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Math, Grade 6, Unit 0, Lesson 6
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Gallery Overview Allow students who have a clear understanding of the content ...

Gallery Overview

Allow students who have a clear understanding of the content thus far in the unit to work on Gallery problems of their choosing. You can then use this time to provide additional help to students who need review of the unit's concepts or to assist students who may have fallen behind on work.

Gallery Description

Represent a Math Problem: Students explore the number line tool and the double number line tool. They use the number line tool to solve a problem about the weights of a cheetah and a fisher cat.
Research Expressions: Students learn the difference between numerical expressions and variable expressions. They watch video tutorials, review worked examples, use the Glossary, and explore other resources.
Fish Tank: Students create diagrams and use text and images as they solve a problem about the size of a fish tank.

Subject:
Numbers and Operations
Provider:
Pearson
Math, Grade 7, Unit 0
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Getting Started Type of Unit: Introduction Prior Knowledge Students should be able ...

Getting Started

Type of Unit: Introduction

Prior Knowledge

Students should be able to:

Understand ratio concepts and use ratios.
Use ratio and rate reasoning to solve real-world problems.
Identify and use the multiplication property of equality.

Lesson Flow

This unit introduces students to the routines that build a successful classroom math community, and it introduces the basic features of the digital course that students will use throughout the year.

An introductory card sort activity matches students with their partner for the week. Then over the course of the week, students learn about the routines of Opening, Work Time, Ways of Thinking, Apply the Learning (some lessons), Summary of the Math, Reflection, and Exercises. Students learn how to present their work to the class, the importance of students’ taking responsibility for their own learning, and how to effectively participate in the classroom math community.

Students then work on Gallery problems, to further explore the resources and tools and to learn how to organize their work.

The mathematical work of the unit focuses on ratios and rates, including card sort activities in which students identify equivalent ratios and match different representations of an equivalent ratio. Students use the multiplication property of equality to justify solutions to real-world ratio problems.

Subject:
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Material Type:
Unit of Study
Provider:
Pearson
Math, Grade 7, Unit 0, Lesson 2
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Students discuss classroom routines and expectations, work with partners to present their ...

Students discuss classroom routines and expectations, work with partners to present their work matching different representations of a ratio situation, and then prepare math summaries.

Introduce classroom routines and expectations prior to the full mathematics lesson. Ask students to discuss how to clearly present their work to their classmates. Model an example of partner work, and then have students work with their partners to match different representations of a ratio situation. Read and discuss a Summary of the Math, and then have students write Reflections about their wonderings.

Key Concepts

Students match a data card with its corresponding ratio, decimal, fraction, percent, and description of the relationship in words. Students construct viable arguments for their matches and critique the reasoning of their partner and other classmates.

Goals and Learning Objectives

Describe the classroom routines and expectations
Consider how to present work clearly to classmates
Collaborate with a partner
Critique a partner’s reasoning
Connect different representations of a ratio situation

Subject:
Ratios and Proportions
Provider:
Pearson
Math, Grade 6, Unit 0, Lesson 2
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Students are introduced to classroom routines and expectations, and complete a full ...

Students are introduced to classroom routines and expectations, and complete a full mathematics lesson. The class discusses how to clearly present work to classmates. Partner work is modeled, and partners then work to match numerical expressions to corresponding word descriptions. Students read and discuss a summary of the math in the lesson, and then write a reflection about their thoughts.

Key Concepts

Students match a numerical expression to its corresponding description in words. Students interpret parentheses and brackets in numerical expressions and they construct viable arguments and critique the reasoning of others. Students learn to use the exponent 2 to represent squaring.

Goals and Learning Objectives

Describe the classroom routines and expectations
Consider how to present work clearly to classmates
Collaborate with a partner
Critique a partner’s reasoning
Connect a numerical expression to its corresponding word description
Learn to use an exponent of 2 to represent squaring

Subject:
Algebra
Provider:
Pearson
Math, Grade 6, Unit 0, Lesson 4
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Students discuss as a class the important ways that listeners contribute to ...

Students discuss as a class the important ways that listeners contribute to mathematical discussions during Ways of Thinking presentations. Students then use the properties of operations to find the value of each fruit used in equations.

Key Concepts

Students use the properties of operations to find the value of each fruit used in different equations. By considering several equations, students can match each of the 10 fruits to the whole numbers 0 through 9. This work helps students see why representing unknown numbers with letters is useful.

