Gse Grade 8 Mathematics Unit 4 Answer Key

In Module 4, students extend what they already know about unit rates and proportional relationships to linear equations and their graphs.

Math Word Problems with Answers - Grade 8

Students understand the connections between proportional relationships, lines, and linear equations in this module. Students learn to apply the skills they acquired in Grades 6 and 7, with respect to symbolic notation and properties of equality to transcribe and solve equations in one variable and then in two variables.

The copy ready materials are a collection of the module assessments, lesson exit tickets and fluency exercises from the teacher materials. Resources may contain links to sites external to the EngageNY. Skip to main content.

Find More Curriculum Print. Grade 8 Mathematics. Grade 8 Mathematics Module 4. Grade 8 Module 4: Linear Equations In Module 4, students extend what they already know about unit rates and proportional relationships to linear equations and their graphs.

gse grade 8 mathematics unit 4 answer key

The student materials consist of the student pages for each lesson in Module 4. Like Grade 8 Mathematics Module 4: Teacher Materials Compare two Curriculum Map Toggle Module 1 Module 1. Lesson 1. Lesson 2. Lesson 3. Lesson 4. Lesson 5.

gse grade 8 mathematics unit 4 answer key

Lesson 6. Lesson 7.

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Lesson 8. Lesson 9.Arrange students in groups of 2—4. Display the image of all four graphs for all to see. Expand Image. Graph A. One line crosses the x axis to the left of the origin and the y axis below the origin.

gse grade 8 mathematics unit 4 answer key

Another line crosses the y axis above the origin and the x axis to the right of the origin. The third line crosses the y axis above the origin and the x axis to the right of the origin. Graph B. Another line crosses the y axis above the origin. Graph C. Three lines that intersect at a single point. One line crosses the y axis above the origin. Another line crosses the x axis to the right of the origin and the y axis below the origin.

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The third line crosses the x axis to the right of the origin. Graph D. Three lines. There are 3 points of intersection between two lines each. Another line crosses the x axis to the left of the origin and the y axis above the origin. After students have conferred in groups, invite each group to share one reason why a particular graph might not belong. Record and display the responses for all to see.

After each response, ask the rest of the class if they agree or disagree. In previous lessons, students have set two expressions equal to one another to find a common value where both expressions are true if it exists.

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A system of two equations asks a similar question: at what common pair of values are both equations true? In this activity, students focus on a context involving coins and use multiple representations to think about the context in different ways. What might be in my pocket? Read the problem context together. Give 1—2 minutes for students to read and complete the first problem. Display the table for all to see and ask students for values to fill in the table.Write another number puzzle with at least three steps.

On a different piece of paper, write a solution to your puzzle. Trade puzzles with your partner and solve theirs. Make sure to show your thinking. With your partner, compare your solutions to each puzzle.

Did they solve them the same way you did? Be prepared to share with the class which solution strategy you like best. Reasoning and diagrams help us see what is going on and why the answer is what it is.

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But as number puzzles and story problems get more complex, those methods get harder, and equations get more and more helpful. We will use different kinds of diagrams to help us understand problems and strategies in future lessons, but we will also see the power of writing and solving equations to answer increasingly more complex mathematical problems. In a basketball game, Elena scores twice as many points as Tyler. If Mai scores 5 points, how many points did Elena score?

Explain your reasoning. What do you notice?

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What do you wonder? Solve each puzzle. Show your thinking. Organize it so it can be followed by others. The temperature was very cold. Then the temperature doubled. Then the temperature dropped by 10 degrees. Then the temperature increased by 40 degrees.

The temperature is now 16 degrees. What was the starting temperature? Lin ran twice as far as Diego. Diego ran m farther than Jada. Noah ran m. How far did Lin run? Why does this always work?

8.4 Linear Equations and Linear Systems

Back to top Lesson 2.Expand Image. The first hanger is level and has two pink socks, one on each end. The second hanger is lower on the left than the right and has two blue socks, one on each end. Elena takes two triangles off of the left side and three triangles off of the right side. Will the hanger still be in balance, or will it tip to one side? Which side? Explain how you know. Use the applet to see if your answer to question [1] was correct.

Can you find another way to make the hanger balance? If a triangle weighs 1 gram, how much does a square weigh? After you make a prediction, use the applet to see if you were right. Can you find another pair of values that makes the hanger balance? If we have equal weights on the ends of a hanger, then the hanger will be in balance. If there is more weight on one side than the other, the hanger will tilt to the heavier side.

First hanger is unbalanced.

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Left side, 3 triangles. Right side, 1 triangle. Left lower than right. Second hanger is balanced. Right side, 3 triangles.

Grade 8 Mathematics

Third hanger is unbalanced. Left side, 1 triangle.

8 4 11 Part 2 Illustrative Math Grade 8 Unit 4 Lesson 11 Morgan

We can think of a balanced hanger as a metaphor for an equation. An equation says that the expressions on each side have equal value, just like a balanced hanger has equal weights on each side. If we have a balanced hanger and add or remove the same amount of weight from each side, the result will still be in balance. Professional Learning Contact Us.Students rotate a copy of a right isosceles triangle four times to build a quadrilateral.

