Download Math Remediation 3-5

Pre Algebra A
Math Remediation
Unit 3 – The Decimal System
Unit Objectives:
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Evaluate mathematical expressions involving powers of a number.
Express a number in words or in expanded notation.
Read and write expressions for numbers between 0 and 1.
Compare decimals.
Round whole numbers and decimals to a given place.
Add, subtract, multiply, and divide decimals.
Multiply and divide numbers by powers of ten.
Write large numbers in scientific notation.
Use estimation in problem solving.
Solve word problems involving decimals.
Estimate sums, differences, products, and quotients of decimals.
Lesson Objectives
Lesson 1: Exponents and Powers of Ten
 Use exponents to write an expression that involves repeated multiplication.
 Multiply powers of 10.
 Evaluate an expression that contains exponents.
Remediation:
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Use the extension exercise found in the K12 lesson for a small group or enrichment activity. See teacher
guide for answers.
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http://www.math.com/school/subject2/practice/S2U2L3/S2U2L3Pract.html offers electronic problems
where students must evaluate and enter their answer. Site tells students whether answer is correct or
incorrect.
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Vocabulary: Teach the vocabulary first, using an example such as 4 to the 3rd power. Explain
that the base number, the number being multiplied by itself, is 4. The exponent 3, or 3rd power,
is the number of times you will multiply the base by itself. Write the number in expanded form as
4 x 4 x 4 and 64 in standard form. Use an example such as 5 to the 2nd power to reinforce the
vocabulary and write it in standard form: 5 x 5 = 25. Tell the students that when a number is
raised to the 2nd power we can also say the number is squared, and when a number is raised
to the 3rd power we can say the number is cubed. Add vocabulary to a word wall and use
vocabulary often.
Read more: Best Way - Tips on Teaching Exponents With Examples | eHow.com
http://www.ehow.com/way_5200232_tips-teaching-exponents-examples.html#ixzz10HODxEUD
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Misconceptions: Give students exponent questions that may confuse them so you can
address common misconceptions. For example, ask students to find the answer of 2 to the 3rd
power. Many students will incorrectly do 2 x 3 = 6 the first time instead of 2 x 2 x 2 = 8. Remind
students that you don't multiply the exponent and base number together to find the correct
answer. Give students more examples. Remind students that the base is the number you write
down. The exponent is how many times you write the base down.
Lesson 2: The Decimal System
 Write a number in standard form.
 Write a number in word form.
 Write a number in expanded notation.
Remediation:
 Use the worksheet in small groups. Students can practice writing numbers in standard form.
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Below is a small quiz or remediation worksheet that can be used to evaluate student’s knowledge of this
lesson’s skills or can be worked by students who are struggling for remedial work.
Directions - Look at the following numbers and write the type of form it is after each one. (Standard Form,
Word Form, or Expanded Form)
1. 357,595 =
2. Seventeen thousand, five hundred twenty-nine =
3. 13,000 + 5,000 + 700 + 20 + 5 =
4. 64,321 =
5. 20,000 + 3,000 + 500 + 15 + 2 =
6. Twelve thousand, sixteen =
7. 85,305 =
8. 75,000 + 4,000 + 600 + 35 + 7 =
9. Four hundred twenty-five =
10. 871 =
Part Two - Write the following in Word Form.
1. 25,000 =
2. 3,546 =
3. 165 =
4. 120,501=
5. 25 =
6. 45 =
7. 465 =
8. 144 =
9. 42,546 =
10. 15,426 =
Lesson 3: Comparing Decimals
 Compare two or more decimals.
 Find values that make an inequality true.
Remediation:
 http://www.interactivestuff.org/sums4fun/decchall.html . Neat website where students must guess a
decimal while computer gives hints of too high or too low. This is a great site for remediation on decimals,
place value and comparing decimals.
 http://themathgames.com/our-games/decimal-games/place-value/decimal-place-value-math-game . An
asteroids style game where you first answer a question about the smallest decimal, then get to shoot
asteroids, earning points based on the numbers on them.
 Print out the following activity on cardstock and laminate. Have students use this as a review activity.
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Print out the following and laminate. Use with a small group still struggling with comparing decimals.
