# Explore Fraction Patterns

Examples, solutions, and videos to help Grade 4 students learn how to find and use a pattern to calculate the sum of all fractional parts between 0 and 1. Share and critique peer strategies.

Topic H: Explore a Fraction Pattern

Common Core Standards: 4.OA.5

### NYS Common Core Grade 4, Module 5, Lesson 41

The following diagram shows shows the patterns for the sums of fractions. Scroll down the page for more examples and solutions.

Lesson 41 Concept Development
Problem 1: Explore patterns for sums of fractions.
Problem 2: Apply the pattern to find the sum of consecutive fractions with large denominators.

Lesson 41 Problem Set

1. Find the sums. Express each sum as a mixed number.
2. Describe a pattern you notice when adding the sums of fractions with even denominators as opposed to those with odd denominators.
3. How would the sums change if the addition started with the unit fraction rather than with 0?
4. Find the sums.
5. Compare your strategy for finding the sums in Problems 4(d), 4(e), and 4(f) with a partner.
6. Could you apply this strategy to find the sum of all the whole numbers from 0 to 100?

Lesson 41 Homework

1. Find the sums. Express each sum as a mixed number.
2. Describe a pattern you notice when adding the sums of fractions with even denominators as opposed to those with odd denominators.
3. How would the sums change if the addition started with the unit fraction rather than with 0?
4. Find the sums.
5. Could you apply this strategy to find the sum of all the whole numbers from 0 to 50? To 99?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.