# Math 6

*McGraw Hill My Math****Note: All problems listed below from the book are in the "Independent Practice" or "Practice It" section of each lesson unless otherwise noted. The "Guided Practice" problems in each lesson are a good place for the student to get assistance from parents, teacher, etc. before trying the "Independent Practice" problems on his or her own. The "My Homework" Practice problems can also be a good place for extra practice or practice with assistance. The lesson's examples and online videos are good resources for guidance. Many answers can be checked in the back of the book and other answers are online. Extension problems and tasks are for all interested students. They are only listed separately because they are not essential to show a basic understanding of the lesson content.**

**Week 1: Aug 27- Aug 31**

1-1 (Chapter 1 - Lesson 1) #1-9odd, 12, 19, 29-32. Extension: #16.

Page 17 #1-4

1-2 #1-3, 8, 20-25. Extension: #4, 9, 10

*Kahn Academy- Part: whole ratios*

**Task #1A: ** **Hailstone Sequence**

**Task #1B:** How many ways can two numbers multiply to equal 40? Explore and list as many as you can. Task #1:

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1-3 #1-3, 5-7,11, 19, 22, 25-28. Extension: #4, 10, 13.

1-4 #1-4, 8, 9 (can justify without ratio table), 15, 16, 19, 20

1- 5 #18-22

**Task #2: ****Multiples on the 100 Grid**

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**Week 3: Sept 10-14**1-6 #1-5, 7, 10, 18, 19, 21-26. Extension: #9,11.

1-7 #1-3, 5, 9, 14, 15, 19, 21, 24, 25. Extension: #6, 7, 22, 23.

Task #3A: What is a ratio? What is an equivalent ratio? Explain with an example. In your family, what is the ratio of pets to humans? Show how to find two equivalent ratios to your pet to human ratio.

**Task #3B:** John was trying to find an equivalent ratio to 3/4. He decided that he could do the same thing to the numerator and denominator to get a new equivalent ratio, so he added 2 to both numbers and got 5/6. Does this method work to find equivalent ratios? Explain.

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**Week 4: Sept 17-21**

2-1 #1-4, 6-8, 13, 16, 24, 27, 33-38

Page 99-100 #1-8, 17. Extension: #15.

2-2 #1-8, 12, 13, 17, 29, 31, 34-36. Extension: #16, 19.

*Kahn Academy- The Meaning of Percent*

**Task #4:** Flip a coin 20 times. Record the number of heads and tails. Then, determine the percent that was heads and the percent that was tails. Then, just consider the first 19 flips. What percent of the first 19 flips was heads? (You can use a calculator for this one.) Make a list of five to ten possible denominators that make it easy to determine the percent and explain what makes them easy to work with.

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**Week 5: Sept 24 – Sept 28**

2-3 #1-12, 17, 18, 21, 37-41.

2-4 #1-15, 18, 21, 34, 36, 38-40. Extension #19.

*Kahn Academy- Converting Decimals to Percents*

**Task #5:** **Marbles in Boxes**

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**Week 6: Oct 1 – Oct 5**

2-7 #1-4, 15, 18-21, 23, 26, 28-30, 35-38. Extension #5-9, 14, 16.

*Kahn Academy- Finding a Percent *

**Task #6****a:** What do you know about 40%? Brainstorm or show anything you can that relates to 40%.

**Task #6b****:** Consider fractions with a numerator of 1 and the possible denominators of 1-10 (ex 1/1, ½, 1/3, ¼, etc…) Which fractions are easiest to determine the percent without a calculator? Write out all ten fractions, then list the percent next to them. You can use a calculator on some. Look for patterns. With your parent or teacher, decide which ones are important to know by memory, which ones you can figure out in your head, and which ones are best done with a calculator.

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**Week 7: Oct 8 – Oct 12**

These percent problems are very important. Spend extra time practicing and discussing the various ways percent problems can be solved.

2-8 #1-11, 18-21, 27-35. Extensions: #14, 15

*Kahn Academy- Percent Word Problem *

*Kahn Academy- Percent Word Problem*

**Task #7a:** Talk with a parent/adult/teacher about the types of percent situation he or she encounters in everyday adult life? Discuss at least three different situations. How does he or she figure things out? What types of calculations are done using mental math? When is a calculator used? When is an estimate good enough? Solve a few problems that a parent has created for you.