Goals and Learning Objectives

Contribute as listeners during the Ways of Thinking discussion
Identify the whole numbers that make an equation true
Use the properties of operations, when appropriate, to justify which whole numbers represent unknown values

Subject:
Algebra
Provider:
Pearson
Math, Grade 6, Unit 0
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Getting Started Type of Unit: Introduction Prior Knowledge Students should be able ...

Getting Started

Type of Unit: Introduction

Prior Knowledge

Students should be able to:

Solve and write numerical equations for whole number addition, subtraction, multiplication, and division problems.
Use parentheses to evaluate numerical expressions.
Identify and use the properties of operations.

Lesson Flow

In this unit, students are introduced to the rituals and routines that build a successful classroom math community and they are introduced to the basic features of the digital course that they will use throughout the year.

An introductory card sort activity matches students with their partner for the week. Then over the course of the week, students learn about the lesson routines: Opening, Work Time, Ways of Thinking, Apply the Learning, Summary of the Math, and Reflection. Students learn how to present their work to the class, the importance of taking responsibility for their own learning, and how to effectively participate in the classroom math community.

Students then work on Gallery problems to further explore the program’s technology resources and tools and learn how to organize their work.

The mathematical work of the unit focuses on numerical expressions, including card sort activities in which students identify equivalent expressions and match an expression card to a word card that describes its meaning. Students use the properties of operations to identify equivalent expressions and to find unknown values in equations.

Subject:
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Material Type:
Unit of Study
Provider:
Pearson
Math, Grade 7, Unit 0, Lesson 6
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Allow students who have a clear understanding of the content thus far ...

Allow students who have a clear understanding of the content thus far in the unit to work on Gallery problems of their choosing. You can then use this time to provide additional help to students who need review of the unit's concepts or to assist students who may have fallen behind on work.

Gallery Overview

Represent a Math Problem

Explore ways to represent math problems—make an equation using a Double Number Line, a Ratio Table, and a Tape Diagram. Then solve a problem comparing the prices of different types of nails using one of the representations.

Research Ratios and Rates

Research how ratios and rates are related to proportional relationships. Watch the video tutorials and explore the other resources.

Louisiana Purchase

Solve a problem about the Louisiana Purchase.

Subject:
Mathematics
Provider:
Pearson
Math, Grade 6, Unit 0, Lesson 3
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The class reviews the properties of operations. The use of “ask myself” ...

The class reviews the properties of operations. The use of “ask myself” questions to make sense of problems and persevere is modeled. Students review things to do when they feel stuck on a problem. Finally, students use the properties of operations to evaluate expressions.

Content Standards

Key Concepts

Students use the properties of operations to justify whether two expressions are equivalent.

Goals and Learning Objectives

To start to work on a problem, make sense of the problem by using “ask myself” questions
Persevere in solving a problem even when feeling stuck
Use the properties of operations to evaluate expressions

Subject:
Algebra
Provider:
Pearson
Math, Grade 6, Unit 0, Lesson 5
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Students review the ways classroom habits and routines can strengthen their mathematical ...

Students review the ways classroom habits and routines can strengthen their mathematical character. Students learn what a Gallery is and how to choose a Gallery problem to work on. They then choose one of three Gallery problems that introduce the unit’s technology resources. The three Gallery problems combine working with expressions with the resources available with this unit.

Key Concepts

Understand that a Gallery gives students a choice of several problems. Understand what to consider when choosing a problem. Know how to work on a Gallery problem and how to present work on gallery problems.

Goals and Learning Objectives

Know how to choose a problem from a Gallery

Subject:
Mathematics
Provider:
Pearson
Math, Grade 7, Unit 0, Lesson 1
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Lesson Overview Students use ratio cards to find equivalencies and form partnerships ...

Lesson Overview

Students use ratio cards to find equivalencies and form partnerships for the week. As a class, students discuss and decide on classroom norms.

Give each student a ratio card. Instruct students to find a classmate whose card has a ratio that is equivalent to theirs. Classmates with equivalent ratios are now partners for the week. With the class, discuss and decide on classroom norms, or rules. Tell students how to access the application they will use this year.

Key Concepts

Students understand that ratio relationships are multiplicative. They use ratio tables to show ratio relationships.

Goals and Learning Objectives

Distinguish between ratio tables and tables that do no show equivalent ratios
Understand how ratio tables are used to solve ratio problems
Use the basic features of the application
Create and understand the classroom norms
Use mathematical reasoning to justify an answer

Subject:
Ratios and Proportions
Provider:
Pearson
Math, Grade 7, Unit 0, Lesson 4
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Discuss the important ways that listeners contribute to mathematical discussions during Ways ...

