Gse Grade 6 Mathematics Unit 4 Answers

Turn content from Match Fishtank lessons into custom handouts for students in just a few clicks. Download Sample. The essential concepts students need to demonstrate or understand to achieve the lesson objective. Estimate the difference of a mixed number and a fraction, determining whether that estimate will be greater than or less than the actual difference.

Subtract a fraction from a mixed number using a variety of strategies, such as: Converting the mixed numbers to a fraction greater than one and subtracting like units, Subtracting the fraction from the fractional part of the mixed number, regrouping a whole if necessary, or Using simplifying strategies, such as going down over a whole or counting up over a whole.

Assess the reasonableness of answers based on estimates MP. You should modify it by having students subtract a fraction from a mixed number and not a mixed number from a mixed number.

You may also modify it by giving students more denominators to choose from in 1 of the directions e. Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding.

What do you wonder? What did you notice in 1? What does that make you think about the units in fraction subtraction? What did you get as your solution to 1c? How would you write the whole equation using fraction notation? The purpose of this task is to remind students that when we subtract, we subtract like units, which in the case of mixed number and fraction subtraction means subtracting the fractional parts of both numbers. Bseeing that just as you subtract like units of whole numbers, you can subtract like units of fractions MP.

Accessed Dec. Before computing, what do you estimate the difference to be? Do you expect the actual difference to be greater than or less than the estimated difference? How can we use what we learned in Anchor Task 1 to find the difference? How can we model this subtraction on the number line? Can I solve by converting the mixed number to a fraction greater than 1 and then subtracting the fraction?

What would I get as my difference? Is that difference equivalent to the difference we got when we solved using our first strategy? Which strategy do you prefer? Can we rewrite any of our solutions using larger units? Based on our estimate, is the computed difference reasonable? Why or why not? You should discuss both strategies of solving, converting the mixed number to a fraction greater than 1 and subtracting that way, as well as leaving the mixed number as a mixed number and subtracting like fractional units.

While you want to encourage students to use the most efficient strategy, students should understand why both are valid strategies MP.Looking for video lessons that will help you in your Common Core Grade 6 math classwork or homework? Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page. The Lesson Plans and Worksheets are divided into six modules. You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. Mid-Module Assessment Topics A through B assessment 1 day, return 1 day, remediation or further applications 2 days.

End-of-Module Assessment Topics A through C assessment 1 day, return 1 day, remediation or further applications 2 days. End-Module Assessment Topics A through C assessment 1 day, return 1 day, remediation or further applications 2 days. End-Module Assessment Topics C through E assessment 1 day, return 1 day, remediation or further applications 2 days. End-Module Assessment Topics A through D assessment 1 day, return 1 day, remediation or further applications 2 days.In Module 4, Expressions and Equations, students extend their arithmetic work to include using letters to represent numbers in order to understand that letters are simply "stand-ins" for numbers and that arithmetic is carried out exactly as it is with numbers.

Students explore operations in terms of verbal expressions and determine that arithmetic properties hold true with expressions because nothing has changed—they are still doing arithmetic with numbers. Students determine that letters are used to represent specific but unknown numbers and are used to make statements or identities that are true for all numbers or a range of numbers. They understand the relationships of operations and use them to generate equivalent expressions, ultimately extending arithmetic properties from manipulating numbers to manipulating expressions.

Students read, write and evaluate expressions in order to develop and evaluate formulas. From there, they move to the study of true and false number sentences, where students conclude that solving an equation is the process of determining the number s that, when substituted for the variable, result in a true sentence. They conclude the module using arithmetic properties, identities, bar models, and finally algebra to solve one-step, two-step, and multi-step equations.

Resources may contain links to sites external to the EngageNY. Skip to main content. Find More Curriculum Print. Grade 6 Mathematics. Grade 6 Mathematics Module 4. Grade 6 Module 4: Expressions and Equations In Module 4, Expressions and Equations, students extend their arithmetic work to include using letters to represent numbers in order to understand that letters are simply "stand-ins" for numbers and that arithmetic is carried out exactly as it is with numbers.