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Use the following exercises in small groups for a supplemental activity:
Lesson 4: Rounding
 Round a whole number to a given place.
 Round a decimal to a given place.
Remediation:
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Around and Around”
Instructions:
To begin, each player makes a game board as follows:
10
20 30 40 50 60 70 80 90
100
Each player takes a turn rolling dice. The first dice roll is the whole number. The second dice roll this the
decimal number. Each player must then decide which number to make. Then round to the nearest 10,
100 or 1000.
Example: 2.9 can be 29 or 9.2
29 is rounded to 30
92 is rounded to 90.
The player decides on the number and crosses it off his or her game board. If a number has already been
crossed off the player misses that turn. The player to cross off all of his or her numbers wins.
This can be used with playing cards and can be adapted to from easy to challenging.
Lesson 6: Adding and Subtracting Decimals
 Add decimals.
 Subtract decimals.
 Estimate sums of decimals.
 Estimate differences of decimals.
 Solve a word problem involving addition or subtraction of decimals.
Remediation:
 This activity can be used as stations or centers where students could travel from station to station to
calculate their “shopping list.” An alternative may have students using the ads from the local grocery
store. Have students write down a grocery list of things they would need to cook their favorite meal. Then
have students look up prices in the shopping ad from the grocery store. You may want to have students
round their answers to the nearest dollar or cent. You may choose to have students work alone or with a
partner.
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“Grocery Store Math”
Directions: With your partner, start at one table. Partners will work at a table until the time goes off (about
four minutes).
First, record the number of the table you are working with in your math notebook.
Then, in one column, write the actual cost of each item. In the second column, ESTIMATE how much money you
would need.
Next, move to the next table. Repeat the steps for recording.
Fourth, work with your partner to ESTIMATE how much money you need to bring to the store to pay for all your
items.
Finally, calculate the exact amount your purchases would cost. Did you overestimate or underestimate the
amount of money you needed.
EXTRA CREDIT: Calculate how much change you would receive if you brought a $50 bill to pay for your
groceries.
BONUS: For 10 points on your next test: Explain why ESTIMATION is helpful when you are shopping.
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“Matching Game”
Students will have fun with addition of decimal problems using this matching card game. The game takes
approximately 20 minutes or less to play and is quick and easy to grade.
Print the worksheet. Card stock is recommended. Card stock will increase the durability of the cards and
make them easier to use. Cut the cards apart and save each set of cards in an envelope. Students can
work individually or in pairs to play the game. When the game is finished, the cards will form a 3 x 4 grid.
(Note – The letters do not make words)
Each card contains problems and answers around the edge of the card. The students will match the
problem on one card to the correct answer on another card. Students should orient the cards so that the
card descriptions are on the bottom of the card. To check to see if the cards have been matched
correctly, simply have the student record the letters in the middle of the cards on the Matching Game
Recording sheet and check to see if their answers are in the correct order.
This game can be adapted and used for other skills.
0.7132
2.4 + 6.8
Adding Decimals
.593 + .169
0.762
4.5 + 179
183.5
G
E
C
3.5 + 47.0
4.58
1.78 + 2.8
.549 + .868
Adding Decimals
.3 + .755
1.055
A
Y
W
Adding Decimals
14.22
4.56 + 9.66
8.12 + 7.98
16.1
.14 + 7.2
47.22
46.4 + .82
Adding Decimals
1.05
.38 + .67
99.01
8.58
7.85 + .73
Adding Decimals
Adding Decimals
7.34
Adding Decimals
1.017
Adding Decimals
.39 + 98.62
Adding Decimals
.32 + 697
93.9
I
50.5
84.39 + 9.51
K
1.417
10.31
M
7.59
.89 + 6.7
.537 + .1785
40.56
9.2
.76 + 39.8
Adding Decimals
1.04
.58 + .46
91.1
.61 + 9.7
10.3
Adding Decimals
R
Adding Decimals
22.38
22.0 + .38
T
86.0 + 5.1
1.6 + 8.7
V
Name _______________________________
Name _____________________________
Date_________________________________
Date_______________________________
Name of Game Cards
______________________________
Name of Game Cards
______________________________
Name of Game Cards
______________________________
Name of Game Cards
______________________________
Name of Game Cards
______________________________
Name of Game Cards
______________________________
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The following activity can be printed out and used as a worksheet. Delete answers in
red before you print out for the students.
