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2019-2020 HISD @ H.O.M.E. Project-Based Learning ...€¦ · Activity 1: Write the length of each...

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2019-2020 HISD @ H.O.M.E. Project-Based Learning Mathematics Grade 8 Week of March 30 - April 3, 2020 GLOBAL GRADUATE - State Process Standard - Aligned to Upcoming State Readiness Standard - State Readiness Standard - State Supporting Standard © Houston ISD Curriculum 2019-2020 Page 1 of 20 Student Weekly Learning Targets Students will be able to apply the Pythagorean Theorem to solve problems in real-life and mathematical situations (MATH.8.2A, MATH.8.2B). The student should be able to demonstrate and verify the following: I can identify types of numbers: whole numbers, naturual numbers, integers, rational numbers, and irrational numbers. I can explain how types of rational numbers are related to each other. I can explain the difference between rational numbers and irrational numbers. I can explain how squared numbers and square roots are related. I can define a perfect square. I can calculate the square root of a number using the number line. Monday Rational Numbers In grade 8 mathematics, we have reached a point in our year that we can review all of the content in preparation for algebra 1 next year. First, we will begin with reviewing the different types of numbers that we have encountered. You and your friends decide to go to the movies together. When deciding what to watch, you and your friends might talk about the TYPE of movies you enjoy comedy, science-fiction, romance, drama, or horror. In math, we talk about the TYPE of numbers we are working with, just as we talk about the TYPE of movies we like to watch. We do this with many things in our lives: music, animals, food, clothing style, and so much more! Let’s talk about different TYPES of numbers. First, when we talk about the TYPE, we are talking about the SET that a number belongs to. From now on, that is the word we will use: SET.
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Page 1: 2019-2020 HISD @ H.O.M.E. Project-Based Learning ...€¦ · Activity 1: Write the length of each side of the squares below and find the area. 1 unit 1 ... unit2 Student Thinking:

2019-2020 HISD @ H.O.M.E. – Project-Based Learning

Mathematics – Grade 8

Week of March 30 - April 3, 2020

GLOBAL GRADUATE

- State Process Standard

- Aligned to Upcoming State Readiness Standard

Ⓡ - State Readiness Standard

Ⓢ - State Supporting Standard

© Houston ISD Curriculum 2019-2020

Page 1 of 20

Student Weekly Learning Targets

Students will be able to apply the Pythagorean Theorem to solve problems in real-life and mathematical situations (MATH.8.2A, MATH.8.2B). The student should be able to demonstrate and verify the following:

• I can identify types of numbers: whole numbers, naturual numbers, integers, rational numbers, and irrational numbers.

• I can explain how types of rational numbers are related to each other.

• I can explain the difference between rational numbers and irrational numbers.

• I can explain how squared numbers and square roots are related.

• I can define a perfect square.

• I can calculate the square root of a number using the number line.

Monday – Rational Numbers

In grade 8 mathematics, we have reached a point in our year that we can review all of the content in preparation for algebra 1 next year. First, we will begin with reviewing the different types of numbers that we have encountered. You and your friends decide to go to the movies together. When deciding what to watch, you and your friends might talk about the TYPE of movies you enjoy – comedy, science-fiction, romance, drama, or horror. In math, we talk about the TYPE of numbers we are working with, just as we talk about the TYPE of movies we like to watch. We do this with many things in our lives: music, animals, food, clothing style, and so much more! Let’s talk about different TYPES of numbers. First, when we talk about the TYPE, we are talking about the SET that a number belongs to. From now on, that is the word we will use: SET.

Page 2: 2019-2020 HISD @ H.O.M.E. Project-Based Learning ...€¦ · Activity 1: Write the length of each side of the squares below and find the area. 1 unit 1 ... unit2 Student Thinking:

2019-2020 HISD @ H.O.M.E. – Project-Based Learning

Mathematics – Grade 8

Week of March 30 - April 3, 2020

GLOBAL GRADUATE

- State Process Standard

- Aligned to Upcoming State Readiness Standard

Ⓡ - State Readiness Standard

Ⓢ - State Supporting Standard

© Houston ISD Curriculum 2019-2020

Page 2 of 20

Monday – Rational Numbers

Natural Numbers: Sometimes we call natural numbers, counting numbers. We do this because the Natural Number SET includes all the numbers we learned when we first learned to count: 1, 2, 3, 4, 5, 6, . . . and so on. The Natural Number SET does NOT include 0. Let’s Give It A Try: Identify all the numbers that are included in the Natural Number Set. Put a check under the correct column (either Natural Number or Not a Natural Number).