**Task #7b:** Create as many percent problems as you can that would have an answer of 20. See if you can make up five or ten different problems! (Examples: What is 20% of 100? What is 4% of 500?)

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**Week 8: Oct 15 – 29**

3-1 #1-13, 18-21, 25, 28-33. Extensions: #14-16.

*Kahn Academy - Adding Decimals *

*Kahn Academy- Subtracting Decimals *

*Kahn Academy - Add & Subtract Decimals *

**Task #8:** **Working With Percent**

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**Week 9: Oct 22 – 26**

3-2 #1-6, 9, 12, 14, 21-24, 28-32. Extension: #15. This estimation with mental math is very important. When we multiplication with decimals, a rough estimate helps us know if our answer is reasonable. For example, if we do 3.4 times 5.6 and get 190.4 (because of simply putting the decimal in the wrong place), we need to know that this answer is not reasonable! Note: It doesn’t matter has much how a student rounds… the rounding is flexible.

3-3 #1-5, 8, 10, 12, 16, 23, 30-33. Extensions: #6, 7.

3-4 #1-4, 6, 8, 14, 15, 19, 32-35. Extensions: #5, 7, 16, 17, 28. Most importantly, we should be proficient with the standard multiplication procedure for simple problems and estimation regarding the reasonability of an answer. If there are more than one or two decimal places, most adults will use a calculator, so we don’t care as much about being able to accurately perform 14.7 times 11.361, like in #5. We do, however, need to be able to do 0.4 times 3.7 by hand and know that if we misplace the decimal and get 14.8 that it is unreasonable and incorrect!

*Kahn Academy- Intro to Multiplying Decimals *

**Task #9:** **Estimating Multiplication with Decimals** (Don’t skip these tasks!)

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**Week 10: Oct 29 - Nov 2**

3-5 #1-9odd, 17, 33-36. Extension: #16. You will have to decide how important these are to you. Recognizing reasonable vs. unreasonable answers by estimating is super valuable, but you may want to practice simpler arithmetic if you are still struggling with division and multiplication. Obviously, students will soon (starting in 7th/8th grade) be doing these mostly by calculator.

3-6 #1-5, 7, 9, 10, 23-28. Extensions: #6, 7. Resist the urge to calculate any exact answers.

3-7 #1-3, 7, 12, 14, 15, 28-33. Extensions: #4-6.

3-8. #26-31. Then, look at #s 1-8 on page 243. Estimate based on the numbers. Will the answer be big? Small? Close to one? Estimate an answer if you can. Discuss with an adult. Then check with calculator. If you decide you want to divide these out by hand, then give them a try!

*Kahn Academy - Dividing Decimals*

Task #10: Look at the problems assigned in 3-6 (page 227) and discuss different options for estimating with an adult. Talk about (or go out and experience!) real-world situations (tax, tip at restaurant, shopping, etc.) when adults estimate. Take 1st Quarter Benchmark Test. Check answers with Answer Key. Discuss mistakes and do some test corrections with your parent, teacher, or tutor.

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**Week 11: Nov 5 - 9**

4-1#1-6, 8-13, 22, 23, 25-33. This is essential practice. Though you need not worry about doing an estimate a certain way… just make sure you can anticipate a reasonable range of answers. For example, 5/7 of 22 cannot be more than 22 or less than 11. Another example: 4½*5¼ must be more than 20.

4-2 #1-7, 8-12, 13-15, 19-24, 28-32.

*Kahn Academy- Multiplying Fractions by Whole Numbers on the Number Line*

*Kahn Academy -Multiplying Fractions: Word Problem*

Task #11: Write two different real-world problems that involve multiplying a fraction by a whole number. For each problem, create it so that the answer is a number from 20-25.

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**Week 12: Nov 12 - 16**

4-3 #1-9, 12-15, 22-32. Extension #10.

4-4 #1-10, 14-16, 24-31. Extensions #12-13, 23.

*Kahn Academy - Multiplication as Scaling *

*Kahn Academy - Multiplying a Fraction by a Fraction*

*Kahn Academy- Multiplying Mixed Numbers*

Kahn Academy - Multiplying Fractions: Word Problems

Task #12: Part 1: Explain why it would be easy to create problems that involve multiplying fractions if you were allowed to use “1” in the denominator or “0” in the numerator. Show a couple examples. Part 2: Create three multiplication of fraction problems, none of which have 1 in the denominator or 0 in the numerator, that all have answers between 4 and 5.

