Sec1 Mod1 Getready Tnh 81313

8/13/2019 Sec1 Mod1 Getready Tnh 81313

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Secondary One Mathematics:

An Integrated Approach

Module 1 HonorsGetting Ready

By

The Mathematics Vision Project:

Scott Hendrickson, Joleigh Honey,

Barbara Kuehl, Travis Lemon, Janet Sutoriuswww.mathematicsvisionproject.org

In partnership with the

Utah State Office of Education

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Name: Getting Ready 1.2

© 2012 Mathematics Vision Project | M P

In partnership with the Utah State Office of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.

Ready, Set, Go!

ReadySolve the following equations for the unknown variable.

1. ( ) 2. 3.

4.

5.

6. ( )

Set

For the growing pattern below, each line segment is one unit in length.

7. How much total perimeter in Step 5? Step 6? (Remember to focus on the perimeter.)

8. How can you determine the amount of perimeter in Step 25?

9. Write a rule to predict the total amount of perimeter for any step. Show how your rule relates to

the pattern.

10. Marsha also solved this problem and came up with following expression: 1 + 5n -(n-1). How does

each piece of her expression show up in the pattern?

11. Tyler came up with the expression 6n – 2(n-1). How does each piece of his expression show up in

the pattern?

Step 1 Step 2 Step 3

© 2012 /www.flickr.com/photos/laurenmanning

9

Getting Ready 9





In partnership with the Utah State Office of EducationLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.

Go

For problems 12 and 13, the y-intercept and the slope of a line are given. Graph the line on the

coordinate axes, clearly labeling the slope and y-intercept.

12. (0, 2); m =

13. (0, -3); m = 4

The equations below are represented in the above graphs. Explain how the slope and y-intercept

show up in both the graph and algebraic representations.

y =

x + 2 y = 4x – 3

For problems 14-16, graph the following equations on the provided coordinate axes.

14. y = 2x-1 15. y =

x +2 16. y = -3x + 5

Need Help? Check out these related videos:

http://www.khanacademy.org/math/algebra/solving-linear-equations/v/solving-equations-1

http://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/v/graphing-a-line-in-slope-intercept-form

http://www.youtube.com/watch?v=WXzpisUh0AU

10

Getting Ready 10












In partnership with the Utah State Office of Education

Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license

1.3 Serving Up Symbols A Develop Understanding Task

As you look around your school cafeteria, you may see many

things that could be counted or measured. To increase theefficiency of the cafeteria, the cafeteria manager, Elvira, decided to take a close look at the

management of the cafeteria and think about all the components that affect the way the cafeteria

runs. To make it easy, she assigned symbols for each count or measurement that she wanted to

consider, and made the following table:

Symbol Meaning(description of what the symbol means in context)

Units(what is counted or measured)

S Number of students that buy lunch in the

cafeteria each daystudents or

studentsday

S M Number of students who have passed

through a line in M minutesC Number of classes per lunch period

P Number of lunch periods per day

B Number of boys that buy lunch each day boys or students or

boysday

G Number of girls that buy lunch each day

F Number of food servers in the cafeteria

T Total number of food items in one lunch

(Each entrée, side dish, or beverage counts as

1 item.)

M Number of minutes passed since the

beginning of the lunch period

N e Number of entrees in each lunch

N s Number of side dishes in each lunch

N b Number of beverages in each lunch

C e Cost of each entrée

C s Cost of each side dish

C b Cost of each beverage

L Number of lines in the cafeteria

W The number of food servers per line

i Average number of food items that a server

can serve each minute (Each entrée, side dish,or beverage counts as 1 item.)

H Number of hours each food server works

each day

P L Price per lunch

2 0 1 2

. f l i c k r . c o

/ p h o t o s / s p e c i a l k r b

11

Getting Ready 11






Using the given symbols, it is possible to write many different algebraic expressions.

1. Using these symbols, what would the expression

mean?

2. Using these symbols, what would the expression S + F + L mean?

Elvira hopes to use the symbols in the chart to come up with some meaningful expressions that will

allow her to analyze her cafeteria. Your job is to help her by writing as many expressions as you

can and describe what they mean. Put each of your expressions in the following chart, adding lines

if you need to:

Expression Description

Write an expression for the average number of lunches served in a line each day.