NUMBERS NATURAL NUMBER NOT A NATURAL NUMBER

43

3

4

12

-516

3

1,075

216

-2

0

1

−1

2

Great work! Let’s talk about the next SET.

Page 3: 2019-2020 HISD @ H.O.M.E. Project-Based Learning ...€¦ · Activity 1: Write the length of each side of the squares below and find the area. 1 unit 1 ... unit2 Student Thinking:

2019-2020 HISD @ H.O.M.E. – Project-Based Learning

Mathematics – Grade 8

Week of March 30 - April 3, 2020

GLOBAL GRADUATE

- State Process Standard

- Aligned to Upcoming State Readiness Standard

Ⓡ - State Readiness Standard

Ⓢ - State Supporting Standard

© Houston ISD Curriculum 2019-2020

Page 3 of 20

Monday – Rational Numbers

Whole Numbers: Whole Numbers INCLUDE all the Natural Numbers, but also INCLUDE 0. This means that Whole Numbers start at 0 and include all the positive counting numbers that we listed earlier: 0, 1, 2, 3, 4, 5, 6, . . . and so on. Notice that Whole Numbers do NOT include negative numbers or numbers that can only be written as a fraction (we’ll get into this later). Let’s Give It A Try: Identify the set that a number belongs to. It can belong to one set, two sets or neither set. Put a check under the correct column showing which set(s) a number belongs to.

NUMBERS NATURAL NUMBER WHOLE NUMEBR NEITHER

43

3

4

12

-516

3

1,075

216

-2

0

1

−1

2

Great work! Let’s talk about the next SET.

Page 4: 2019-2020 HISD @ H.O.M.E. Project-Based Learning ...€¦ · Activity 1: Write the length of each side of the squares below and find the area. 1 unit 1 ... unit2 Student Thinking:

2019-2020 HISD @ H.O.M.E. – Project-Based Learning

Mathematics – Grade 8

Week of March 30 - April 3, 2020

GLOBAL GRADUATE

- State Process Standard

- Aligned to Upcoming State Readiness Standard

Ⓡ - State Readiness Standard

Ⓢ - State Supporting Standard

© Houston ISD Curriculum 2019-2020

Page 4 of 20

Monday – Rational Numbers

Integers: Integers INLUDE all Natural Numbers and Whole Numbers, but also INCLUDE Whole Number’s opposites. When you look in the mirror, you see your reflected image. Look at the number line below. Can you see how negative numbers are a reflection of whole numbers?

Number Lines by HISD Secondary Mathematics using HandyGraph

Let’s Give It A Try: Identify the set that a number belongs to. It can belong to one set, two sets, three sets or none of the sets. Put a check under the correct column showing to which set(s) a number belongs.

NUMBERS NATURAL NUMBER

WHOLE NUMEBR INTEGER NONE

43

3

4

12

-516

3

1,075

216

-2

0

1

−1

2

Great work! Let’s talk about the next SET.

Page 5: 2019-2020 HISD @ H.O.M.E. Project-Based Learning ...€¦ · Activity 1: Write the length of each side of the squares below and find the area. 1 unit 1 ... unit2 Student Thinking:

2019-2020 HISD @ H.O.M.E. – Project-Based Learning

Mathematics – Grade 8

Week of March 30 - April 3, 2020

GLOBAL GRADUATE

- State Process Standard

- Aligned to Upcoming State Readiness Standard

Ⓡ - State Readiness Standard

Ⓢ - State Supporting Standard

© Houston ISD Curriculum 2019-2020

Page 5 of 20

Monday – Rational Numbers

Rational Numbers: Rational Numbers INCLUDE all Natural Numbers (1, 2, 3, 4, 5, 6, . . .), Whole Numbers (0, 1, 2, 3, 4, 5, 6, . . .) and Integers (. . ., -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, . . .). Rational Numbers ALSO INCLUDE numbers that can only be written as a fraction.

