Students begin module 2 by using visual models and an understanding of divisibility to find the greatest common factor and least common multiple of pairs of numbers. Then, students apply their previous understanding of multiplication and division to divide fractions by fractions. They model fraction division expressions with tape diagrams and double number lines, use common denominators to divide fractions by fractions, and then develop and apply the invert and multiply strategy. Students use standard algorithms to fluently add, subtract, and multiply decimals, and apply those skills in real-world applications. They extend their understanding of division from prior grades to use the standard division algorithm to divide multi-digit numbers and decimals.
Topic C introduces the invert and multiply strategy for dividing fractions. Students use tape diagrams to reason about why the strategy works. Then they apply the strategy to fluently divide fractions and mixed numbers. Students use fraction division to solve real-world problems and make multiplicative comparisons. At the end of the topic, students add, subtract, multiply, and divide fractions in a real-world task involving designing wood box race cars.
6.C.3: Solve real-world problems with positive fractions and decimals by using one or two operations.
6.C.4: Compute quotients of positive fractions and solve real-world problems involving division of fractions by fractions. Use a visual fraction model and/or equation to represent these calculations.
I can...
Use a tape diagram to divide a fraction by a fraction.
Relate division of a fraction by a fraction to an unknown factor problem.
Lesson at a Glance
In this lesson, students build upon fraction division strategies from the previous lesson by using tape diagrams and unknown factor equations to determine quotients. Students first use a sorting task to reason about division expressions and compare quotients. In pairs, students evaluate division expressions, analyze quotients, and look for patterns. Finally, students apply their understanding of fraction division to solve real-world problems.
I can...
Use the invert and multiply strategy to divide a fraction by a fraction.
Lesson at a Glance
In this lesson, students build a conceptual understanding of why the invert and multiply strategy for dividing fractions works. They base their understanding on both the unknown factor equation and the tape diagram. Through a Whiteboard Exchange, students work independently to divide fractions and mixed numbers by using the invert and multiply strategy. Students also examine fraction division work for common errors. This lesson introduces the term reciprocal.
I can...
Solve real-world problems by dividing fractions and mixed numbers.
Lesson at a Glance
In this lesson, students work in small groups to determine whether tiles with fractional lengths and widths can cover a tabletop without any tiles being cut. Students examine multiple contextual situations that use the same fractional numbers to determine which arithmetic operation could be used to solve each problem. Students draw diagrams to support their reasoning. In a small group activity, students solve real-world problems that require multiplying and dividing fractions and mixed numbers. Students apply their understanding of fraction division to make multiplicative comparisons about measurements of objects.
I can...
Add, subtract, multiply, and divide fractions and mixed numbers to solve real-world problems.
Lesson at a Glance
In this digital lesson, students watch a video introduction of wood box car racing. Students are asked to predict which characteristics of the wood box car affect its speed. In the interactive, students are then given options of how they want to build a race car. After each decision, students use operations with fractions to find the total weight of the car. Once students’ cars are complete, they find the speed of their car by using division of fractions. They then race their car against the cars of other students in their class. Finally, students look at the characteristics of the fastest cars in the class and compare them to their initial prediction. A video at the end reveals how to increase car speed.
Use the digital platform to prepare for and facilitate this lesson. Students will also interact with the lesson content and activities via the digital platform.
If student computers or devices are not available, use the alternate version of this lesson.