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Below are links to different textbook series, grade level curriculum and the resources that have been put together to help you be successful in math this year!

Illustrative Mathematics (6-8 OUR Mathematics)

6th Grade Resources

U1 , U2 , U3 , U4 , U5 , U6 , U7 , U8

7th Grade Resources

8th Grade Resources

Preparation for High School Algebra or Integrated Math 1

University High School Summer Bridge Course

High School Illustrative M athematics - McGra w Hill, Kendall Hunt, Imagine Learning, Learn Zillion)

Algebra 1 Resources

U1 , U2, U3, U4, U5, U6, U7

OPEN UP RESOURCES Mathematics - OUR

OUR - Algebra 1 Resources

U1 , U2 , U3, U4, U5, U6, U7, U8, U9

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8th grade (Illustrative Mathematics)

Unit 1: rigid transformations and congruence, unit 2: dilations, similarity, and introducing slope, unit 3: linear relationships, unit 4: linear equations and linear systems, unit 5: functions and volume, unit 6: associations in data, unit 7: exponents and scientific notation, unit 8: pythagorean theorem and irrational numbers.

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8.4: Homework

• Last updated
• Save as PDF
• Page ID 70331

• Julie Harland
• MiraCosta College
• Submit homework separately from this workbook and staple all pages together. (One staple for the entire submission of all the unit homework)
• Start a new module on the front side of a new page and write the module number on the top center of the page.
• Answers without supporting work will receive no credit.
• Some solutions are given in the solutions manual.
• You may work with classmates but do your own work.

Find GCF(252, 350) using:

Find GCF(140, 315) using:

Use the Euclidean Algorithm to compute the greatest common factor of the numbers given. Use correct notation, and show each step. Then, show how you check your answer. Also, compute the LCM of the two numbers.

State whether each of the following statements is true or false. If it is false, provide a counterexample. If it is true, provide an example.

a. If (a + b)|c, then a|c and b|c

b. If a|b and a|c, then a|(bc)

c. If a|b and a|(b + c), then a|c

d. If a|bc, then a|b and a|c

e. If a|b and a|c, then a|(b + c)

Write the prime factorization for the following numbers. If it is prime, write "prime" and explain how you know it is prime.

Assume m and n are composite whole numbers in each of the following. Find the following. Then provide an example using numbers for m (and n where used). Remember not to use prime numbers in your example.

a. GCF(m,m) =

b. LCM(m,m) =

c. GCF(m,0) =

d. GCF(m,1) =

e. If GCF(m,n) = 1, then LCM(m,n) =

f. If GCF(m,n) = m, then LCM(m,n) =

g. If LCM(m,n) = mn, then GCF(m,n) =

Find the following sums using methods from this module: Show all work

a. 1 + 2 + 3 + . . . + 313 + 314 + 315 =

b. 111 + 112 + 113 + . . . + 287 + 288 + 289 =

c. 15 + 30 + 45 + . . . + 900 + 915 + 930 =

d. 102 + 105 + 108 + . . . + 300 + 303 + 306 =

On each number line, state all whole number possibilities less than 100 that the man could be standing on.

The factors of a number that are less than the number itself are called proper factors . For instance, the proper factors of 10 are 1, 2 and 5. A number is classified as deficient if the sum of its proper factors is less than the number itself. 10 is a deficient number since 1 + 2 + 5 < 10. A number is classified as abundant if the sum of its proper factors is greater than the number itself. For instance, the proper factors of 18 are 1, 2, 3, 6, and 9. 18 is a deficient number since 1 + 2 + 3 + 6 + 9 > 18. A number is classified as perfect if the sum of its proper factors equals the number itself. For each number, list its proper factors. Then find the sum of its proper factors. Then, classify each number as deficient, abundant or perfect.

Are prime numbers deficient, perfect, or abundant? ________ Explain why.

Answer true or false for each of the following. If it is true, provide an example. If it is false, provide a counterexample.

a. Every prime number is odd.

b. If a number is divisible by 6, then it is divisible by 2 and 3.

c. If a number is divisible by 2 and 6, then it is divisible by 12.

d. If a number is divisible by 3 and 4, then it is divisible by 12.

e. If a \(\neq\) b, then GCF(a, b) < LCM(a, b).

f. If 6 is a factor of mn, then 6 is a factor of m or a factor of n.

g. If 5 is a factor of mn, then 5 is a factor of m or a factor of n.