For example, the value of a quarter is $0.25, we can also express this value as 1

4. Is there anyway we could write the

value of a quarter without using a decimal or fraction? There is not.

***Sometimes, things can get tricky. What if your math teachers wrote the fraction 8

4 ? There are two circles below, can

you shade in 8

4 ?

Fraction Circles by HISD Secondary Mathematics using MS Word

HINT: Another way to state 8

4 is to say that 8 regions that have been quartered are shaded. In other words, 8 quarters

need to be shaded.

Is there another way to express the number 8

4 ? _______________________________________

Page 6: 2019-2020 HISD @ H.O.M.E. Project-Based Learning ...€¦ · Activity 1: Write the length of each side of the squares below and find the area. 1 unit 1 ... unit2 Student Thinking:

2019-2020 HISD @ H.O.M.E. – Project-Based Learning

Mathematics – Grade 8

Week of March 30 - April 3, 2020

GLOBAL GRADUATE

- State Process Standard

- Aligned to Upcoming State Readiness Standard

Ⓡ - State Readiness Standard

Ⓢ - State Supporting Standard

© Houston ISD Curriculum 2019-2020

Page 6 of 20

Monday – Rational Numbers

If you said, 2, then you are CORRECT! And we know from earlier that 2 is a Natural Number, a Whole Number, an Integer and a now we know it is also a Rational Number. The DIFFERENCE is that it is NOT only a Rational Number. Let’s Give It A Try: Identify the set that a number belongs to. It can belong to one set, two sets, three sets, four sets or none of the sets. Put a check under the correct column showing to which set(s) a number belongs.

Great work!

NUMBERS NATURAL NUMBER

WHOLE NUMEBR

INTEGER RATIONAL NUMBER

NONE

43

3

4

12

-516

3

1,075

216

-2

0

1

−1

2

Page 7: 2019-2020 HISD @ H.O.M.E. Project-Based Learning ...€¦ · Activity 1: Write the length of each side of the squares below and find the area. 1 unit 1 ... unit2 Student Thinking:

2019-2020 HISD @ H.O.M.E. – Project-Based Learning

Mathematics – Grade 8

Week of March 30 - April 3, 2020

GLOBAL GRADUATE

- State Process Standard

- Aligned to Upcoming State Readiness Standard

Ⓡ - State Readiness Standard

Ⓢ - State Supporting Standard

© Houston ISD Curriculum 2019-2020

Page 7 of 20

Monday – Rational Numbers

Summary: Did you notice that Natural Numbers were included in all the sets that you learned about after you first learned about Natural Numbers? Sometimes classifying numbers can make our brain CONFUSED! That is okay, it just takes practice. Here is another diagram to help you think about the set(s) to which a number might belong.

Image from ©HMH Go Math 6-8 with permission

Tuesday – Squared Numbers

Before moving on, let’s talk about squares and square roots. In order to understand the relationship between squares and square roots, let’s first look at inverse operations. Answer the following questions:

1. 3 + 9 = __________ 2. 2 + 8 = __________

3. 6 + 7 = __________ 4. 4 + 5 = __________

As you solve the next 4 questions, think about what you NOTICE about the first set of problems and the second.

5. 12 - 9 = __________ 6. 10 - 8 = __________

7. 13 - 7 = __________ 8. 9 - 5 = __________

Did you notice that the answer to #5 was the same number we started with on #1? Is this true of all the problems you completed? Addition and Subtraction “undo” each other. In mathematics, we call these two operations, “inverse operations.” Can you think of two other inverse operations? Try a few more problems to help you answer this last question.

1. 9 • 5 = __________ 2. 3 • 8 = __________

3. 2 • 6 = __________ 4. 4 • 7 = __________

Page 8: 2019-2020 HISD @ H.O.M.E. Project-Based Learning ...€¦ · Activity 1: Write the length of each side of the squares below and find the area. 1 unit 1 ... unit2 Student Thinking:

2019-2020 HISD @ H.O.M.E. – Project-Based Learning

Mathematics – Grade 8

Week of March 30 - April 3, 2020

GLOBAL GRADUATE

- State Process Standard

- Aligned to Upcoming State Readiness Standard

Ⓡ - State Readiness Standard

Ⓢ - State Supporting Standard

© Houston ISD Curriculum 2019-2020

Page 8 of 20

Tuesday – Squared Numbers

As you solve the next 4 questions, think about what you NOTICE about the first set of problems and the second.