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**Week 13: Nov 26 – Nov 30**

4-5 #1-9, 26-29, 31-35. Extension #30.

Page 300 #1-7.

*Kahn Academy- Converting Pounds to Ounces*

Task #13: Multiplying Fractions

**______________________________________****Week 14: Dec 3 – Dec 7**

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**Week 15: Dec 10 – Dec 14**

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**Week 16: Dec 17 – Dec 21**

5-2 #7-11, 14-16, 19, 36-38, 43-47. Extensions #41,42.

5-3 #1-8, 12, 25-30 . Extension #13.

5-4 #1-3, 8-11, 33-42. Extension #32.

*Kahn Academy - converting a fraction to a repeating decimal*

Task #16: Case #3 and Case #6 on page 373.

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**Week 17: Jan 7 – Jan 11**

5-5 #1-9 odd, 12, 13, 31-39.

5-6 #1-11 odd, 32, 34-37. Extension #14, 31, 33.

5-7 #1-11, 38-42. Extension #13-17.

*Kahn Academy - Coordinate Plane Examples*

Task #17: Determine three points on a graph, such that when connected by three lines, the resulting triangle has an area of 10 units2.

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**Week 18: Jan 14 – Jan 18**

6-1 #1-9, 11-13, calculator OK, 15, 31-36.

*Kahn Academy - Introduction to Exponents*

6-2 #1-12, 14, 29-33. Extension #13, 15, 27, 28.

*Kahn Academy - Introduction to order of operations*

Task #18: Write an expression using at least five different numbers that has a value of 12. Your expression should contain at least three of the four math operations (add, subtract, multiply, divide) and at least one set of parenthesis. Then, see how many different ways you can write it such that is still simplifies to 12. If you only used three operations, try to write another one that uses all four.

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**Week 19: Jan 21 – Jan 25**

6-3 #1-9, 11 (calc OK), 12-14, 27, 35-40. Extension #15-17.

*Kahn Academy - What is a Variable? *

*Kahn Academy - Evaluating Expressions in two variables *

6-4 #1-7, 10-13, 15-19, 25-28. Extensions #9, 14.

*Kahn Academy - Writing Expressions with Variables Resource*

Task #19: Carlos spends $5 every day on a delicious broccoli smoothie. He usually buys some scrumptious organic seaweed and brown rice wraps, which cost $1.50 each, but the exact amount of wraps he buys each day varies. #1. Define a variable and then write an expression that represents the total cost of his purchase on any given day. #2. Determine how much it will cost him to buy 3 wraps (with his smoothie of course)? #3. Determine how many wraps he bought on that big day in October when he spend a whopping $23.

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**Week 20: Jan 28 – Feb 1**

6-5 #1-5, 8-11, 14, 25-30, 32. Extension #31. Memorizing the property names is not important, but simplifying and checking for equivalence is very important.

6-6 #1, 2, 4-6, 11-13, 17, 22-24, 30-33, 35-38. Extension #18.

*Kahn Academy - Distributive Property** of Multiplication Over Addition *

Task #20: Jim has 12 gold coins of unknown value and 18 silver dollar coins that are worth $1 each. PART I: If x = the value of a gold coin, write an expression that represents the total value of his coin collection. PART II: If he wants to share these coins evenly with his siblings, then how many total kids (including Jim) would be able to split the collection? Remember: it needs to be able to be split evenly. For each number of siblings that works, show the value of each kid’s collection, in terms of x and numbers, and then show how that expression times the number of kid’s equals your answer from Part I.

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**Week 21: Feb 4 – Feb 8**

6-7 #1-6, 9-11, 15-19, 22-26, 36-40. Extension #7-8, 13, 14.

*Kahn Academy - Manipulating Expressions/Combining Like Terms*

7-1 #1-13, 15, 19, 34-42. Extension #14.

*Kahn Academy - Variables - Expressions & Equations*

Task #21: 10x + 5. Determine at least 10 different expressions that simplify to 10x + 5. Use a variety of expressions, some short and easy and others that are more complicated and involve different math operations and symbols, lots of terms or other variables, or different types of numbers like fractions, decimals. Be creative. Show work on some of your more complicated expressions so you and your teacher can be sure they do in fact simplify to 10x + 5.

Take 2rd Quarter Benchmark Test. Check answers with Answer Key. Discuss mistakes and do some test corrections with your parent, teacher, or tutor.

