Subject:
Algebra
Material Type:
Lesson Plan
Level:
Middle School
7
Provider:
Pearson
Tags:
Language:
English
Media Formats:
Text/HTML

# Gallery Problems Exercise # Gallery Overview

Allow students who have a clear understanding of the content thus far in the unit to work on Gallery problems of their choosing. You can then use this time to provide additional help to students who need review of the unit's concepts or to assist students who may have fallen behind on work.

# Gallery Descriptions

Match Inequalities
Students match inequalities to their solutions.

Product Between One-Half and One
Students find a range of values for an inequality situation.

Students write inequalities to solve problems about the sums of three consecutive numbers.

School Dance
Students use equations and an inequality to model the costs and revenues of holding a school dance.

What Could My Number Be?
Students use inequalities to identify possibilities for a number given certain conditions.

Batting Average
Students use an inequality to find the number of hits needed to get a desired batting average.

# Match Inequalities

$10>8+6x$

| $x<\frac{1}{3}$
$6x+10>8$ | $x>-\frac{1}{3}$
$-4x-15>-27$ | $x<3$
$15x+10<5$ | $x<-\frac{1}{3}$
$4x+7>19$ | $x>3$
$-7x+25<46$ | $x>-3$

# Match Inequalities

Match the inequality cards with their corresponding solution cards.

HANDOUT: Matching Inequalities

# Product Between One-Half and One

1a. $\frac{1}{2}$
$\begin{array}{c}2a<1\\ 2a÷2<1÷2\\ a<\frac{1}{2}\end{array}$
or
$\begin{array}{c}2a<1\\ 2a\cdot \frac{1}{2}<1\cdot \frac{1}{2}\\ a<\frac{1}{2}\end{array}$

1b. $\frac{1}{4}$
$\begin{array}{c}2a>\frac{1}{2}\\ 2a÷2>\frac{1}{2}÷2\\ a>\frac{1}{4}\end{array}$
or
$\begin{array}{c}2a>\frac{1}{2}\\ 2a\cdot \frac{1}{2}>\frac{1}{2}\cdot \frac{1}{2}\\ a>\frac{1}{4}\end{array}$

1c. Possible answers: $\frac{1}{3},\text{\hspace{0.17em}}\frac{3}{8},\text{\hspace{0.17em}}\frac{5}{12}$

2a. $-\frac{1}{4}$
$\begin{array}{c}-2b>\frac{1}{2}\\ -2b÷-2<\frac{1}{2}÷-2\\ b<-\frac{1}{4}\end{array}$
or
$\begin{array}{c}-2b>\frac{1}{2}\\ -2b\cdot -\frac{1}{2}<\frac{1}{2}\cdot -\frac{1}{2}\\ b<-\frac{1}{4}\end{array}$

2b. $-\frac{1}{2}$
$\begin{array}{c}-2b<1\\ -2b÷-2>1÷-2\\ b>-\frac{1}{2}\end{array}$
or
$\begin{array}{c}-2b<1\\ -2b\cdot -\frac{1}{2}>1\cdot -\frac{1}{2}\\ b>-\frac{1}{2}\end{array}$

2c. Possible answers: $-\frac{1}{3},\text{\hspace{0.17em}}-\frac{3}{8},\text{\hspace{0.17em}}-\frac{5}{12}$

# Product Between One-Half and One

1. The product of 2 and some number a is between $\frac{1}{2}$ and 1.

$2a>\frac{1}{2}$

and $2a<1$

a. What number does a have to be less than? Justify your answer mathematically.

b. What number does a have to be greater than? Justify your answer mathematically.

c. Write three possible values for a.

2.  The product of –2 and some number b is between $\frac{1}{2}$ and 1.

a. What number does b have to be less than? Justify your answer mathematically.

b. What number does b have to be greater than? Justify your answer mathematically.

c. Write three possible values for b.

1. 33, 34, 35
$n+\left(n+1\right)+\left(n+2\right)>100$
2. 31, 33, 35
$n+\left(n+2\right)+\left(n+4\right)<100$
3. 30, 32, 34
$n+\left(n+2\right)+\left(n+4\right)<100$
4. –36, –34, –32
$n+\left(n+2\right)+\left(n+4\right)<-100$

# Work Time

Write an inequality to solve each problem.

1. What are the least three consecutive whole numbers that have a sum greater than 100?
2. What are the greatest three consecutive odd numbers that have a sum less than 100?
3. What are the greatest three consecutive even numbers that have a sum less than 100?
4. What are the greatest three consecutive even integers that have a sum less than –100?

# School Dance

1.  $d=4\cdot 50-60$
$d=140$
2. $d=ab-c$

# Aswers

1. Possible values: 2, 1, 0

$\begin{array}{c}2n<6\\ n<3\end{array}$
2. Possible values: 54, 55, 56

$\begin{array}{c}848\end{array}$
3. Possible values: −2, 0, 2

$\begin{array}{c}-6n<18\\ n>-3\end{array}$
4. Possible values: −12, −13, −14

$\begin{array}{c}n+7<-4\\ n<-11\end{array}$
5. Possible values: $4\frac{1}{2},\text{}5,\text{}10$

$\begin{array}{c}\frac{n}{2}>2\\ n>4\end{array}$
6. Possible values: −11, −12. −13

$\begin{array}{c}8+n<-2\\ n<-10\end{array}$
7. Possible values: 16, 17, 18

$\begin{array}{c}16>n-3\\ n<19\end{array}$
8. Possible values: 3, 2, 0

$\begin{array}{c}7+3n<18\\ n<3\frac{2}{3}\end{array}$

# What Could My Number Be?

For each problem, write and solve an inequality that shows possible values for your number. Then give three possible values for the number.

1. The product of 2 and my number is less than 6.
2. 8 is less than my number divided by 6.
3. The product of –6 and my number is less than 18.
4. The sum of my number and 7 is less than –4.
5. My number divided by 2 is greater than 2.
6. The sum of 8 and my number is less than –2.
7. 16 is greater than my number minus 3.
8. 7 plus the product of 3 and my number is less than 18.

# Batting Average

1. A batting average of 0.286, or $\frac{6}{21}=0.2857$.

2. At least 10 more hits.

$\begin{array}{c}\frac{\left(6+x\right)}{53}>0.300\\ 6+x>15.900\\ x>9.900\end{array}$

# Batting Average

A baseball player’s batting average is determined by dividing the total number of hits by the total number of official at bats (total number of at bats not including walks). The average is always rounded to the nearest thousandth.

1. So far this season, you have been at bat 21 times and have gotten 6 hits. What is your batting average so far?
2. Suppose you have 32 more times at bat this season. How many hits will you need in order to reach a batting average of more than 0.300 by the end of the season?