It turns out that the quadrilateral is a square. Students are not asked or expected to justify this but it can be addressed in the discussion. Expand Image. Ask students what they notice and wonder about the quadrilateral that they have built.

Likely responses include:. Ask the students how they know the four triangles fit together without gaps or overlaps to make a quadrilateral. Here the key point is that the triangle is isosceles, so the rotations match up these sides perfectly. The four right angles make a complete degrees, so the shape really is a quadrilateral. The fact that the quadrilateral is a square can be deduced from the fact that it is mapped to itself by a 90 degree rotation, but this does not need to be stressed or addressed.

They are experimenting with a particular line segment but the conclusions that they make, especially in the last problem, are for any line segment. Tell them that they will investigate this further in the next lesson.

gse grade 8 mathematics unit 4 answer key

Arrange students in groups of 2. Provide access to geometry toolkits. What is the image of A? Let 0 comma 0 be the bottom left corner of the grid. Here are two line segments. Is it possible to rotate one line segment to the other? If so, find the center of such a rotation. If not, explain why not. Students may be confused when rotating around the midpoint because they think the image cannot be the same segment as the original.

Assure students this can occur and highlight that point in the discussion. Invite groups to share their responses. Ask the class if they agree or disagree with each response. When there is a disagreement, have students discuss possible reasons for the differences. If any of the ideas above are not brought up by the students during the class discussion, be sure to make them known. Even if students are not using the digital version of the activity, you may want to display and demonstrate with the applet.

In this activity, students use rotations to build a pattern of triangles. In the previous lesson, students examined a right triangle and a rigid transformation of the triangle. In this activity, several rigid transformations of the triangle form an interesting pattern. This pattern will play an important role later when students use this shape to understand a proof of the Pythagorean Theorem.Grade 8 math word problems with answers are presented.

Also solutions and explanations are included. Answers to the Above Questions. Free Mathematics Tutorials. About the author Download E-mail. Privacy Policy. Search website. A car traveled miles in 4 hours 41 minutes. What was the average speed of the car in miles per hour? In a group of people, 90 have an age of more 30 years, and the others have an age of less than 20 years.

If a person is selected at random from this group, what is the probability the person's age is less than 20? The length of a rectangle is four times its width.

If the area is m2 what is the length of the rectangle? A six-sided die is rolled once. What is the probability that the number rolled is an even number greater than 2? Point A has the coordinates 2,2. What are the coordinates of its image point if it is translated 2 units up and 5 units to the left, and reflected in the x axis?

The length of a rectangle is increased to 2 times its original size and its width is increased to 3 times its original size. If the area of the new rectangle is equal to square meters, what is the area of the original rectangle? Each dimension of a cube has been increased to twice its original size.The purpose of this warm-up is for students to reason about two situations that can be represented with linear equations.

Students are asked to explain their reasoning. Poll the class on which situation they would choose. Record and display these ideas for all to see. If no one reasoned about babysitting for less than 5 hours and therefore chose the second option, mention this idea to students. Students may not use linear equations or graphs to decide which situation they would choose. Give students 2—3 minutes to read the context and answer the first problem.

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Give 3—4 minutes for the remaining problems followed by a whole-class discussion. The purpose of this discussion is to elicit student thinking about why setting the two expressions in the task statement equal to one another is both possible and a way to solve the final problem. In this activity, students work with two expressions that represent the travel time of an elevator to a specific height. As with the previous activity, the goal is for students to work within a real-world context to understand taking two separate expressions and setting them equal to one another as a way to determine more information about the context.

Arrange students in groups of 2. Give 2—3 minutes of quiet work time for the first two question and then ask students to pause and discuss their solutions with their partner. Expand Image. One elevator is above a line labeled ground level with an arrow pointing down. Another elevator is below a line labeled ground level with an arrow pointing up. Students may mix up height and time while working with these expressions. This discussion should focus on the act of setting the two expressions equal and what that means in the context of the situation.

Ask partners to think of another situations where two quantities are changing and they want to know when the quantities are equal. Give groups time to to discuss and write down a few sentences explaining their situation. Invite groups to share their situation with the class. For example, in a race where participants walk at steady rates but the slower person has a head start, when will they meet?

Consider allowing groups to share their situation by making a picture, a graph, in words, or by acting it out. Imagine a full 1, liter water tank that springs a leak, losing 2 liters per minute. Now imagine at the same time, a second tank has liters and is being filled at a rate of 6 liters per minute.

Since one tank is losing water and the other is gaining water, at some point they will have the same amount of water—but when? So after minutes, the number of liters of the first tank is equal to the number of liters of the second tank. But how much water is actually in each tank at that time? That means that after minutes, each tank has 1, liters. Professional Learning Contact Us.

Lesson 9 When Are They the Same? Give students 2 minutes of quiet work time followed by a whole-class discussion. Student Facing. Explain your reasoning.