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**Week 22: Feb 11 – Feb 15**

7-2 #1-9, 11, 13, 14, 17-21, 25, 36. Extension #10.

7-3 #1-8, 15, 18, 21, 23, 27, 29, 34-40. Extensions #10-12, 17.

*Kahn Academy - Solve One Step Equations*

Page 545 Case #3-6.

Page 546 #1-11. Extension #12.

Task #22: x = 7. Write at least 5 different equations such that x must equal 7 in order to make the equation true. How many equations are possible that could have the solution of x=7?

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**Week 23: Feb 18 – Feb 22**

7-4 #1-7, 13-15, 24-26 (use a calculator on #24-26), 31, 33, 35, 37-44. Extension #8-10, 16, 29.

Kahn Academy -Resource:

7-5 #1-3, 5, 8, 9, 11, 17-21, 24, 26-34. Extension: Explain how you would solve 18.2 / x = 0.4.

*Kahn Academy - One Step Equations - Multiplicatio*n

Task #23A: Jason has three beans and seven pennies. Nicole has five beans and one penny. They know that the value of what they have is equal. In other words, Jason’s stuff is equal in value to Nicole’s stuff. What is one bean worth? (What is the value of one bean?) Create this situation with beans and coins at home and put an equal sign between the piles. How can you use subtraction and eventually division to solve this problem? Try showing your work in terms of an equation as well (with “x” representing the value of a bean).

Task #23B: Consider the problem: four fifths of x is equal to 16. First estimate the value of x. Should it be more than 16? Less then 16? Why? Then, write an equation that represents this situation. Explain why you would need both division and multiplication to solve this problem for x. Show work that leads to the correct solution. You might also consider another way of solving this problem that involves changing 4/5 to a decimal. Show work and solve this problem in as many ways as you can.

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**Week 24: Feb 25 – Mar 1**

8-1 #1-7, 18, 20, 28.

8-2 #1-9, 14, 21-23, 28-32. Extension: #15.

*Kahn Academy -Reading and Interpreting Data*

8-3 #1-3, 7, 9, 13, 19-30. Extension: #8.

*Kahn Academy - Dependent & Independent Variables*

Task #24: Ch 6 and 7 Review handout below.. Can be taken as a quiz and corrections made afterwards.

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**Week 25: Mar 4 – Mar 8**

8-4 #1-4, 7, 9. Extension: #11.

8-5 #1-4, 7, 9, 16, 17, 22 . Extensions: #10-13.

*Kahn Academy - Test Solutions to Inequalities Resource*

8-6 #1-10, 23-28. Extension: #12.

8-7 #1-5, 25-32. Extensions: #7-10.

Task #25: Do any two problems among Case #3-6 on page 613. After brainstorming and working to solve the problems, consider how to organize your work and clearly show your thinking. Then make a final draft version of your work and solutions for these problems.

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**Week 26: Mar 11 – 15**

Task #26A: Where have you heard the term “area” before? If something has a big area, what does that mean? How is it different than length or volume? Can something be really long but have a small area? How do you determine the area of a rectangle if you know the dimensions?

Page 657-660: Do the hands-on activity and investigation.

9-1 #1-4, 7, 8, 10, 25-30.

*Kahn Academy - Area of a parallelogram *

Task #26B: Explore what types of enclosed chicken run areas (fenced area for chickens to graze) you can create if you have a fixed length of fencing that is 20 ft long and want to cut it into four parts so the enclosed shape is a four-sided figure (quadrilateral). Is a parallelogram an efficient design to create a large area? Explain or show with drawings or examples. Is there a specific quadrilateral design that would create the largest area? Can you prove or justify your answer?

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**Week 27: Mar 25 - 29**

Page 669-671: Do the Inquiry lab through #12.

9-2 #1, 6, 9, 14, 15, 24-29.

*Kahn Academy - Area of a Triangle*

Optional Extension: Pages 681-683 and Lesson 9-3 #s 1-3. (If you skip this make sure that you have a good understanding of Task B below.)

Task #27: For this task, use graph paper and consider each square to be one unit by one unit. Also, make sure all of your corner points (or vertices) are at exact points on the grid paper.

Task A: Draw a triangle that would have an area that is between 20 and 30 square units. Calculate the exact area.

Task B: Draw a trapezoid that would have an area that is at least 20 units. Show that you can calculate the area of a trapezoid by breaking it down into triangles and rectangles.

