Find the Four digit number

1

On separate sticky notes write the digits 0 – 9.

A special four-digit number has the following traits:

•All the digits are different•The digit in the thousands place is 3 times the digit in the tens place.•The number is odd.•The sum of the digits is 27.

What is the special four-digit number?

Handout 3NCTM (2006). Mathematics Teaching in the Middle School, Volume 11, number 6.

2

EXPRESSIONS for 10:

5 + 5 12 – 2 2 X 5 30 ÷ 3

1 x 6 + 4 8 + 6 ÷ 3 20 ÷ 4 + 5

EQUATIONS equaling 10: 5 + 5=10 12 – 2=10 2 x 5=10 30 ÷ 3=10

1 x 6 + 4=10 8 + 6 ÷ 3=10 20 ÷ 4 + 5=10

Write expressions representing 10.

BALANCED EQUATIONS: 5 + 5 = 12 – 2 2 x 5 = 30 ÷ 3

1 x 6 + 4 = 8 + 6 ÷ 3 20 ÷ 4 + 5 = 5 + 5

Write equations equaling 10.

Use the above to write balanced equations.

3

1 X 6 + 4 8 + 6 ÷ 3=

Use number and operation tiles to build “Balanced

Equation Puzzles”

-

6 1+

6

= 1

3

24

2 x 3+

0

=

2(6= 1+6 0

Separate the number tiles from the operation tiles. Draw 6 numbers and 2 operations. Put down an equation or draw until an equation is possible.

88

5

2

=

7

SLE….NO. 2.7.2, 2.7.3, 3.7.2, 2.8.1, 2.8.4, 3.8.2

÷

÷

1

1

Draw to replace the tiles played. If no tiles are played draw a tile from either pile and advance to the next person.

)

Handout 4

4

5

NUMBER & OPERATION GAME BOARD WHEN USING PAPER TILES…FOR EVERY 2 to 4 PLAYERS. PRINT 4 PAGES, PUT TOGETHER AND LAMINATE. (Handout 4)

6

Copy this grid paper for teams to write down their puzzle to be turned in to the teacher.. (Handout 4)

ALGEBRA…. Decisions, Decisions, Decisions

Dear Bill,

Today is my 55th birthday. I have decided to give away some of my money each year to my relatives. You may choose one of the following options:

Option 1: $100 dollars now, $90 next year, then $80 the year after, and so on.Option 2: $10 dollars now, $20 next year, then $30 the year after, and so on.Option 3: $1 now, $2 next year, $4 the year after and so on doubling each year.You will only receive money until I retire.Write to me soon and tell me how you want your money.

With Love,Aunt Judy

7Handout 5

8

Decis

ion

s, D

ecis

ion

s, D

ecis

ion

s D

ear B

ill, Tod

ay is m

y 5

5th b

irthday. I h

ave d

ecid

ed to

giv

e a

way so

me o

f my m

oney

each

year to

my re

lativ

es. Y

ou m

ay ch

oose

one o

f the fo

llow

ing o

ptio

ns:

 Op

tion 1

: $100

dolla

rs now

, $90 n

ext y

ear, th

en $

80 th

e y

ear a

fter, a

nd so

on

. O

ptio

n 2

: $10 d

olla

rs now

, $2

0 n

ext y

ear, th

en $

30

the y

ear a

fter, a

nd so

on.

 Op

tion 3

: $1 n

ow

, $2 n

ext y

ear, $

4 th

e y

ear a

fter a

nd so

on d

oublin

g e

ach

year.

 You

will o

nly

rece

ive m

on

ey u

ntil I re

tire.

 Write

to m

e so

on a

nd te

ll me h

ow

you w

ant y

ou

r money.

With

Love,

Aunt Ju

dy

   1. B

ill starts to

figure

out h

ow

much

he w

ill rece

ive fro

m th

e th

ree o

ptio

ns.

If Judy re

tires a

t age 5

9 w

hich

optio

n d

o y

ou th

ink B

ill should

choose

? Ju

stify y

ou

r answ

er.