Can the sum of two odd prime numbers be a prime number? Explain why or why not.

Find the least common multiple of the following sets of numbers:

a. LCM(2, 4, 5, 7, 8, 12, 14, 15)

b. LCM(3, 4, 6, 8, 9, 10, 12, 18)

If GCF(30, x) = 6 and LCM(30, x) = 180, then what is x? (Hint: see page 65)

The theory of biorhythm states that your physical cycle is 23 days long, your emotional cycle is 28 days long, your intellectual cycle is 33 days long. If your cycles all occur on the same day, how many days until your cycles again occur on the same day? About how many years is this?

Functions with Multiple Parts

These materials, when encountered before Algebra 1, Unit 4, Lesson 12 support success in that lesson.

12.1: Notice and Wonder: Ticket Price (10 minutes)

Routines and Materials

Instructional Routines

• Notice and Wonder

The purpose of this warm-up is to elicit the idea that boundary conditions on intervals are important, which will be useful when students write domain intervals for piecewise functions in a later activity. While students may notice and wonder many things about this table, the price of a ticket for people on the boundary between 2 intervals are the important discussion points.

Display the table for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time and then 1 minute to discuss the things they notice and wonder with their partner followed by a whole-class discussion.

Student Facing

What do you notice? What do you wonder?

Student Response

For access, consult one of our IM Certified Partners .

Activity Synthesis

Ask students to share the things they noticed and wondered. Record and display their responses for all to see. If possible, record the relevant reasoning on or near the table. After all responses have been recorded without commentary or editing, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to respectfully disagree, ask for clarification, or point out contradicting information.

If the cost of a ticket for people whose ages are on the boundary of the age ranges does not come up during the conversation, ask students to discuss this idea.

12.2: Group Ticket Cost (15 minutes)

CCSS Standards

Building Towards

• HSF-IF.C.7.b

In this activity, students use a step function to determine the price of tickets for groups composed of people in different age groups. In the associated Algebra 1 lesson, students examine piecewise functions and their graphs. Although this activity does not mention piecewise functions, understanding how to compute the ticket price for the group will help students think about this kind of function.

A community orchestra charges different amounts for tickets to shows based on the age of the person attending. A sign in front of the box office where tickets are sold shows the prices.

• 2 adults aged 40 and 36, and 2 kids aged 4 and 1
• 3 adults aged 74, 37, and 36
• 5 adults in their 30s and 25 students aged 15 and 16
• 1 adult aged 25 and 4 kids aged 1, 9, 13, and 16
• A mother arrives and tells the box office clerk that her child is 35 months old. How much should the clerk charge for the child?
• What is the domain for the rule?
• What is the range for the rule?

The purpose of the discussion is to get students thinking about functions for which there are different rules for different domains. Select students to share their solutions. Ask students,

• “Is there an equation for the function that connects the input and output?” (There is not a single, nice equation that works for all the ages.)
• “Are there people for whom the price of a ticket would be confusing or unknown?” (No. The convention for ages is that if someone is turning 14 tomorrow, they will still be charged the $ 4 price since they are still currently 13. So, everyone should fit into one of the categories listed.)
• “If we graphed the information in the table, can you visualize what that graph would look like?” (There would be horizontal lines for each range of ages to look a little like steps.)

12.3: A Light Trip (15 minutes)

In this activity students analyze graphs representing situations to select the intervals within the domain in which certain events are happening. In the associated Algebra 1 lesson students examine piecewise functions and use the function notation that includes domain restrictions. Students are supported by examining scenarios and noting what is happening on different parts of the domain.

Noah leaves his home, sometimes running, sometimes walking, sometimes stopping until he remembers that he doesn’t have his wallet, then he goes back home. A graph representing his journey is shown in the graph.

Description: <p>Graph on coordinate grid, origin O. Horizontal axis, 0 to 400, by 40s, time, seconds. Vertical axis, 0 to 300, by 30s, distance from home, meters. Line starts at origin and passes through points, 20 comma 45, 60 comma 45, 120 comma 135, 180 comma 285, 210 comma 285, 400 comma 0.</p>

• Describe what is happening on the domain \(210 < x < 400\) .
• What are the domain intervals that represent the times when Noah was running?
• What are the domain intervals that represent the times when Noah was stopped?
• What are the domain intervals that represent the times when Noah was walking away from home?

