6th Grade Prealgebra Distance Learning Activity, Day 1: Math

Overview: Add, Subtract, Multiply, and Divide Signed Numbers

Estimated Time: Approximately 45 minutes

Explanation: You will simplify expressions with positive and negative numbers without a calculator.

Things to know: 1. Absolute Value: The distance a number is from zero

Example: |−4| , this is read the absolute value of −4. |−4| = 4 since −4 is 4 units away from zero on the number line.

Example: |4| is also 4 since 4 is 4 units away from zero on the number line. 2. Signed numbers

Addition o To add integers with the same sign, add their absolute values

• The sum is positive if both integers are positive Example: 5 + 3 = 8

• The sum is negative if both integers are negative Example: - 5 + - 3 = -8

o To add integers with different signs, subtract their absolute values • The sum is positive if the positive integer's absolute value is greater.

Example: 5 + - 3 = 2 • The sum is negative if the negative integer's absolute value is greater.

Example: -5 + 3 = -2 Subtraction o To subtract an integer, add its additive inverse.

Example 1: 2 - 7 is rewritten as 2 + (-7) which means 2 - 7 = 2 + (-7) = -5 Example 2: - 7 - 8 is rewritten as -7 + (-8) which means - 7 - 8 = -7 + (-8) = -15

Multiplication and Division o The product or quotient of two numbers with the same sign is positive.

Example 1: 3 ∙ 5 = 15 Example 2: −3 ∙ −5 = 15 Example 3: 15 ÷ 3 = 5 Example 4: −15 ÷ −3 = 5

o The product or quotient of two numbers with different signs is negative. Example 1: 3 ∙ −5 = −15 Example 2: −3 ∙ 5 = −15 Example 3: 15 ÷ −3 = −5 Example 4: −15 ÷ 3 = −5

Tasks: 1. Review the Things to Know above and make sure you understand the examples 2. Watch the following video. This video shows an example with more than 2 numbers. It also shows

the addition and subtraction visually. If you are more comfortable with the rules, then you can just use the rules to complete your problems. https://www.khanacademy.org/math/arithmetic/arith-review-negative-numbers/arith-review-add-and-sub-integersss/v/adding-integers-with-different-signs

3. Complete the practice. https://www.khanacademy.org/math/arithmetic/arith-review-negative-numbers/arith-review-add-and-sub-integersss/e/integer-addition-and-subtraction-2

If you struggle on these problems feel free to watch additional Khan Academy videos, videos in the online textbook, or review the concept in your book on pages 55 – 67. You can also email your questions to me and I will provide support and feedback during my online hours.

4. Complete the odd numbered problems on the addition and subtraction, multiplication, and division of signed numbers practice sheets I provided for you through _________. If you do not have a printer, complete your work on notebook paper.

How is this assignment turned in to the teacher: (Teacher completes this section based on the tool they are using with their class.)

6th Grade Prealgebra Distance Learning Activity, Day 2: Math

Overview: Simplify Expressions Using the Order of Operations

Estimated Time: Approximately 45 minutes

Explanation: You will simplify expressions following the order of operations.

Things to know:

Please complete all activities in order. This is a review of a skill you already know and have practiced. 1. To simplify expressions, you must follow the order of operations 2. Key Concept: Order of Operations

First: Parenthesis (or Grouping Symbols) Second: Exponents Third: Multiply and/or divide in order from left to right Fourth: Add and/or subtract in order from left to right

3. Common misconceptions: Sometimes students think you multiply before you divide. When you have multiplication and division in the same problem, you simply work from left to right. Similarly, after simplifying any multiplication and/or division, addition and subtraction is completed from left to right.

Tasks: 1. Review the Things to Know above 2. Watch the video : https://www.khanacademy.org/math/pre-algebra/pre-algebra-arith-prop/pre-

algebra-order-of-operations/v/introduction-to-order-of-operations?modal=1 Read the review and practice the problems in the review : https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-arithmetic-operations/cc-6th-order-of-operations/a/order-of-operations-review

3. Complete the practice sheet on Order of Operations I provided for you through _________. If you do not have a printer, complete your work on notebook paper.