     2. B

ill thin

ks that h

is Aunt Ju

dy is lik

ely

to w

ait u

ntil sh

e is 6

5 y

ears o

ld to

re

tire. W

hat is h

is best ch

oice

optio

n fo

r her re

tirem

en

t at a

ge 6

5? Ju

stify y

our

answ

er

     3. S

ince

Bill is n

ot su

re w

hat a

ge A

unt Ju

dy w

ill retire

, how

do y

ou th

ink B

ill sh

ou

ld re

ply

to A

unt Ju

dy’s le

tter? E

xp

lain

clearly

which

optio

n y

ou th

ink B

ill sh

ou

ld ch

oose

. Show

your re

aso

nin

g.

Nam

e: _________________________________

BULGING BACKPACKS

• Students will estimate the weight of his/her backpack, record this number

• Everyone estimates the weights of three chosen students• Weigh the chosen backpacks• Graph the actual weight vs. estimate

9Handout 8Lesson’s For Algebraic Thinking, Grades 6-8, Marilyn Burns, Math Solutions

What should a person know by looking at the points and lines you added later to your scatter plot?

What are the main things you learned from this activity?

Some questions to ponder…

10

Calculator Instructions for TI 84 To clear data in all lists:Press 2nd MEM.Choose ClrAllLists.Press Enter.Press Enter. You will see DONEPress 2nd MEM.Choose 7 – ResetChoose 2 – DefaultChoose 2 - Reset. Enter your data in lists:Press STAT.Press Enter.Enter the estimates in L1. Press ENTER after each number.Enter actual weights in L2. Press ENTER after each number.

11

To create a scatter plot: Press 2nd Y= (STAT PLOT).Press ENTER for Plot 1.Press ENTER for On.Arrow down to Type: Press ENTER for Scatter Plot.Arrow down to Xlist: Press 2nd STAT and choose L1.

Arrow down to Ylist: Press 2nd STAT and choose L2.

Arrow down to Mark: Press ENTER for the box.Press WINDOW. Set the appropriate window for this problem.Press TRACE and use the right and left arrow keys.

12

 To create two box-and-whisker plots: Press 2nd Y= (STAT PLOT).Press ENTER for Plot 1.Press ENTER for On.Arrow down to Type: Press ENTER on the box and whisker icon.Arrow down to Xlist: Press 2nd STAT and choose L1.

Press ENTER.Set Freq to 1.Press WINDOW.Set the appropriate window for this problem.Press TRACE and use the right and left arrow keys to see the values for each quartile. Repeat steps 1-7 choose Plot 2 and L2 .

Some questions to ponder…

• What should a person know by looking at the points and lines you added later to your scatter plot?

• What are the main things you learned from this activity?

13

14

BULGING BACKPACKS Overview: Students will estimate and find the actual weight for each of their backpacks. The class constructs a scatter plot to display some of the data; then each student creates a personal scatter plot. This lesson gives students experience plotting points on a Cartesian plane and interpreting those points in terms of a real-world situation. The function y=x is used to describe the meaning for points above and below this line. With numerous similar experiences, students develop an intuitive understanding of function and correlation. Prerequisite Concepts and Vocabulary:Finding explicit and recursive rules for patternsGraphing pointsScaling axes for specific dataUnderstanding the vocabulary function, scatter plot, coordinate, variable, and axis Time: This lesson takes approximately 90 minutes.  Materials: Bathroom scalesStudent backpacksLarge sheet of graph paper for class scatter plot 1 sheet of graph paper per student Graphing Calculator (optional) 