1. 45 ÷ 5 = __________ 2. 24 ÷ 6 = __________

3. 12 ÷ 8 = __________ 4. 28 ÷ 7 = __________

Did you notice that the answer to #5 was the same number we started with on #1? Is this true of all the problems you completed? In your own words, explain what it means when two operations are inverse operations: ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Activity 1: Write the length of each side of the squares below and find the area.

1 unit

1 unit

Area: 1 • 1 = 1 unit2

Area:

Area:

Area:

Page 9: 2019-2020 HISD @ H.O.M.E. Project-Based Learning ...€¦ · Activity 1: Write the length of each side of the squares below and find the area. 1 unit 1 ... unit2 Student Thinking:

2019-2020 HISD @ H.O.M.E. – Project-Based Learning

Mathematics – Grade 8

Week of March 30 - April 3, 2020

GLOBAL GRADUATE

- State Process Standard

- Aligned to Upcoming State Readiness Standard

Ⓡ - State Readiness Standard

Ⓢ - State Supporting Standard

© Houston ISD Curriculum 2019-2020

Page 9 of 20

Tuesday – Squared Numbers

Area:

Area:

Page 10: 2019-2020 HISD @ H.O.M.E. Project-Based Learning ...€¦ · Activity 1: Write the length of each side of the squares below and find the area. 1 unit 1 ... unit2 Student Thinking:

2019-2020 HISD @ H.O.M.E. – Project-Based Learning

Mathematics – Grade 8

Week of March 30 - April 3, 2020

GLOBAL GRADUATE

- State Process Standard

- Aligned to Upcoming State Readiness Standard

Ⓡ - State Readiness Standard

Ⓢ - State Supporting Standard

© Houston ISD Curriculum 2019-2020

Page 10 of 20

Tuesday – Squared Numbers

Let’s record your findings in the table below and extend the information to include squares with side-lengths up to 15.

Side Length Area

1 1 • 1 =

2 2 • 2 =

3 3 • 3 =

4 4 • 4 =

5 ____ • ____ =

6 ____ • ____ =

7 ____ • ____ =

8 ____ • ____ =

9 ____ • ____ =

10 ____ • ____ =

11 ____ • ____ =

12 ____ • ____ =

13 ____ • ____ =

14 ____ • ____ =

15 ____ • ____ =

This is fantastic work! You just found the “square” of the numbers 1 – 15. We represent this operation with an exponent. Here is what it looks like:

72 = 49

Do you think there is an inverse operation that “undoes” the square of a number? ___________ If you said yes, then you are correct! In order to undo the square of a number, we find the square root. Tomorrow, we’ll investigate square roots in more detail.

Page 11: 2019-2020 HISD @ H.O.M.E. Project-Based Learning ...€¦ · Activity 1: Write the length of each side of the squares below and find the area. 1 unit 1 ... unit2 Student Thinking:

2019-2020 HISD @ H.O.M.E. – Project-Based Learning

Mathematics – Grade 8

Week of March 30 - April 3, 2020

GLOBAL GRADUATE

- State Process Standard

- Aligned to Upcoming State Readiness Standard

Ⓡ - State Readiness Standard

Ⓢ - State Supporting Standard

© Houston ISD Curriculum 2019-2020

Page 11 of 20

Wednesday – Square Roots

Look back to Activity 1. Look at the side lengths of each square, that is the square root! Let’s try another activity. Activity 2: Write the side length of each side of the squares below based on the area.

Side Length: 1 unit

Side Length: 2 units

Side Length:

Side Length:

Side Length:

Side Length:

Area

= 1

unit2

Student

Thinking:

1 • 1 = 1

So, the side

length must

be 1.

Area = 4

units2

Student

Thinking:

2 • 2 = 4

So, the side

length must

be 2.

