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.
In topic D, students fluently add, subtract, and multiply multi-digit decimals. First, students use number sense and place value reasoning to add and subtract decimals and determine the placement of the decimal point in sums and differences. Then students reason about the products of decimal factors and use the standard multiplication algorithm to efficiently multiply decimals. At the end of the topic, students apply these skills in a real-world task by calculating costs and revenue of a building project and adjusting their building model to try to increase profit.
6.C.2: Compute with positive fractions and positive decimals fluently using a standard algorithmic approach.
6.C.3: Solve real-world problems with positive fractions and decimals by using one or two operations.
I can...
Add and subtract decimals by using the standard algorithms for each operation.
Lesson at a Glance
In this lesson, students build fluency in adding and subtracting multi-digit decimals. Students estimate sums and differences to predict or confirm the reasonableness of their answers. After solving a puzzle that has them insert decimal points in addends, students work in pairs to create their own puzzles. They then switch puzzles with their classmates to practice inserting decimals in addends. Students analyze and discuss two strategies for subtracting decimals and compare subtraction of decimal fractions with subtraction of decimals. Through discussion, students realize the importance of place value when adding and subtracting decimals. This lesson introduces the term compute.
I can...
Recognize and apply patterns in factors when multiplying whole numbers and decimals.
Lesson at a Glance
In this digital lesson, students use several interactives to recognize the relationship between factors and products in multiplication expressions with decimals. By creating different rectangles with a fixed area or a fixed width, students discover patterns in the relationship between the measurements for length and area. Then students use a place value chart to multiply decimals that extend beyond the hundredths place. Students observe patterns in the place value of factors and products and create strategies to help them multiply decimals efficiently.
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.
I can...
Multiply decimals by using the standard algorithm.
Lesson at a Glance
In this lesson, students study a piece of art made of pennies and determine what information they need and what operations they could use to answer a series of questions about the portrait. In a Whiteboard Exchange, students estimate products and use their estimates to determine where to insert decimal points in products. While working in small groups, students recognize the importance of precision and place value when they use the standard algorithm to multiply decimals. Students apply these skills to multiply decimals in real-world contexts.
I can...
Create a model of a building and use decimal operations to calculate cost, revenue, and profit or loss.
Lesson at a Glance
In this lesson, students practice and gain fluency with decimal operations as they complete an open-ended, real-world task. Following building guidelines inspired by the architectural landmark Habitat 67, students work in groups to build structures out of cubes to model their own habitats. Students use given rates to calculate total cost and total revenue and determine whether their habitat resulted in a profit or a loss. Then they adjust their models to increase the profits of their habitats.