Write an expression for the total price of the items served in a line.

12

Getting Ready 12






1.3 Serving Up Symbols – Teacher Notes A Develop Understanding Task

Purpose: The purpose of the task is to develop understanding of the use of variables given a story

context. Students are asked to interpret expressions written with variables, which will open upstrategies for using units to analyze expressions. Students will also combine variables to make

meaningful expressions and describe the meaning of the expressions they have written.

In mathematics, things we can count or measure are referred to as “quantities”. The references we

use to count or measure those things are called “units”. When modeling a situation mathematically,

two questions that generally arise are “What are we going to count or measure,” and “What units

will we use to count or measure those things?” In this task, students work with quantities and

units.

Core Standards:

A.SSE.1 Interpret expressions that represent a quantity in terms of its context.a. Interpret parts of an expression, such as terms, factors, and coefficients.

b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For

example, interpret P(1+r)n as the product of P and a factor not depending on P.

N.Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems;

choose and interpret units consistently in formulas.

Launch (Whole Class): Start by familiarizing students with the context of the problem. Before

giving the task to students, ask them to think of some of the things that could be counted or

measured in the cafeteria. Hand out the task and ask them to read through the list of variables

identified by the cafeteria manager to see if they can find the things that they thought of. You mayneed to explain the use of subscripts for some of the variables, since many students may not have

used them previously. Have students consider the units they might use to count or measure the

quantities being described, and have them enter these units in the third column of the chart. Note

that the given examples suggest that we can change units on a quantity if it is helpful in thinking

about computation. For example, “boys that each lunch in the cafeteria each day” could be

measured in units such as: boys/day, boys or students.

Introduce students to the idea that variables can be combined to make meaningful expressions.

Using question #1, ask students what the expression

means. Help students to break down the

various parts of the expression. In this case, G + B represents the number of students that eat lunchin the cafeteria each day. Since C represents the number of classes per lunch period and P

represents the number of lunch periods, C × P represents the number of classes and the expression

represents the average number of students served lunches per class.






Give students a few minutes to think individually about the meaning of #2, S + F + L. After they

have translated each of the variables, ask what they believe the sum of these expressions means.

They should recognize that the expression formed by adding these variables doesn’t make sense.

Introduce their task, which is to write as many meaningful expressions as they can. As they have

seen in #2, they must be careful to combine the variables with operations that make sense in thecontext.

Explore (Small Group or Pairs): Assign students to work on the remainder of the task. Monitor

their work, pressing students to make sense of each expression they write. Encourage students to

use as many of the variables as they can in their expressions. Be prepared to record interesting

expressions and their descriptions so that they can be used later in the discussion.

Discuss (Whole Group): Using the expressions that students have written, facilitate the first part

of the discussion by giving several expression, one at a time, and asking the whole class to interpret

them. Switch to giving the students several descriptions that student have written and see if the

class can come up with an expression that goes with it. Ask students to volunteer the mostcomplicated meaningful expression they could create.

Close the discussion with the last two questions. There may be several different expressions for

each of the questions. If this occurs, ask students if the expressions are equivalent, and how they

know.

Aligned Ready, Set, Go: Getting Ready 1.3







Ready, Set, Go!

Ready

Topic: Evaluating Expressions

Evaluate the following expressions for .

1. 2a + 3b 2. 4c + d

3. 5ac – 2b 4.

5.

6.

The equation represents the cost in dollars (c) of producing remote controls

(r).

7. What is the cost of producing 1000 remote controls?



©2012 www.flickr.com/photos/specialkrb

13

Getting Ready 13







Set

Solve each equation, justifying each step you use.

10. 11.

12. 13.

14. 15.

x – 10 = 2 Justification3 x = 15 Justification

– 16 = x + 11 Justification6 – x = 10 Justification

6 x + 3 = 15 Justification 3 x – 10 = 2 Justification

14

Getting Ready 14







Go

Graph the following equations on the provided coordinate grids.

16.

17. 18.

19.

20. 21.

22. 23. 24.

Need Help? Check out these related videos:




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15

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50

Getting Ready 50





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-$""'. &'()*+) ,')$

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team—

Definitely not enough!

