Extending the number system Block 1 Student Activity Sheet · 2018-09-01 · Student: Class: Date: Extending the number system Block 3 Student Activity Sheet Copyright 2016 Agile

Student: Class: Date:

Extending the number system Block 1 Student Activity Sheet

Copyright 2016 Agile Mind, Inc. ® Content copyright 2016 Charles A. Dana Center, The University of Texas at Austin

Page 1 of 5 With space for student work

1. Draw a line of symmetry through zero. Then create a reflection by folding your paper. Label the rest of your number line.

2. Investigate a variety of contexts where integers are used.

a. Consider Archibald’s account balances. How can you

tell when Archibald is in debt? What does zero mean in this context?

b. On which date did Archibald have the greatest balance?

c. On which date did Archibald have the greatest debt?

Date Balance October 1 $12 October 2 $23 October 5 $-5 October 7 $0 October 8 $10 October 10 $-27 October 12 $4 October 14 $-3





d. Consider the Fahrenheit thermometer. What does zero mean in this context?

e. Integers are also used to describe altitude or distance from sea level. What does zero represent in this context?

f. Estimate the altitude of the plane and the submarine.





Lake levels rise and fall depending upon the amount of rain. Lake Travis is considered "full pool" when its depth is 681 feet. The table shows lake level measurements in feet for Lake Travis for 6 different months.

Lake Level Measurements for Lake Travis (in feet)

January 2010

April 2010

July 2010

October 2010

February 2011

May 2011

679 686 681 678 675 672

3. Use words to describe how each month’s lake level compares to the "full REINFORCE

pool" level. Follow the example given.

Month Description

January 2010 2 feet below full pool

a. April 2010

b. July 2010

c. October 2010

d. February 2011

e. May 2011





4. Consider the Lake Travis lake level measurements again. Use an integer to REINFORCEdescribe each month’s lake level measurement in relation to the "full pool" level. Then locate and label this integer on the number line.

5. Beth is an art appraiser. She appraises each piece of art and assigns a value REINFORCEfor what she believes the art is worth. When the art is sold, she compares the selling price to her appraisal value and notes any price differences in a table like this one.

Art work Price difference in dollars

Impressionist painting 4000

Watercolor -575

Abstract painting -4500

Modern sculpture -1800

Still life 1200

Bronze statue 900

Portrait 3750

a. What does a negative value mean in this context?

b. What does a positive value indicate?





c. What would a value of 0 indicate in this situation?

d. Which item’s selling price was closest to its appraisal value?

e. Which item’s selling price was farthest from its appraisal value?





1. On the number line, show the location of each of these values.





2. Draw a Venn diagram to represent how rational numbers, integers, and whole numbers are related. Include examples of each type of number in your diagram.

3. Reflect on what you are learning about absolute value.

a. In your own words, write a description of absolute value. Give a few examples using

absolute value notation.

b. If two different numbers have the same absolute value, what must be true about the two numbers?





4. Locate and label each rational number on the number line. REINFORCE

−0.85 1

210

−1

56

1.37 −2

18

− 3

8 1.45

179





1. You can use equality and inequality symbols to represent comparisons of rational

numbers.

Symbol In words Example in symbols In words < Less than 5 < 9 5 is less than 9 > Greater than 12 > -15 12 is greater than -15

= equal 3.5 = 312

3.5 is equal to 312

a. Comparisons are used in a variety of contexts. Study the examples in the table. Then

write some of your own and discuss them with a partner. Remember to use different kinds of rational numbers: positive, negative, whole numbers, fractions, and decimals.

Example in symbols Possible context and meaning $5 < $9 $5 is less money than $9.

-12 °F > - 20 ° F -12 °F is warmer than - 20 ° F.

-200.8 meters < -20 meters -200.8 meters is further below sea level than 20 meters.





b. Fill in the blanks to form true mathematical statements.

c. Translate this pair of statements by replacing the symbols with words. How do they compare?

-4 < -1 -1 > -4





2. Fill in the blanks to make true statements.

distance integers fractions negative opposites positive decimal absolute value ratio

Integers are the set of whole numbers and their ____________. Rational numbers are numbers that can be written as a ____________, where the

denominator is not zero. Rational numbers are the set of numbers that include

____________, and both ____________ and ____________ fractions. Every

fraction can also be written as a ratio and as a ____________.

The ____________ of a number is its ____________ from zero.

3. Ms. Smith assigns seats in math class by having students sit in numerical REINFORCEorder. Students randomly draw a number card and then seat themselves in numerical order from least to greatest. Six students drew the cards shown. Write the students’ names in the empty boxes to show the correct seating assignment.