Like Grade 6 Mathematics Module 4: Teacher Materials Related Resources Resource Document. Curriculum Map Toggle Module 1 Module 1.

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Lesson 1. Lesson 2. Lesson 3. Lesson 4. Lesson 5. Lesson 6. Lesson 7. Lesson 8. Lesson 9.

gse grade 6 mathematics unit 4 answers

Lesson Toggle Module 2 Module 2. Toggle Module 3 Module 3. Toggle Module 5 Module 5.

6 4 7 Illustrative Mathematics Grade 6 Unit 4 Lesson 7 Morgan

Lesson 19a. Toggle Module 6 Module 6. View PDF.Played times. Print Share Edit Delete.

Grade 6 Mathematics

Live Game Live. Finish Editing. This quiz is incomplete! To play this quiz, please finish editing it. Delete Quiz. Question 1. Find the midpoint of 8,-4 and 6, Distance between -3, -2 and -5, 0. If E is between D and F. Find XZ. The term non collinear refers to:. Lines not in the same plane. Points on the same line. Rays that have different endpoints. Points that do not lay on the same line. Part of a line with two endpoints. The picture represents a compass and straightedge construction of? What is a ray?

Part of a line with 2 endpoints. Part of a line with 1 end point and goes on forever. Part of a line with 0 endpoints. Part of a line with 5 endpoints. What is a plane? What is a line? What is a point? Quizzes you may like. Basics of Geometry. Segment and Angle Addition Postulate. Basic Geometry Vocabulary. Lines and Angles.Students start to operate on fractions, learning how to add fractions with like denominators and multiply a whole number by any fraction.

In this unit, students begin their work with operating with fractions by understanding them as a sum of unit fractions or a product of a whole number and a unit fraction. Students will then add fractions with like denominators and multiply a whole number by any fraction. Students will apply this knowledge to word problems and line plots. In Grade 3, students developed their understanding of the meaning of fractions, especially using the number line to make sense of fractions as numbers themselves.

They also did some rudimentary work with equivalent fractions and comparison of fractions. Thus, in this unit, armed with a deep understanding of fractions and their value, students start to operate on them for the first time.

The unit is structured so that students build their understanding of fraction operations gradually, first working with the simplest case where the total is a fraction less than 1, then the case where the total is a fraction between 1 and 2 to understand regrouping when operating in simple casesand finally the case where the total is a fraction greater than 2.

gse grade 6 mathematics unit 4 answers

With each of these numerical cases, they first develop an understanding of non-unit fractions as sums and multiples of unit fractions. Next, they learn to add and subtract fractions. And finally, they apply these understandings to complex cases, such as word problems or fraction addition involving fractions where one denominator is a divisor of the other, which helps prepare students for similar work with decimal fractions in Unit 7.

After working with all three numerical cases in the context of fraction addition and subtraction, they work with fraction multiplication, learning strategies for multiplying a whole number by a fraction and a mixed number and using those skills in the context of word problems. Students will solve problems by using information presented in line plots, requiring them to use their recently acquired skills of fraction addition, subtraction, and even multiplication, creating a contextual way for this supporting cluster content to support the major work of the grade.

The unit provides lots of opportunity for students to reason abstractly and quantitatively MP. Then, in Grade 5, students extend their understanding and ability with operations with fractions 5.

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Students then develop a comprehensive understanding of and ability to compute fraction division problems in all cases in Grade 6 6. Beyond these next few units and years, it is easy to find the application of this learning in nearly any mathematical subject in middle school and high school, from ratios and proportions in the middle grades to functional understanding in algebra.

This assessment accompanies Unit 6 and should be given on the suggested assessment day or after completing the unit. Additional assessment tools to help you monitor student learning and identify any skill or knowledge gaps. Download Sample. The central mathematical concepts that students will come to understand in this unit.

gse grade 6 mathematics unit 4 answers

Quantities cannot be added or subtracted if they do not have like units. This explains why one must find a common denominator to be able to add fractions with unlike denominators when adding and subtracting fractions. Further, when you add or subtract quantities with like units, their units do not change. Just like one adds 5 bananas and 2 bananas and gets 7 bananas, one adds 5 eighths and 2 eighths and gets 7 eighths.

