Data

This bar graph shows the favorite sports of 5th graders:

24
Soccer
16
Basketball
12
Baseball
20
Swimming
8
Tennis

Question: How many more students chose soccer than tennis?

1 Find the value for soccer ▶
Looking at the bar graph, soccer has 24 students.
2 Find the value for tennis ▶
Looking at the bar graph, tennis has 8 students.
3 Calculate the difference ▶
24 - 8 = 16 more students chose soccer than tennis.

Your Turn:

What is the total number of students surveyed?

4 Multiplication Patterns

Find the rule and the next term:

3 → 6 → 12 → 24 → ?
1 Check if it's an addition pattern ▶
6 - 3 = 3
12 - 6 = 6
24 - 12 = 12
The differences are NOT constant, so it's not addition!
2 Check if it's a multiplication pattern ▶
6 / 3 = 2
12 / 6 = 2
24 / 12 = 2
Each term is multiplied by 2!
3 Apply the rule ▶
24 x 2 = 48

Your Turn:

What is the 7th term in this pattern?

Practice Problems

Problem 1

A pattern starts at 100 and subtracts 8 each time. What is the 6th term?

Problem 2

In a data set: 15, 22, 18, 25, 20. What is the range (highest - lowest)?

Problem 3

What comes next: 5, 15, 45, 135, ?

Problem 4

A graph shows sales of: Mon-$40, Tue-$55, Wed-$35, Thu-$60, Fri-$50. What is the mean daily sales?

Problem 5

In the pattern 2, 5, 11, 23, 47, ?, the rule involves both doubling and adding. What is the next term?

Problem 6

A line graph shows temperature rising from 50F to 80F over 6 hours. What is the average change per hour?

Problem 7

Which data set has the greatest range?

Problem 8

The pattern 1, 1, 2, 3, 5, 8, 13, ? is called the Fibonacci sequence. What comes next?

Summary

📊

Read Data Carefully

Look at labels, titles, and values before answering questions.

🔍

Find Differences First

Check if consecutive differences are constant for addition patterns.

x2

Check for Multiplication

If differences vary, divide consecutive terms to find the multiplier.

📐

Use Formulas

Apply formulas to find any term without counting through the whole sequence.

Keep Practicing! The more problems you solve, the faster you'll recognize patterns and interpret data. Try creating your own problems to challenge friends and family!

Next Steps

  • Continue to the Word Problems lesson to apply these skills in real-world contexts
  • Review any problems you found challenging
  • Create your own data tables and patterns to share with classmates
  • Look for patterns in everyday life - sports scores, weather data, prices