Discuss the important ways that listeners contribute to mathematical discussions during Ways of Thinking presentations. Then use ratio and rate reasoning to solve a problem about ingredients in a stew.

Key Concepts

Students find the unit rate of a ratio situation.

Goals and Learning Objectives

Contribute as listeners during the Ways of Thinking discussion
Understand the concept of a unit rate that is associated with a ratio
Use rate reasoning to solve real-world problems

Subject:
Ratios and Proportions
Provider:
Pearson
Math, Grade 7, Unit 0, Lesson 3
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Review the multiplication property of equality. Demonstrate the use of “ask myself” ...

Review the multiplication property of equality. Demonstrate the use of “ask myself” questions to understand a problem before solving it. Have students discuss the strategies that they can use when they feel stuck on a problem. Direct partners to solve a problem using a ratio table and equations, and then justify their solution in a presentation using the multiplication property of equality. Have each student write a Summary of the Mathematics in the lesson and work together to create a classroom summary.

Key Concepts

Students use the multiplication property of equality to justify their solution to a ratio problem.

Goals and Learning Objectives

Before starting to work on a problem, make sense of the problem by using “ask myself” questions
Persevere in solving a problem even when feeling stuck
Solve a ratio problem using two different strategies
Link arithmetic and algebraic methods to solving a ratio problem
Use the multiplication property of equality to solve ratio problems

Subject:
Ratios and Proportions
Provider:
Pearson
Math, Grade 7, Unit 0, Lesson 5
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Review the ways classroom habits and routines can strengthen students’ mathematical character. ...

Review the ways classroom habits and routines can strengthen students’ mathematical character. Explain what a Gallery is and how to choose a Gallery problem to solve. Direct students to choose one of three Gallery problems that introduce the unit’s technology resources. The three Gallery problems combine working with ratios and rates with the application resources available with this unit.

Key Concepts

Students understand that a Gallery gives them a choice of problems to solve. Students think about the features of the problems to use when choosing a problem. Students know how to work on a Gallery problem and present a solution.

Goals and Learning Objectives

Know how to choose a problem from a Gallery

Subject:
Ratios and Proportions
Provider:
Pearson
Math, Grade 6, Unit 0, Lesson 1
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Students participate in an icebreaker activity, finding a classmate whose card contains ...

Students participate in an icebreaker activity, finding a classmate whose card contains an expression equivalent to the expression on their own card. The resulting student pairs will be partners for this unit. Students spend time exploring the digital course. They learn new symbols for multiplication and detect possible errors in evaluating numeric expressions. The class discusses and decides upon norms for math class.

Key Concepts

Students evaluate numerical expressions and identify equivalent expressions. They explore why the order of operations affects calculation results and how to use parentheses to clearly describe the order of the operations.

Goals and Learning Objectives

Evaluate numerical expressions
Understand the reason for the order of operations and how to use parentheses in numerical expressions
Use the basic features of the application
Create and understand the classroom norms
Use mathematical reasoning to justify an answer

Preparation

Print out the Expression Icebreaker cards. Select the number of pairs of Partner 1 and Partner 2 cards needed for your class. Shuffle the cards before distributing to students.
Write on the board or chart paper: Find a classmate whose card has an expression that is equivalent to the expression on your card.
Choose a hand signal or phrase for common activities, such as putting technology away and focusing on the teacher.

Subject:
Algebra
Provider:
Pearson
Math, Grade 6, Unit 1, Lesson 1
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Students watch a video showing the highest and lowest locations on each ...

Students watch a video showing the highest and lowest locations on each of the continents. Then they create a diagram (a number line) for a book titled The World’s Highest and Lowest Locations . Students show four of the highest elevations and four of the lowest elevations in the world on their diagrams.

Key Concepts

A complete number line has both positive numbers (to the right of 0) and negative numbers (to the left of 0).
Negative numbers are written with a minus sign; for example, –12, which is pronounced “negative 12.”
Positive numbers can be written with a plus sign for emphasis, such as +12, but a number without a sign, such as 12, is always interpreted as positive.
Every number except 0 is either positive or negative. The number 0 is neither positive nor negative.

Goals and Learning Objectives

Create a number line to show elevations that are both above and below sea level.

Subject:
Numbers and Operations
Provider:
Pearson
Math, Grade 6, Unit 1, Lesson 2
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Students watch a lever swing from one number on a number line ...

Students watch a lever swing from one number on a number line to the opposite of the number. Students predict where the lever will stop each time based on its starting location.