Below is Sofie and Kirk’s shopping list for their trip to the shopping center:
Item
a jar of peanut butter
a bar of cream cheese
a box of cereal
aluminum foil
a candy bar
mashed potatoes
tape measure
wrench
screwdriver
Total
Amount
$ 1.50
$ 2.18
$ 3.00
$ 4.00
$ 2.79
$ 3.85
$ 13.39
$ 34.99
$ 7.00
?
Before they leave, Sofie and Kirk decided to split the expenses this way: Sofie will pay
for all the groceries. Kirk will pay for all the tools. To find out how much money they
each need to pay, Sofie and Kirk first will solve for the answers to these problems:
1) What is the total amount they spent for the whole shopping list? $72.70
2) What is the total amount of grocery expenses in the shopping list? $17.32
3) What is the total amount of hardware expenses in the shopping list? $55.38
4) Kirk has $60 for his trip to the hardware store. When Kirk pays for the items, how
much money should he get back? $4.26
5) Sofie has $20 for her trip to the grocery store. How much money should Sofie
have left from the $20? $2.68
Lesson 7: Multiplying or Dividing by a Power of Ten
 Multiply a whole number by a power of 10.
 Multiply a decimal by a power of 10.
 Divide a whole number by a power of 10.
 Divide a decimal by a power of 10.
 Write a large number in scientific notation.
Remediation:
 Have 4 ones cubes, 4 tens rods, 4 hundreds flats, and 4 thousands cubes from the base ten block kit.
Students can use the blocks to answer the following questions (don’t give students the answers) –
o
o
o
o
o
o
o
4x1=4
4 x 10 = 4
4 x 100 = 400
4 x 1000 = 4000
Describe the pattern that you see.
Can you complete the pattern? 40,000 x 10 = 400,000; 400,000 x 10 = 40,000,000
Can you create another multiplication pattern with different numbers?
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Mister Rabbit Died Laughing (Multiply-Right, Divide-Left) – cute way for students to remember which
way to move the decimal.
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To multiply by a power of ten:
Move the decimal point to the right for each zero or exponent value in the “power of ten” number.
Example: 24 x 10 or 101 = 240 There is one zero in 10 and the number 1 is an exponent therefore, the
decimal is moved one place to the right, so 24 becomes 240.
Example: 2.65 x 100 or 102 = 265
There are two zeros in 100 and the number 2 is an exponent
therefore, the decimal must be moved two places to the right.
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To divide by a power of ten:
To divide by a power of ten, move the decimal point to the left for each zero or exponent value in the
“power of ten” number.
Example: 24  10 or 101 = 2.4
the left.
There is one zero in 10. Therefore, the decimal is moved one place to
Example: 2.65  100 or 102 = 0.0265 There are two zeros in 100. Therefore, the decimal is moved
two places to the left.
Lesson 8: Multiplying Decimals
 Multiply decimals.
 Estimate the product of decimals.
 Solve a word problem involving multiplication of decimals.
Remediation:
 Use graph paper to help line up numbers.
 Use the following as a supplemental activity. Delete answers before printing for students.
.4
x 15
.24
x 15
2.4
x 1.5
.24
x .15
36
3.6
3.6
.36
3.5
x .3
.35
x .3
3.5
x .03
.35
x .05
1.05
.105
.105
.0105
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.8
x .6
.05
x .6
.07
x .03
.82
x .9
.48
.030
.0021
.738
.45
x .4
.63
x .5
.52
x .24
.29
x .12
.18
.315
.1248
.0348
.34
x .52
.008
x 5
.004
x .6
.035
x .04
.1768
.04
.0024
.0014
Use the following quick decimal quiz as a warm-up, group activity or assessment.
Lesson 9: Dividing Decimals
 Divide a decimal by a whole number.
 Divide a whole number by a decimal.
 Divide a decimal by a decimal.
 Solve a word problem involving the division of decimals.
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Remediation:
“Leftovers Game”
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Play a game of “Division Roll” with your student.
Write a different multiple of 10 between 10 and 90 on each of nine index cards.