How is this assignment turned in to the teacher: (Teacher completes this section based on the tool they are using with their class.)

6th Grade Prealgebra Distance Learning Activity, Day 3: Math

Overview: Multiplication and Division of Rational Numbers

Estimated Time: Approximately 45 minutes

Explanation: You will multiply and divide fractions without a calculator.

Things to know: 1. Multiplication of Fractions

2. Division of Fractions

3. Example 1

1

4∙

1

2=

1

4 ∙ 2=

1

8

Example 2

−23

5÷

1

5= −

13

5÷

1

5= −

13

5∙

5

1= −

13 ∙ 5

5 ∙ 1= −

13 ∙ 1

1 ∙ 1= −

13

1= −13

Tasks: 1. Review the Things to Know above and make sure you understand the examples 2. Review Examples 1 - 3 (all examples) in your textbook, page 107 - 109. Do the same thing for

Examples 2 - 3 (all examples) problems in your textbook, page 115. Write down the example and then turn your book upside down. Complete the example problem on your own and check to make sure you have it correct. If you are able to complete the problems on your own, you are ready to complete the practice on your own. If not, submit your work to me on these examples so I can provide you with feedback and help. Then try them again to be sure you understand before you do the last task.

3. Complete the practice on Adding and Subtracting Fractions I provided for you through _________. If you do not have a printer, complete your work on notebook paper.

How is this assignment turned in to the teacher: (Teacher completes this section based on the tool they are using with their class.)

6th Grade Prealgebra Distance Learning Activity, Day 4: Math

Overview: Addition and Subtraction of Rational Numbers

Estimated Time: Approximately 30 minutes

Explanation: You will add and subtract fractions without a calculator.

Things to know: 1. Addition of Fractions with Unlike Denominators

2. Subtraction of Fractions with Unlike Denominators

3. Example 1

1

4+

3

8=

1

4∙

2

2+

3

8=

2

8+

3

8=

5

8

Example 2

−3

8−

5

6= −

3

8∙

3

3−

5

6∙

4

4= −

9

24−

20

24= −

29

24 𝑜𝑟 − 1

5

24

Tasks: 1. Review the Things to Know above and make sure you understand the examples 2. Review Example 2 and Example 3 problems in your textbook, page 127. Write down the example

and then turn your book upside down. Complete the example problem on your own and check to make sure you have it correct. If you are able to complete the problems on your own, you are ready to complete the practice on your own. If not, submit your work to me on these examples so I can provide you with feedback and help. Then try them again to be sure you understand before you do the last task.

3. Complete the practice on Adding and Subtracting Fractions I provided for you through _________. If you do not have a printer, complete your work on notebook paper.

How is this assignment turned in to the teacher: (Teacher completes this section based on the tool they are using with their class.)

6th Grade Prealgebra Distance Learning Activity, Day 5: Math

Overview: You will complete application problems from the last 4 review lessons.

Estimated Time: Approximately 30 minutes

Explanation: This is an opportunity to apply what you have reviewed over the last 4 lessons to

complete application problems. You will write your work on paper and send it to me for review.

Things to know: 1. Do your best on each problem. 2. Complete the problems on notebook paper. 3. You do not need to write the entire word problem down, but you do need to show all of your work.

Tasks: 1. On page 88, complete problems 22 and 23 2. On page 89, complete problems 52 and 54 3. On page 90, complete problems 65 and 66 4. On page 133, complete problems 37, 38, 55 and 56 5. On page 134, complete problems 63, 65, 66 and 75 and 77 6. Turn this assignment in to me and I will provide you with feedback and ask you to correct problems

that are not correct. How is this assignment turned in to the teacher: (Teacher completes this section based on the tool they are using with their class.)