Description: <p>Coordinate plane, time after midnight in hours, 0 to 24 by 2, light level in room by lux, 0 to 1,100 by 100. From 0 to 4, y = 0 until slight upturn just before 4. From 4 to 5 point 5, horizontal line at y = 200. Function jumps to 260 and increases rapidly toward 8 comma 1,000 and then levels out until 16 comma 1,000 where it drops rapidly toward 19 comma 170. From x = 19 to 23, y = 200.</p>

The purpose of the discussion is to recognize that using the domain is important when describing graphs of situations where different things may be happening. Select students to share their solutions. If students describe the domain for the light levels in words (like “between 9am and 4pm”), ask students how they might write that as an inequality.

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Eureka Math Grade 8 Module 4 Lesson 12 Answer Key

Engage ny eureka math 8th grade module 4 lesson 12 answer key, eureka math grade 8 module 4 lesson 12 opening exercise answer key.

Eureka Math Grade 8 Module 4 Lesson 12 Exercise Answer Key

Exploratory Challenge/Exercises

Question 4. Consider the linear equation \(\frac{2}{5}\) x+y=11. a. Will you choose to fix values for x or y? Explain. Answer: If I fix values for x, it will make the computations easier. Solving for y can be done in one step.

b. Are there specific numbers that would make your computational work easier? Explain. Answer: Values for x that are multiples of 5 will make the computations easier. When I multiply \(\frac{2}{5}\) by a multiple of 5, I will get an integer.

Question 5. At the store, you see that you can buy a bag of candy for $2 and a drink for $1. Assume you have a total of $35 to spend. You are feeling generous and want to buy some snacks for you and your friends. a. Write an equation in standard form to represent the number of bags of candy, x, and the number of drinks, y, that you can buy with $35. Answer: 2x+y=35

Eureka Math Grade 8 Module 4 Lesson 12 Exit Ticket Answer Key

Question 1. Is the point (1,3) a solution to the linear equation 5x-9y=32? Explain. Answer: No, (1,3) is not a solution to 5x-9y=32 because 5(1)-9(3)=5-27=-22, and -22≠32.

Eureka Math Grade 8 Module 4 Lesson 12 Problem Set Answer Key

Students practice finding and graphing solutions for linear equations that are in standard form.

Question 1. Consider the linear equation x-\(\frac{3}{2}\) y=-2. a. Will you choose to fix values for x or y? Explain. Answer: If I fix values for y, it will make the computations easier. Solving for x can be done in one step.

b. Are there specific numbers that would make your computational work easier? Explain. Answer: Values for y that are multiples of 2 will make the computations easier. When I multiply \(\frac{3}{2}\) by a multiple of 2, I will get a whole number.

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Master Math 8 Homework with Morgan's Help!

Updated on Dec 06,2023

Master Math 8 Homework with Morgan's Help!

Table of contents, introduction, understanding balanced equations, balancing hangers and socks, activity: hanging blocks.

• The Weight of Squares and Triangles

Solving Equations to Determine Square Weights

Exploring hanger balance with circles and triangles, problem solving: andre's family ages, writing equations for parallel lines.

In this article, we will Delve into the concept of balancing equations, specifically focusing on examples related to weights and hangers. We will explore various activities and problem-solving scenarios to better understand the principles behind balanced equations and their applications in real-life situations. By the end of this article, You will have a solid grasp of balancing equations and its relevance in everyday scenarios.

Before we dive into specific examples, it's important to understand the concept of balanced equations. In the realm of weight and hangers, a balanced equation refers to a state where the weight on each side of the hanger is equal. Just like a hanger needs equal weights on both sides to maintain balance, an equation requires equality between its expressions.

To grasp the concept of balancing equations, let's begin by examining the Scenario of balancing hangers using socks. Imagine having two socks hanging on a hanger. If one sock is HEAVIER than the other, the hanger will tilt towards the side with the heavier sock. This imbalance occurs because the weight on each side of the hanger is not equal.