Area = 9

units2

Area = 16 units2

Area = 25 units2 Area = 36 units2

Page 12: 2019-2020 HISD @ H.O.M.E. Project-Based Learning ...€¦ · Activity 1: Write the length of each side of the squares below and find the area. 1 unit 1 ... unit2 Student Thinking:

2019-2020 HISD @ H.O.M.E. – Project-Based Learning

Mathematics – Grade 8

Week of March 30 - April 3, 2020

GLOBAL GRADUATE

- State Process Standard

- Aligned to Upcoming State Readiness Standard

Ⓡ - State Readiness Standard

Ⓢ - State Supporting Standard

© Houston ISD Curriculum 2019-2020

Page 12 of 20

Wednesday – Square Roots

Sometimes, textbooks or teachers ask us to find the side length of a square. They do this by using the square root

symbol √ . Here is an example from the last problem you completed:

√𝟑𝟔 = 6 Complete the table below to show the reverse relationship between squaring a number and finding the square root.

Square Square Root

1 12 = 1 √1 = 1

2 22 = 4 √4 = 2

3 32 = 9 √9 = 3

4 42 = ____ √16 = ____

5 52 = ____ √25 = ____

6 62 = ____ √36 = ____

7 72 = ____ √49 = ____

8 82 = ____ √64 = ____

9 92 = ____ √81 = ____

10 102 = ____ √100 = ____

11 112 = ____ √121 = ____

12 122 = ____ √144 = ____

13 132 = ____ √169 = ____

14 142 = ____ √196 = ____

15 152 = ____ √225 = ____

Page 13: 2019-2020 HISD @ H.O.M.E. Project-Based Learning ...€¦ · Activity 1: Write the length of each side of the squares below and find the area. 1 unit 1 ... unit2 Student Thinking:

2019-2020 HISD @ H.O.M.E. – Project-Based Learning

Mathematics – Grade 8

Week of March 30 - April 3, 2020

GLOBAL GRADUATE

- State Process Standard

- Aligned to Upcoming State Readiness Standard

Ⓡ - State Readiness Standard

Ⓢ - State Supporting Standard

© Houston ISD Curriculum 2019-2020

Page 13 of 20

Wednesday – Square Roots

The answers you found in the middle column are called perfect squares because they are the product (the answer to a multiplication problem) of two whole numbers (You just learned about those!). What if you were trying to find the square root of a number that was not a perfect square? Let’s play mathematician! You are a world-renowned mathematician that has just been given a problem nobody else has been able to solve. Can you figure it out? Problem: How do you find the square root of 78? Can you make a prediction as to what the answer might be? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ If you guessed a number between 8 and 9, you are spot on! There is a way to find the square root of numbers that are not perfect squares. Here’s how: Step 1: Find the two perfect squares that your number is between.

Step 2: Find the square root of the two perfect squares.

Page 14: 2019-2020 HISD @ H.O.M.E. Project-Based Learning ...€¦ · Activity 1: Write the length of each side of the squares below and find the area. 1 unit 1 ... unit2 Student Thinking:

2019-2020 HISD @ H.O.M.E. – Project-Based Learning

Mathematics – Grade 8

Week of March 30 - April 3, 2020

GLOBAL GRADUATE

- State Process Standard

- Aligned to Upcoming State Readiness Standard

Ⓡ - State Readiness Standard

Ⓢ - State Supporting Standard

© Houston ISD Curriculum 2019-2020

Page 14 of 20

Wednesday – Square Roots

Step 3: Determine which perfect square your number is closest to.

Step 4: Your answer will be closer to the square root of that perfect square.

Number Lines by HISD Secondary Mathematics using HandyGraph

Activity 3: Why don’t you give it a try? Find the square root of 20.

1. √20 = _16__ _25__

2. √41 = _____ _____

3. √11 = _____ _____

√64

√64

√64

√64

√64

√64

Page 15: 2019-2020 HISD @ H.O.M.E. Project-Based Learning ...€¦ · Activity 1: Write the length of each side of the squares below and find the area. 1 unit 1 ... unit2 Student Thinking:

2019-2020 HISD @ H.O.M.E. – Project-Based Learning

Mathematics – Grade 8

Week of March 30 - April 3, 2020

GLOBAL GRADUATE

- State Process Standard

- Aligned to Upcoming State Readiness Standard

Ⓡ - State Readiness Standard

Ⓢ - State Supporting Standard

© Houston ISD Curriculum 2019-2020

Page 15 of 20

Wednesday – Square Roots

4. √115 = _____ _____

5. √61 = _____ _____

6. √202 = _____ _____

You need to pat yourself on the back, you have done a lot of really GREAT work!