6th Grade Prealgebra Distance Learning Activity, Day 6: Math

Overview: This assignment provides a review of simplifying Algebraic Expressions

Estimated Time: Approximately 30 minutes

Explanation: You will simplify algebraic expressions without using a calculator.

Things to know: 1. Definitions

Term: Parts of an expression that are separated by addition or subtraction signs. Like Terms: Terms that contain the same variable with the same exponent.

Example: 3x and 5x are like terms; 5y and -2y are like terms; 5 and -1 are like terms 2x and 3 are not like terms; 5x and -y are not like terms

Coefficient: The numerical part of a term that is multiplied to a variable. Example: For the term 2x, 2 is a coefficient; For the term 5y, 5 is the coefficient

Constant: A term without a variable. Example: In the expression 3x + 2, 2 is the constant

2. Distributive Property

Tasks:

1. Review the Things to Know above and make sure you understand the vocabulary. 2. Review pages 299 and 300, examples 1 – 3. 3. Complete the odd numbered problems on the Simplifying Algebraic Expressions Sheet of I

provided for you through _________. If you do not have a printer, complete your work on notebook paper.

4. Turn the assignment into me and I will provide you with feedback. If you have any incorrect, I will ask you to correct them to be sure you understand simplifying algebraic expressions.

How is this assignment turned in to the teacher: (Teacher completes this section based on the tool they are using with their class.)

6th Grade Prealgebra Distance Learning Activity, Day 7: Math

Overview: This assignment provides a review of ratio

Estimated Time: Approximately 30 minutes

Explanation: You will write ratios as fractions in simplest form.

Things to know:

Please complete all activities in order. This is a review of a skill you already know and have practiced.

You will receive a practice sheet through email. If you do not have a printer, you should write the

problems on notebook paper.

1. Ratio: A comparison of two quantities by division 2. You can represent a ratio using the word “to”, a colon “ : “, or a fraction bar

3. Example: 3 to 5, 3 : 5, 3

5

4. Example: Twenty out of thirty Americans own a cell phone. Express as a fraction in simplest form. Explain its meaning. 20

30 =

2

3 ; so, 2 out of 3 Americans own a cell phone

Tasks: 1. Review the Things to Know above 2. Watch the video : https://www.khanacademy.org/math/pre-algebra/pre-algebra-ratios-rates/pre-algebra-

ratios-rates/pre-algebra-ratios-intro/v/ratios-intro?modal=1 Watch the video: https://www.khanacademy.org/math/pre-algebra/pre-algebra-ratios-rates/pre-algebra-ratios-rates/pre-algebra-ratios-intro/v/ratio-example-problems?modal=1

3. Complete the practice sheet on Ratio I provided for you through _________. If you do not have a printer, complete your work on notebook paper. I will ask you to correct any problem you do not have correct.

How is this assignment turned in to the teacher: (Teacher completes this section based on the tool they are using with their class.)

6th Grade Prealgebra Distance Learning Activity, Day 8: Math

Overview: This assignment provides a review of rates

Estimated Time: Approximately 30 minutes

Explanation: You will express rates as unit rates.

Things to know: 1. Rate: A ratio of two quantities having different kinds of units.

Example: $11

4 𝑏𝑜𝑥𝑒𝑠

2. Unit Rate: A rate simplified so that it has a denominator of 1.

Example: $12

3 𝑠𝑎𝑛𝑑𝑤ℎ𝑖𝑐ℎ𝑒𝑠 =

$4

𝑠𝑎𝑛𝑑𝑤ℎ𝑖𝑐ℎ = $4 per sandwhich

Tasks: 1. Review the Things to Know above and make sure you understand the examples. 2. Watch the following videos, take any notes you find helpful in understanding the concept of rates.

https://www.khanacademy.org/math/pre-algebra/pre-algebra-ratios-rates/pre-algebra-rates/v/finding-unit-rates?modal=1 https://www.khanacademy.org/math/pre-algebra/pre-algebra-ratios-rates/pre-algebra-rates/v/finding-unit-

prices?modal=1 3. Complete the practice on Rates I provided for you through _________. If you do not have a printer,

complete your work on notebook paper. How is this assignment turned in to the teacher: (Teacher completes this section based on the tool they are using with their class.)