Additional vocabulary tools that help reinforce and support student vocabulary development. The materials, representations, and tools teachers and students will need for this unit. Area model Buttons with various diameters Fraction strips made from paper, or the plastic kind Line plot Number line Rulers Tape diagram.

Decompose fractions as a sum of unit fractions and as a sum of smaller fractions. Decompose non-unit fractions and represent them as a whole number times a unit fraction.

Solve word problems that involve the addition and subtraction of fractions where the total is less than or equal to one. Decompose non-unit fractions less than or equal to 2 as a sum of unit fractions, as a sum of non-unit fractions, and as a whole number times a unit fraction.

Add and subtract fractions that require regrouping where the total is less than or equal to two. Add two fractions where one denominator is a divisor of the other using the denominators 2, 3, 4, 5, 6, 8, 10, and Decompose and compose non-unit fractions greater than two as a sum of unit fractions, as a sum of non-unit fractions, and as a whole number times a unit fraction.

Solve word problems involving addition, subtraction, and multiplication of fractions.Identifying Tranformations b. Identifying Lines of Symmetry c. Identifying Rotational Symmetry d. Identifying Congruent vs Similar Triangles b. Reflecting Geometric Figures on a Coordinate system b.

Translating Geometric Figures on a Coordinate system c. Rotating Geometric Figures on a Coordinate system d. Finding Scale Factors of Similar Triangles b. Finding the Missing Angle in a Triangle d.

Common Core Grade 6 Math (Worksheets, Homework, Lesson Plans)

Classifying Triangles e. Identifying Perfect Squares b. Calculating Square Roots of Squares c. Approximating Square Roots d. Fixing Square and Cube Roots e. Multiplying with Scientific Notation b. Dividing with Scientific Notation c. Solving Equations by Adding b. Solving Equations by Subtracting c. Solving Equations by Multiplying d. Solving Equations by Dividing e.

Representing Solutions with Set Notation f. Solving 2 Step Equations g. Solving Equations with Variables on Both Sides h. Solving Equations with the Distributive Law i.

Classifying Numbers in Subsets of the Real Numbers b. Comparing Subsets of the Real Numbers c. Converting Fractions to Terminating Decimals d.

Converting Terminating Decimals to Fractions e.

gse grade 6 mathematics unit 4 answers

Converting Fractions to Repeating Decimals f. Converting Repeating Decimals to Fractions g. Illustrating the Density of Rational Numbers b.

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Graphing Rational Numbers on a Number Line c. Finding Volumes of Prisms b. Finding Volumes of Cylinders c. Finding Volumes of Pyramids d. Finding Volumes of Cones e.An artist makes necklaces. Work with your group to find the best plan for shipping the boxes of necklaces. Each member of your group should select a different type of flat-rate shipping box and answer the following questions. Which of the flat-rate boxes should she use to minimize her shipping cost? Read the problem statement.

Discuss this information with your group. Make a plan for using this information to find the most inexpensive way to ship the jewelry boxes. Once you have agreed on a plan, write down the main steps. For each type of flat-rate shipping box: Find how many jewelry boxes can fit into the box. Draw a sketch to show your thinking, if needed. Calculate the total cost of shipping all jewelry boxes in shipping boxes of that type. Show your reasoning and organize your work so it can be followed by others.

Share and discuss your work with the other members of your group. Your teacher will display questions to guide your discussion. Note the feedback from your group so you can use it to revise your work. Using the feedback from your group, revise your work to improve its correctness, clarity, and accuracy. Correct any errors. You may also want to add notes or diagrams, or remove unnecessary information.

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Which shipping boxes should the artist use? As a group, decide which boxes you recommend for shipping jewelry boxes. Be prepared to share your reasoning. Lesson 16 Back to top.