Label each side of three number cubes with a digit between 0 and 9, or draw three spinners with six sections
each and label the sections the same way.
Have the first player roll the cubes (or spin the spinners with a pencil and paper clip) to form a three-digit
dividend. Then have him pick a card at random to represent the divisor and find the quotient (and remainder).
The player who has the greatest quotient in each round scores one point. In case of a tie, the player whose
remainder is less scores the point.
The first player to score five points is the winner.
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Some teachers find it is helpful for students to work division problems on graph paper to help keep numbers
aligned.
 “Compatible Numbers”
Practice working with compatible numbers by completing the problems below.
1. 830
38 =
a. What are 2 sets of compatible numbers can you use to solve this problem? ______________
b. Solve the problem using both sets of numbers.
c. Which do you predict is closest to the correct answer? _______________________
2. 273
57 =
a. What are 2 sets of compatible numbers can you use to solve this problem? ______________
b. Solve the problem using both sets of numbers.
c. Which do you predict is closest to the correct answer? _______________________
3. 421
46 =
a. What are 2 sets of compatible numbers can you use to solve this problem? ______________
b. Solve the problem using both sets of numbers.
c. Which do you predict is closest to the correct answer? _______________________
4. $16.92
$4.14
a. What are 2 sets of compatible numbers can you use to solve this problem? ______________
b. Solve the problem using both sets of numbers.
c. Which do you predict is closest to the correct answer? _______________________
Lesson 10: Problem Solving: Using Estimation
 Solve a word problem involving decimals.
 Use estimation when solving a word problem.
Remediation:
 Print out the following sheet and have students keep in their math notebook. Use sheet to refer to when
solving word problems.
The Mystery of Math Problems
 Read the problem carefully.
 Problem solving requires practice!
 What are my key words?
 Can a picture help me see it better?
 The first thing you will do is look for clues.
 Start looking for CLUE words.
Clue Words for Addition:
sum
total
in all
perimeter
Clue Words for Subtraction:
difference
how much more
exceed
Clue Words for Multiplication
product
total
area
times
Clue Words for Division
share
distribute
quotient
average
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The following word problems may be printed on index cards (the teacher may change the names to
students in the class) .Students may check their solutions with the task card answer card. The teacher
should review the work to ensure that the process is followed and accuracy is shown in the steps.
One-step problems:
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Elena bought 2.5 kg of flour, 5.34 kg of sugar and 0.35 kg of margarine. What is the total weight of the
things bought by Elena? (Ans: 8.19 kg)
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The mass of a papaya is 1.54 kg. A watermelon is 2.69 kg heavier than the papaya. What is the mass of
the watermelon? (Ans: 4.23 kg)
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Alice has 9.8 m of cloth. She used 1.95 m of the cloth to make a blouse. What is the length of cloth left?
(Ans: 7.85 m)
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Bottle A holds 4.3 liters of water and bottle B holds 2.9 liters less water than bottle A. What is the volume
of water in bottle B? (Ans: 1.4 l)
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David is 1.76 meters tall and Caleb is 0.12 meters taller. What is Caleb’s height? (Ans: 1.88 m)
Two-step problems:
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Andrea has a ribbon that is 12.6 meters long. Linda has a ribbon that is 3.8 meters shorter. What is the
total length of the two ribbons? (Ans: 21.4 m)
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Bottle A has 2.17 liters of water and Bottle B has 0.79 liters less water than Bottle A. Find the total volume
of water in the two bottles. (Ans: 3.55 l)
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A coconut tree is 7.6 meters tall and an orange tree is 3.4 meters shorter than the coconut tree. Find the
total height of the two trees. (Ans: 11.8 m)
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Sack A contains 32.5 kg of potatoes and Sack B contains 3.7 kg more potatoes than Sack A. Find the
total mass of potatoes in the two sacks. (Ans: 68.7 kg)
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EIizabeth saved $175.35 in June and $132.50 in July. Then she bought a bicycle for $195.80. How much
of her savings from June and July was left? (Ans: $112.05)
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Janet’s mass was 46.9 kg and Ingrid’s mass was 51.2 kg. Six months later, Janet gained 1.8 kg, but
Ingrid lost 2.1 kg. Find their new total mass. (Ans: 97.8 kg)
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“Bag It Up”