6th Grade Prealgebra Distance Learning Activity, Day 9: Math

Overview: This lesson provides a review of proportion

Estimated Time: Approximately 30 minutes

Explanation: You will solve problems using proportions.

Things to know: 1. Proportion: An equation stating two ratios or rates are equal.

2. Property of Proportion

3. Example 1

1

4=

3

12, then 1 · 12 = 3 · 4

Example 2

3

8=

12

32, then 3 · 32 = 12 · 8

4. Cross products provide one way to solve for an unknown value in the proportion

c

3=

20

12

c · 12 = 20 · 3

12c = 60

12c

12=

60

12

c = 5

Tasks:

1. Review the Things to Know above and make sure you understand the examples 2. Watch the following video, take any notes you find helpful in understanding the concept of solving

proportions. The video highlights a few ways to solve a proportion. You only need to understand one way that works well for you. https://www.khanacademy.org/math/pre-algebra/pre-algebra-ratios-rates/pre-algebra-write-and-solve-proportions/v/find-an-unknown-in-a-proportion

4. Watch the following video, take any notes you find helpful in understanding how to set up a proportion from a word problem. This video only shows how to set up a proportion that could be used to solve a variety of problems. https://www.khanacademy.org/math/pre-algebra/pre-algebra-ratios-rates/pre-algebra-write-and-solve-proportions/v/writing-proportions

5. Complete the odd number problems from the proportion practice I provided to you for this lesson. If you do not have a printer, complete your work on notebook paper. I will provide feedback on this assignment and ask you to correct any problems you did not get correct.

6. EXTRA – Only complete if you want more practice. Complete the even number problems from the practice sheet.

How is this assignment turned in to the teacher: (Teacher completes this section based on the tool they are using with their class.)

6th Grade Prealgebra Distance Learning Activity, Day 10: Math

Overview: This lesson provides an opportunity to review applications incorporating algebraic

expressions, ratio, rates, and proportion.

Estimated Time: Approximately 30 minutes

Explanation: This is an opportunity to apply what you have reviewed over the last 4 lessons to

complete application problems. Print the practice sheet I provided, or you can write your work on

paper and send it to me for review.

Things to know: 1. Do your best on each problem. 2. Complete the problems on notebook paper. 3. You do not need to write the entire word problem down, but you do need to show all of your work.

Tasks: 1. Review the things to know. 2. Complete the practice sheet. 3. Submit to me to review.

How is this assignment turned in to the teacher: (Teacher completes this section based on the tool they are using with their class.)

6th Grade Prealgebra Distance Learning Activity, Day 11: Math

Overview: You will complete a review of the work you have done during the first 3 weeks of the

Distance Learning Plan.

Estimated Time: Approximately 30 minutes

Explanation: This is an opportunity think about, and then to show how well you know the content of

the first 10 days of work you have completed.

Things to know: 1. Do your best on each problem. 2. You do not need to print the practice. You can write it on notebook paper. Write the problem and

show your work. 3. You do not need to write any word problems down, but you do need to show all of your work.

Tasks: 1. Start by reflecting on what you completed over the last 10 days of work you completed.

• What was the hardest for you to do?

• Are you better at it now than you were before you started?

• What have you learned about yourself through the work you have done that will help you as we enter the next part of distance learning?

2. Share your answers to #1 above with me through email. 3. Complete the practice sheet I sent to you for Day 11.

How is this assignment turned in to the teacher: (Teacher completes this section based on the tool they are using with their class.)