Key Concepts

The opposite of a number is the same distance from 0 as the number itself, but on the other side of 0 on a number line.
In the diagram, m is the opposite of n, and n is the opposite of m. The distance from m to 0 is d, and the distance from n to 0 is d; this distance to 0 is the same for both n and m. The absolute value of a number is its distance from 0 on a number line.
Positive numbers are numbers that are greater than 0.
Negative numbers are numbers that are less than 0.
The opposite of a positive number is negative, and the opposite of a negative number is positive.
Since the opposite of 0 is 0 (which is neither positive nor negative), therefore –0=0. The number 0 is the only number which is its own opposite.
Whole numbers and the opposites of those numbers are all integers.
Rational numbers are numbers that can be expressed as ab, where a and b are integers and b≠0 .

Goals and Learning Objectives

Identify a number and its opposite
Locate the opposite of a number on a number line
Define the opposite of a number, negative numbers, rational numbers, and integers

Subject:
Numbers and Operations
Provider:
Pearson
Math, Grade 6, Unit 1, Lesson 11
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Students revise their work on the assessment task based on feedback from ...

Students revise their work on the assessment task based on feedback from the teacher and their peers.

Key Concepts

Concepts from previous lessons are integrated into this assessment task: the opposite of a number, integers, absolute value, and graphing points on the coordinate plane. Students apply their knowledge, review their work, and make revisions based on feedback from the teacher and their peers. This process creates a deeper understanding of the concepts.

Goal and Learning Objectives

Apply your knowledge of the opposite of a number, integers, absolute value, and graphing points on the coordinate plane to solve problems
Track and review your choice of strategy when problem solving

Subject:
Numbers and Operations
Provider:
Pearson
Math, Grade 6, Unit 4, Lesson 1
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Students explore what makes a math trick work by analyzing verbal math ...

Students explore what makes a math trick work by analyzing verbal math expressions that describe each step in the trick.

Key Concepts

Words can be used to describe mathematical operations.
In a math trick, a person starts with a number, follows mathematical directions given in words, and ends up with the original number.
Math tricks can be explained by examining the mathematical expressions that represent the verbal directions.

Goals and Learning Objectives

Explore verbal expressions.
Predict and test which sets of expressions will result in the original number.

Subject:
Mathematics
Provider:
Pearson
Math, Grade 7, Unit 1, Lesson 2
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Students use the Hot Air Balloon simulation to model integer addition. They ...

Students use the Hot Air Balloon simulation to model integer addition. They then move to modeling addition on horizontal number lines. They look for patterns in their work and their answers to understand general addition methods.

Key Concepts

To add two numbers on a number line, start at 0. Move to the first addend. Then, move in the positive direction (up or right) to add a positive integer or in the negative direction (down or left) to add a negative integer.

Here is −6+4 on a number line:

The rule for integer addition (which extends to addition of rational numbers) is easiest to state if it is broken into two cases:

If both addends have the same sign, add their absolute values and give the result the same sign as the addends. For example, to find −5+(−9), first find |−5|+|−9|=14. Because both addends are negative the result is negative. So, −5+(−9)=−14.
If the addends have different signs, subtract the lesser absolute value from the greater absolute value. Give the answer the same sign as the addend with the greater absolute value. For example, to find 5+(−9), find |−9|−|5|=9−5=4. Because −9 has the greater absolute value, the result is negative. So, 5+(−9)=−4.

Goals and Learning Objectives

Model integer addition on a number line
Learn general methods for adding integers

Subject:
Numbers and Operations
Provider:
Pearson
Math, Grade 7, Unit 1, Lesson 11
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Students solve division problems by changing them into multiplication problems. They then ...

Students solve division problems by changing them into multiplication problems. They then use the relationship between multiplication and division to determine the sign when dividing positive and negative numbers in general.

Key Concepts

The rules for determining the sign of a quotient are the same as those for a product: If the two numbers have the same sign, the quotient is positive; if they have different signs, the quotient is negative. This can be seen by rewriting a division problem as a multiplication of the inverse.

For example, consider the division problem −27÷9. Here are two ways to use multiplication to determine the sign of the quotient:

The quotient is the value of x in the multiplication problem 9⋅x=−27. Because 9 is positive, the value of x must be negative in order to get the negative product.
The division −27÷9 is equivalent to the multiplication −27⋅19. Because this is the product of a negative number and a positive number, the result must be negative.

Goals and Learning Objectives

Use the relationship between multiplication and division to solve division problems involving positive and negative numbers
Understand how to determine whether a quotient will be positive or negative

Subject:
Numbers and Operations
Provider:
Pearson