15

BULGING BACKPACKSLesson Plan:Discuss plan with the classEach student makes a table and records his or her own data (Table included).Students make estimates for only three backpacks, then find their actual weight, to help students get some general idea of how much backpacks weigh.Students use the bathroom scale to weigh each of the backpacks to the nearest half-pound.For the class data have each student record their estimate and actual weight on a table on the board.Label the x-axis actual weight and the y-axis estimates.(This allows us to talk about the points above the line y=x being overestimated and the points below being underestimated as well as anyone on the line as being perfect)Next assign the individual scatter plots for their estimates of all backpacks. The next three can be done as a class on the class scatter plot or assigned for each individual to write about.Draw the function y=x+2 and discuss what that tells us.Draw the function y=x-3 and discuss what that tells us.Draw the function y= 7 and discuss what that tells us. Extension Using the graphing calculator, create a box and whisker plot for estimates in Plot 1 and another box and whisker plot in Plot 2.Display both plots in the same window.Discuss the differences in the range of the estimates and the actual weights.Check for outliers and compare the statistics for estimates and actual weights using the trace feature of the calculator. Adapted from: Lawrence, Ann, and Charlie Hennessy. Lessons for Algebraic Thinking, Grades 6-8. Math Solutions Publications, 2002.

16

Name Actual Weight Estimate

Name: _____________________________

BULGING BACKPACKS…STUDENT WORKSHEET

How much

does each shape

weigh? Explain.

From Teaching Student Centered MathematicsP. 280 17

1.

2.

Most weight is the cylinder; least weight is the cube

2 spheres = 1 cylinder….and 3 cubes = 1 sphere….therefore 6 cubes = 1 cylinder

1 cube = 2 cylinders …so… 1 cube + 1 cylinder = 3 cylinders3 cylinders = 6 spheres…therefore 1 cylinder = 2 spheres

Handout 9

What will balance two spheres? Explain.

From Teaching Student Centered MathematicsP. 280

18

3.

4.

5.

1 cylinder + 1 cube = 13 2 spheres + (1 cylinder + 1 cube) = 21

Use substitution: 2 spheres + 13 = 21, 2 spheres = 8, 1 spheres = 4.

1 cube + 2 spheres = 14, 1 cube + 8 = 14, 1 cube = 6.

1 cylinder + 6 = 13, 1 cylinder = 7.

2 cubes + 1 sphere = 8 and 3 spheres = 12 therefore 1 sphere = 4 2 cubes + 4 = 8, 2 cubes =4, 1 cube = 2

Equation 1: 1 sphere + 1 cylinder = 7 Equation 2: 1 sphere + 1 cube = 6Since 7 is one more than 6 and the spheres are the same, then 1 cylinder = 1

cube + 1 Equation 3: 1 cylinder + 1 cube = 6 Substitute: (1 cube + 1) + 1 cube =

6, 2 cubes + 1 = 9, 2 cubes =8, Therefore 1 cube = 4 Equation 2 Substitute: 1 sphere + 4 = 6, 1 sphere = 2

Equation 1 Substitute: 2 + 1 cylinder = 7, 1 cylinder = 5

How much

does each shape

weigh? Explain.

From Teaching Student Centered MathematicsP. 280 19

1.

2.

Handout 9

What will balance two spheres? Explain.

Name: _______________________________________Student Worksheet

From Teaching Student Centered MathematicsP. 280

20

3.

4.

5.

Arkansas Benchmark Questions

7th grade 2007

21Handout 10

8th grade 2007

7th grade Open Response 2007

22

1. 3x + 2x + x=1802. 3x + 2x + x=180

6x = 180 6x = 180

6 6 x = 30

3. Angle x = 300

Angle 2x = 2(30) = 600

Angle 3x = 3(30) = 900

23

Pam and Greg are each building a pyramid of tiles. The number of tiles needed is represented by the rule , where n is the number of levels in the pyramid. The pattern for the pyramid is shown below.

8th grade Open Response

1. Draw the next pattern in the sequence.

2. How manytiles would be in a 10-level pyramid? Show your work.

3. Greg has 4-inchtiles, and Pam has 2-inchtiles. They are each going to build a 24-inch tall pyramid. Greg predicts he will need half as many tiles as Pam since his tiles are twice as large. Compare the pyramids to see why Greg is incorrect.

n(n+1) 2

55

See handout 10

See handout 10

24

Consumable Handout 11

Grade 7

25

26

27

Grade 7

Grade 7

28

Grade 8

29

30

31

Grade 8

Grade 8

*