Allen -1.99

Beatrice |2.3|

Cathy -2.02

Ella |-2|

Daniel

Frankie





4. Fill in the blanks to make true mathematical statements. REINFORCE

Using symbols < , > or =

Using words Less than, greater than, or equal to

a. −23

25

−23

15

−23

25

−23

15

b. |−5.23| −|5.23| |−5.23| −|5.23|

c. 3

18

3.18 3

18

3.18

d. |−5| |−7| |−5| |−7|

e. −0.02 −0.019 −0.02 −0.019





1. Label the x-axis, the y-axis, and the origin on the coordinate plane.

2. Give the coordinates for each location shown on the coordinate plane.





3. Give the coordinates for each point. REINFORCE

A ________ F ________

B ________ G ________

C ________ H ________

D ________ I ________

E ________ J ________





1. Study the coordinate plane. Find what is located at each of the following coordinates.

a. What is located at (6,0)? b. What is located at (-7,-4)? c. What is located at (0,0)? d. What is located at (-6,8)?

e. What is located at (6,8)?





2. Fill in the table to describe the sign of the x- and y–coordinates of a point in each quadrant.

Quadrant number x-coordinate y-coordinate

I

II

III

IV





3. Graph the following coordinate pairs in the coordinate plane provided.

! (−0.75,1.4) !

234,−2

14

⎛⎝⎜

⎞⎠⎟ ! −1.9,−0.75( )

! 94,1.25

⎛⎝⎜

⎞⎠⎟





4. REINFORCE Follow the steps to represent this table of data in a coordinate graph.

Point a Point b Point c Point d Point e

x

34

-1.75 − 1

2 2.25 -2.5

y 5 4

12

−3.5 −1

12

2

34

a. Label the x-axis on the graph below. What scale did you use and why?

b. Label the y-axis on the graph below. What scale did you use and why?





c. Plot and label each point.





5. REINFORCE For each graph, give the scale used on the x-axis and the y-axis. Hint: What is the value between each grid line?

a.

b.

x-axis scale:__________ y-axis scale:__________


c.

d.







1. Follow the directions to create a figure on the coordinate plane. Pay REINFORCEattention to the scale when you number your axes.

a. Label and number the axes.

(Scale = 10) Plot the following points and connect them as you go.

A (35,90) B (85,35) C (85,−35) D (35,−90) E (−35,−90) F (−85,−35) G (−85,35) H (−35,90) J (35,90)





b. Label and number the axes.

(Scale = 14

)

Plot the following points and connect them as you go.

A (0,112

)

B (34

,14

)

C (212

,14

)

D (1,− 34

)

E (134

,−214

)

F (0,−112

)

G (−134

,−214

)

H (−1,− 34

)

J (−212

,14

)

K (− 34

,14

)

L (0,112

)





2. Number each axis with a scale of 1. Then list the coordinates for each point REINFORCEin the figure.

A.

B. C.

D. E.

F. G.

H. I.

J. K.

L. M.

N. O.

P. Q.

R. S.

T. U.

V. W.

X.

What do you notice about the drawing or the coordinates? How are the points related in the quadrants?





3. Follow the directions to create a figure on the coordinate plane. Pay REINFORCEattention to the scale when you number your axes.

a. Label and number the axes. (Scale = 1 unit)

b. Plot each set of points and connect with a line. Start with a new line for each new set of points.

Set 1 Set 2 Set 3 Set 4

Start (4, 3

12

)

(3,6) (2,4) (−3,2.5) (−4,4) (−4.5,2) (-4,-3)

( −1

12

,−4)

(4, −2) (4,3.5) stop

Start (−1,0) (−1,1.5) (−2.5,1.5) (−1,0) stop

Start (

12

,0)

(

12

, 112

)

( 112

, 112

)

(

12

,0) stop

Start (−1, −1)

(0, −1

12

)

(1, −1) (−1, −1) done





4. Follow the directions to create the first letter of your name on the REINFORCE coordinate plane.

a. Draw the first letter of your name on the grid using straight-line segments only. You

may use either first or last name.

b. Label the axes on the grid. (Scale =

12

)

c. For each endpoint in your letter design, write a set of coordinates that could be used to re-create your letter.





1. Plot a point on the coordinate plane and then reflect the point across the y-axis. Label the coordinates of each point. Compare your reflection with a partner.

2. Using a different color, graph another point and then reflect the point across the x-axis.

Label the coordinates of each point. Compare your reflection with a partner.





3. Graph another point and then reflect the point across the x-axis. Label the coordinates of each point. Then reflect the reflected point across the y-axis. Compare your reflection with a partner.

4. Here are two pairs of points. Have the points been reflected across the x-axis or the

y-axis?

a. Original coordinates: (−13,−7) Reflected coordinates: (13,−7)

b. Original coordinates: (6,−8) Reflected coordinates: (6,8)

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Extending the number system Block 1 Student Activity Sheet · 2018-09-01 · Student: Class: Date: Extending the number system Block 3 Student Activity Sheet Copyright 2016 Agile