Number Lines by HISD Secondary Mathematics using HandyGraph

Thursday – Irrational Numbers

Think back to lesson 1, what did you learn about? ______________________________________________________________________________ ______________________________________________________________________________

______________________________________________________________________________

√64

√64

√64

√64

√64

√64

Page 16: 2019-2020 HISD @ H.O.M.E. Project-Based Learning ...€¦ · Activity 1: Write the length of each side of the squares below and find the area. 1 unit 1 ... unit2 Student Thinking:

2019-2020 HISD @ H.O.M.E. – Project-Based Learning

Mathematics – Grade 8

Week of March 30 - April 3, 2020

GLOBAL GRADUATE

- State Process Standard

- Aligned to Upcoming State Readiness Standard

Ⓡ - State Readiness Standard

Ⓢ - State Supporting Standard

© Houston ISD Curriculum 2019-2020

Page 16 of 20

Thursday – Irrational Numbers

If you said that you learned about the different TYPES of numbers, you are correct? Do you remember another name for TYPES of numbers? SETS of numbers, exactly! You are now going to learn about one more SET of numbers, the irrational set. Irrational Numbers cannot be written as any other TYPE of number. You cannot write them as Natural Numbers. You cannot write them as Whole Numbers. You cannot write them as Integers. You cannot write them as a Fraction (Rational Numbers). If I asked you to write 0.25 as a fraction, what would your answer be? ________________

That’s right, 1

4 .

If I asked you to write 0. 33̅̅̅̅ as a fraction, what would your answer be? ________________

That’s right, 1

3 .

There are two things to notice about the two examples above: (1) the first rational number (0.25) is terminating. That means the number does not continue, it stops. (2) the second rational number (0.3333333333333 . . . ) repeats, it creates a pattern. An Irrational Number does NOT terminate or repeat. Can you think of an irrational number that you used when finding the circumference and area of a circle? __________________________

Page 17: 2019-2020 HISD @ H.O.M.E. Project-Based Learning ...€¦ · Activity 1: Write the length of each side of the squares below and find the area. 1 unit 1 ... unit2 Student Thinking:

2019-2020 HISD @ H.O.M.E. – Project-Based Learning

Mathematics – Grade 8

Week of March 30 - April 3, 2020

GLOBAL GRADUATE

- State Process Standard

- Aligned to Upcoming State Readiness Standard

Ⓡ - State Readiness Standard

Ⓢ - State Supporting Standard

© Houston ISD Curriculum 2019-2020

Page 17 of 20

Thursday – Irrational Numbers

If you said pi, you are absolute right! Pi is famous because its numbers go on FOREVER! They don’t ever repeat, and they don’t ever end. This is why pi is an Irrational Number. Many square roots are also irrational numbers, but not when they are perfect squares. Let’s take a look at t a few examples:

1. √49 = 7

7 is a Natural Number, Whole Number, Integer and Rational Number. So, √49 is NOT an Irrational Number.

2. √29 = 5.385164807134504 . . .

The answer does not end and does not repeat. So √29 IS an Irrational Number.

Let’s Give It A Try: Identify the set that a number belongs to. It can belong to one set, two sets, three sets, or four sets. Put a check under the correct column showing to which set(s) a number belongs.

NUMBERS NATURAL NUMBER

WHOLE NUMEBR

INTEGER RATIONAL NUMBER

IRRATIONAL NUMBER

43

3

4

12

-516

3

1,075

216

-2

0

1

−1

2

√144

√38

√175

Great work!