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**Week 28: Apr 1 – 5**

9-4 #1-3, 6, 15. Extensions #8, 9.

9-5 #1-8, 16, 17, 22. Extensions #10, 12.

*Kahn Academy - Area of a Triangle in Grid *

Task #28: Choose to do any two of the four problems on page 695.

Take 3rd Quarter Benchmark Test. Check answers with Answer Key. Discuss mistakes and do some test corrections with your parent, teacher, or tutor.

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**Week 29: Apr 8 – 12**

9-6 #1, 5, 16-21.

*Kahn Academy - Area Breaking Up Shape*

Inquiry Lab: Page 735 only. (Can be done with or without actual cubes.)

10-1 #1-7odd, 10, 11. (Use a calculator.)

10-2 #1-3, 6, 9, 11, 13, 23. (Use a calculator.) Extension #12.

*Kahn Academy - Volume of a Rectangular Prism*

*Kahn Academy - Volume of Triangular Prism & Cube*

Task #29: Choose to do at least any two of the four problems on page 757.

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**Week 30: Apr 15 - 19**

10-3 #1-4, 7, 14, 18-23. (Use a calculator.)

10-4 #1, 4, 5, 8, 21, 23-26. Extension #10. (Use a calculator.)

10-5 #1, 2, 9, 23-28. Extension #3. (Use a calculator.)

*Kahn Academy - Intro to Nets of Polyhedra*

Task #30: Determine all of the possible rectangular boxes (prisms) that have integer side lengths that would have a volume of 12 ft3. (Hint: there are 4 possible boxes—assume that a 4x3x2 box is the same as a 3x2x4 or 2x3x4 box, etc.) Then, determine which of the boxes would have the greatest surface area. Show your work clearly.

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**Week 31: Apr 22 - 26**

11-1 #1, 2, 6, 7, 9, 14, 15, 17-23. (Use a calculator.)

11-2 #1-3, 6, 9, 10, 16, 18-25. Extension #7. (Use a calculator.)

*Kahn Academy - Statistics Intro: Mean, Median & Mode*

Task #31A: Create a survey question that will have a numerical answer. Survey at least five people and determine the measures of center (mean, median, and mode).

Task #31B: Create a set of 5 numbers that has a mean of 10, a median of 11, and a mode of 12.

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**Week 32: Apr 29 - May 3**

Page 827 Solve any two of the four cases. Show work or justify your thinking

11-4 #1, 17, 21, 22. Extensions #11-13. (Use a calculator.)

*Kahn Academy - Mean Absolute Deviation *

11-5 #3, 6, 11. Extension #7. (Use a calculator.)

*Kahn Academy - Impact on Mean & Median: Removing an Outlier*

Task #32: Do #8 on page 850. Choose data related to something you are interested in.

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**Week 33: May 6 - 10**

12-1 #1, 3.

12-2 #1-5, 9-11, 19. Extension #9. (Use a calculator.)

*Kahn Academy - Creating a Histogram *

12-3 #1, 4, 11.

*Kahn Academy - Constructing a Box Plot*

12-4 #1, 2, 15-23.

Task #33: Flip a coin five times. Record the number of heads that come up. Do this experiment ten times—you will have recorded a number from 0-5 for the number of heads you got on 10 separate “rounds” or “trials” of 5 tosses each. (50 tosses total.) Show the data with a histogram or bar graph and state the mean, median, and mode number of heads. Discuss any surprising results and make a prediction about the number of heads you would expect to get in five tosses.

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**Week 34: May 13 - 17**

12-5 #1-4, 8, 11-21.

12-6 #16. 28.

Task #34: Year-End Exam. Take the 6th Grade Year-End Math Assessment. Get the assessment from your supervising teacher. You can take it at home or at school. It might take from 1-1.5 hrs. Do this test without any notes or assistance. The first two pages are done without a calculator and then the rest of the test is to be done with a calculator. Your test can be corrected by your parent, your supervising teacher, or an OVS math teacher (Jason). There is a scoring template that relates to the grade-level evaluation criteria.

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**Week 35-36: May 20 - June 7**

Task #35: **Year End Exam Corrections**. Complete the test corrections handout from the year-end exam. See the hand-out for instructions.

Complete the **Year End Project: Math Journal **

Work on and complete as many of the **Year- End Challenge Problems ** as you can.