-$""'. &'()*+) ,')$

Ordered 5 dozen cookiesfor the drama club—

I really like those kids!

-$""'. &'()*+) ,')$

Ordered 4 gallons of

drinks for the soccer

team—Warned them not to

repeat last year’s prank!

-$""'. &'()*+) ,')$


drinks for the drama

club—drinks were gone

long before the chips

-$""'. &'()*+) ,')$

Ordered 7 dozen cookies

for the soccer team—

Should I have ordered

more?

-$""'. &'()*+) ,')$

Ordered 12 packages of

chips for the drama club—

Sent extra home with kids



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team—My neighbor is on

the team!

&/01 &'()*+) ,')$

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They talked a lot with fake

accents

&/01 &'()*+) ,')$


for the drama club—Too

much drama, too little

character!

&/01 &'()*+) ,')$


for the soccer team—

slipped a few extra to my

neighbor.

&/01 &'()*+) ,')$


drinks for the soccer

team—Watched the

players like a hawk!

&/01 &'()*+) ,')$


drinks for the drama

club—

Seemed about right



Getting Ready 1.11H

© 2012 Salt Lake City School District | M P



Ready, Set, Go!

Ready

Topic: Ratios, Proportions and making predictions

The table below shows how Marco spends his time on a

typical day. Use the table to answer the questions below.

ActivityHours Spent per

DayHours Spent per

WeekHours Spent per

Month

Exercise 1

Watch TV 2Reading .75

Math 1.5Household Chores 1.75

Other Schoolwork 3Video games .5

Talk with Friends 2

Eating 1.5

Sleeping 10

1. What fraction of a day does Marco spend sleeping?

2. What percent of the day does Marco spend doing “Other Schoolwork”?

3. What amount of time would you predict Marco would spend on video games for anentire week?

4. Add a column to the table and fill it in with predictions for Marco’s activities for an

entire week. What other activities might Marco engage in that are not on the table? Whyis it possible that not every activity is listed?

5. Add another column to the table and fill it in with predictions for Marco’s activities for

an entire month. How do you use the given data to make predictions for an entire week

or month? Explain your reasoning.

2012 www.flickr.com/photos/peretzp

51

Getting Ready 51



Getting Ready 1.11H




Set

Topic: Organizing information in matrices

Elvira has been running a private catering business to make extra money. She needs some help

organizing the information in problems 6 through 8 below so that she can better predict amounts to

purchase and improve her profits. Assist her by organizing the information in a meaningful way so

that she can average the years and do better for the coming year.

6. The last three years Elvira has catered family gatherings and city events. Last year sheprovided the following at family gatherings she catered: 5 bags of chips, 6 dozen cookiesand 4 gallons of drink. Last year at city events she provided the following: 16 bags ofchips, 20 gallons or drink and 24 dozen cookies. Organize this information.

7. Two year ago Elvira provided the following at family events: 5 gallons of drink, 4 bags ofchips and 5 dozen cookies. While she provided the following at city events: 20 dozencookies, 18 gallons or drink and 12 bags of chips.

8. Three years ago Elvira provided the following at city events: 14 bags of chips, 20 gallonsof drink and 19 dozen cookies. She also provided the following at family gatherings: 6bags of chips, 7 dozen cookies and 9 gallons or drink.

9. If you provide Elvira with an average amount to be ordered for the gatherings andevents she caters in the coming year, how much of each item would she need? Presentthe average in an organized way.

52

Getting Ready 52



Getting Ready 1.11H




Go

Topic: Creating expressions and equations

10. If cookies cost $2.50 a dozen, drink is $1.75 a gallon and chips are $2 a bag what wouldbe the total cost for a city event according to your recommendation above (problem 9)?

Show your calculations here.

11. Write an expression based on the information above that will calculate the total cost for

any amounts of cookies c, drink d and chips h.

12. Write an expression that will calculate the cost for any amounts of cookies c, drink d and

chips h, if prices rise to the following: $2.75 for a dozen cookies, $2.25 for a bag of chipsand $2 for a gallon of drink. Using this new expression calculate the costs for Elvira inthe coming year.

Need help? Check out these related videos.

http://www.khanacademy.org/math/algebra/algebra-matrices/v/introduction-to-matrices

53

Getting Ready 53






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Getting Ready 55



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