However, it's crucial to note that the weight of an object does not solely depend on its size. In the case of the socks, the heavier sock may appear skinnier, but it could contain additional items like beans, making it heavier. The wetness of the sock from stepping in a puddle can also affect its weight. These factors highlight the importance of considering perplexity and burstiness in balancing equations.

Now, let's explore an activity called "Hanging Blocks." This activity provides a visual representation of a balanced hanger using squares and triangles. The key takeaway from this activity is that even though the squares and triangles are different shapes, the weight on both sides of the hanger remains balanced. This is because the weight on each side is proportional.

Elena, a participant in the activity, decides to remove two triangles from the left side and three triangles from the right side. The crucial question now is whether the hanger will remain balanced or tip towards one side. In this case, since Elena removed more triangles from one side than the other, the hanger will no longer be balanced. Consequently, it will tip towards the side with fewer triangles.

Additionally, the activity Prompts another question: If a triangle weighs one gram, what is the weight of a square? To determine this, we examine the equation representing the hanger's balance, which consists of three squares and two triangles on one side, and one square and five triangles on the other side. By setting up this equation, we can solve for the weight of one square, which is found to be equal to three over two grams or 1.5 grams.

Moving forward, let's explore a scenario involving different shapes and weights on hangers. Suppose a triangle weighs three grams, and a circle weighs six grams. The task at HAND is to determine the weight of a square on one hanger and the weight of a pentagon on another hanger.

To solve this problem, we need to set up the equations representing the weights on each hanger. For the hanger containing squares and triangles, we have three squares and two triangles on one side and one square and five triangles on the other side. By setting up this equation, we can solve for the weight of a square, which is calculated to be 3.75 grams.

However, when it comes to the hanger with circles and a pentagon, we encounter a challenge. The equation representing this hanger consists of twelve plus two pentagons on one side and six triangles plus six circles plus two pentagons on the other side. Unfortunately, this equation does not provide enough information to determine the weight of the pentagon. Hence, it remains undetermined.

Let's further analyze the concept of balancing hangers by considering their compositions. In this scenario, we have hangers comprised of circles and triangles. By observing the number of circles and triangles on each side, we can determine if the hanger will remain balanced or tilt towards the heavier side.

Suppose we have a hanger with three triangles and six circles on one side and an equal number of x variables on the other side. By analyzing the equation formed from this scenario, we can solve for x and determine that x is equal to 4 or 15/4. This knowledge allows us to calculate the weight of one square, which is found to be equal to -3 grams. However, since a negative weight is illogical, we conclude that this scenario is not possible.

In this problem-solving scenario, Andre presents a Puzzle related to the ages of his family members. Andre claims to be three years younger than his brother and two years older than his sister. Additionally, the age of his mother is one less than three times his brother's age. The sum of all the ages in the family adds up to 87.

To decipher the ages of Andre, his brother, sister, and mother, we need to construct equations Based on the given information. By assigning variables to each family member's age, we can Create a system of equations. Simplifying these equations, we find that Andre's age is 13, his brother's age is 16, his sister's age is 11, and his mother's age is 47.

Lastly, we explore the concept of parallel lines and how to write equations for lines that are parallel to each other. When dealing with parallel lines, it's essential to note that they have the same slope. The slope represents the rate of change between the x and y coordinates of the line.

To write equations for parallel lines, we'll examine two lines and determine their slopes using the given points. By calculating the slope based on the coordinates of the points, we can write equations for each line. In one form, the equation appears as y - y1 = m(x - x1), where m represents the slope and (x1, y1) represents the coordinates of a point on the line. In another form, the equation is y = mx + b, where m is the slope and b is the y-intercept.

By following these methods, we can write equations for two parallel lines and ensure that their slopes and points on the lines match accordingly.

Balancing equations plays a crucial role in various scenarios, from weights on hangers to determining family ages and writing equations for parallel lines. Understanding the principles behind balanced equations enables us to navigate real-life situations effectively. With the knowledge gained from this article, you are equipped to tackle complex problems involving balancing equations and Apply them in practical scenarios.

The above is a brief introduction to Master Math 8 Homework with Morgan's Help!

Let's move on to the first section of Master Math 8 Homework with Morgan's Help!

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