Page 18: 2019-2020 HISD @ H.O.M.E. Project-Based Learning ...€¦ · Activity 1: Write the length of each side of the squares below and find the area. 1 unit 1 ... unit2 Student Thinking:

2019-2020 HISD @ H.O.M.E. – Project-Based Learning

Mathematics – Grade 8

Week of March 30 - April 3, 2020

GLOBAL GRADUATE

- State Process Standard

- Aligned to Upcoming State Readiness Standard

Ⓡ - State Readiness Standard

Ⓢ - State Supporting Standard

© Houston ISD Curriculum 2019-2020

Page 18 of 20

Thursday – Irrational Numbers

Here is a diagram to help you think about the set(s) that a number might belong to. This time, it includes Irrational Numbers. Notice that the 5 sets: Natural Numbers, Whole Numbers, Integers, Rational Numbers, and Irrational Numbers are all part of the set of the Real Number System. You’ll learn more about Real Numbers (and Imaginary Numbers!) in high school.

Image from ©HMH Go Math 6-8 with permission

Friday – Portfolio Performance Task

Are you ready to show mastery? You got this!

1. Write the decimal that equals the fraction 3

8 . _________________________

2. Which of these shows a repeating decimal?

a. 5.6 b. 5

6

10 c. 5.6̅ d. 0.56

3. Which number is not the square of a whole number?

a. 100 b. 800 c. 400 d. 900

4. A garden has an area of 9 square meters. Each square is 1 square meter. What is the

length of one side of this garden? _________________________________

5. Between which two whole numbers is the square root of 18? _________ and ________

Page 19: 2019-2020 HISD @ H.O.M.E. Project-Based Learning ...€¦ · Activity 1: Write the length of each side of the squares below and find the area. 1 unit 1 ... unit2 Student Thinking:

2019-2020 HISD @ H.O.M.E. – Project-Based Learning

Mathematics – Grade 8

Week of March 30 - April 3, 2020

GLOBAL GRADUATE

- State Process Standard

- Aligned to Upcoming State Readiness Standard

Ⓡ - State Readiness Standard

Ⓢ - State Supporting Standard

© Houston ISD Curriculum 2019-2020

Page 19 of 20

Friday – Portfolio Performance Task

6. Which of these integers is not a whole number?

a. -6 b. 0 c. 6 d. 66

7. A teacher divides a class of students into 3 groups of the same size. Write the set(s) that describes the number

of students in each group.

_____________________________________________________________________________

_____________________________________________________________________________

8. The diagram shows sets of numbers. Which set equals set A?

a. Natural Numbers

b. Whole Numbers

c. Rational Numbers

d. Irrational Numbers

9. Which of these cannot be a whole number?

a. A positive

integer b. A negative

integer c. A rational

number

10. Which number is between 61

2 and √64

a. 6.25 b. √68 c. 8.16 d.

71

2

Page 20: 2019-2020 HISD @ H.O.M.E. Project-Based Learning ...€¦ · Activity 1: Write the length of each side of the squares below and find the area. 1 unit 1 ... unit2 Student Thinking:

2019-2020 HISD @ H.O.M.E. – Project-Based Learning

Mathematics – Grade 8

Week of March 30 - April 3, 2020

GLOBAL GRADUATE

- State Process Standard

- Aligned to Upcoming State Readiness Standard

Ⓡ - State Readiness Standard

Ⓢ - State Supporting Standard

© Houston ISD Curriculum 2019-2020

Page 20 of 20

Friday – Portfolio Performance Task

11. Classify each number

NUMBERS NATURAL NUMBER

WHOLE NUMEBR

INTEGER RATIONAL NUMBER

IRRATIONAL NUMBER

3.25

6

2

25

√25

-25

√22

−1

6

1

6

0

89

pi

12. Create a Venn Diagram or other type of illustration that explains your understanding of how numbers are classified. The figure must demonstrate the relationships between natural numbers, whole numbers, integers, rational numbers, and irrational numbers.

For instance, the representation must be able to show how a number such as “2” is a member of natural numbers, whole numbers, integers, and rational numbers … but not irrational numbers. This representation must include:

• An illustration, figure, diagram

• Explanation of how the relationships are depicted

• A justification for how two example numbers would be placed into the representation Alternative Option/Extension for #12: Create a game to illustrate the relationship between types of numbers. The same three characteristics must be included in the game.

Problems 1-10 from ©HMH Go Math 6-8 with permission

Student-Produced Weekly Product

Student successfully completes the portfolio task that includes a demonstration of their understanding for how to classify types of numbers and an illustration of how the types of numbers are related to each other.


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