This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Slide 1 / 215
6th Grade
Fraction & Decimal Computation
2015-10-20
www.njctl.org
Slide 2 / 215
Fraction and Decimal Computation
· Long Division Review· Adding Decimals· Subtracting Decimals
Applying to FractionsThe previous example used whole numbers and grouped the dividend according to the divisor.
The same strategy can be applied when dividing with fractions.
Use the model below to demonstrate: 8 ÷ =
8
The pink rectangle represents .
See how many you can fit in the 8 squares.
12
12
12
Slide 6 / 215
Applying to FractionsThe previous example used whole numbers and grouped the dividend according to the divisor.
The same strategy can be applied when dividing with fractions.
Use the model below to demonstrate: 8 ÷ =
8
The pink rectangle represents .
See how many you can fit in the 8 squares.
12
12
12
[This object is a pull tab]
Teac
her N
otes The "half" square is infinitely
cloned and students should "fill" the 8 squares with 16
half squares to show
8 / 0.5 = 16
Slide 6 (Answer) / 215
ExampleUse the model below to demonstrate 2 ÷ =
2
13
13
Slide 7 / 215
1 Evaluate the following problem using the model below.
3
14
3 ÷ =
14
Slide 8 / 215
1 Evaluate the following problem using the model below.
3
14
3 ÷ =
14
[This object is a pull tab]
Ans
wer
12
Slide 8 (Answer) / 215
2 Evaluate the following problem using the model below.
5
12
5 ÷ =
12
Slide 9 / 215
2 Evaluate the following problem using the model below.
5
12
5 ÷ =
12
[This object is a pull tab]
Ans
wer
10
Slide 9 (Answer) / 215
A fraction can be divided by a whole number using the following visual model. 3/5 ÷ 4
Divide into 4 groups
1 2 3 4
Visual Model
Slide 10 / 215
A fraction can be divided by a whole number using the following visual model. 3/5 ÷ 4
Divide into 4 groups
1 2 3 4
Visual Model
[This object is a pull tab]
Ans
wer
3/5 ÷ 4 = 3/20
Slide 10 (Answer) / 215
The previous expression can be represented by the following word problem: How much will each person receive if 4 friends share a 3/5 pound bag of popcorn?
1 2 3 4
Each friend will receive 3/20 lb. of popcorn.
Word Problem
Slide 11 / 215
Slide 12 / 215
Slide 12 (Answer) / 215
Slide 13 / 215
Slide 13 (Answer) / 215
Slide 14 / 215
Slide 15 / 215
Slide 16 / 215
Slide 17 / 215
Slide 17 (Answer) / 215
Slide 18 / 215
Slide 18 (Answer) / 215
Vocabulary Review
Complex Fraction: A fraction with another fraction in the numerator, denominator or both.
Original Number 4
Reciprocal 2
Reciprocal: The inverse of a number/fraction.
Slide 19 / 215
PatternsDo you notice a pattern between the division of fractions and their solution?
Slide 20 / 215
PatternsDo you notice a pattern between the division of fractions and their solution?
[This object is a pull tab]
Teac
her N
otes
Discuss Patterns either from model or number sentence.
A mixed number can be divided by a mixed number using the following visual model.
First find the least common denominator (LCD) which is 6.
If every 6 lines represents a whole, then how many lines should we draw to make sure both mixed numbers fit?
Visual Model
Slide 41 / 215
A mixed number can be divided by a mixed number using the following visual model.
First find the least common denominator (LCD) which is 6.
If every 6 lines represents a whole, then how many lines should we draw to make sure both mixed numbers fit?
Visual Model
[This object is a pull tab]
Ans
wer
18
Slide 41 (Answer) / 215
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Since our LCD is 6, every 6 lines is considered a whole.
1 1/2 is equivalent to 9 sections on the number line.
1 1/2
2 2/3 is equivalent to 16 sections on the number line.
So 1 1/2 ÷ 2 2/3 = 9/16
2 2/3
Visual Model
Slide 42 / 215
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
1 1/2
2 2/3
1 1/2
What if the problem were written as ?
How many times does 1 1/2 divide into 2 2/3?
Visual Model
Slide 43 / 215
Step 1: Rewrite the Mixed Number(s) as an improper fraction(s). (write whole numbers / 1)
Step 2: Follow the same steps for dividing fractions
Dividing Mixed Numbers Algorithm
6 1
x 2 3
= 12 3
=6 1 2
1 6 1
3 2
= = 4
Slide 44 / 215
5 3
x 2 7
= 1021
2 3
=1 1 2
3 5 3
7 2
=
Example
Evaluate:
Slide 45 / 215
20 )
= 1 2
2 2 3
1
Slide 46 / 215
20 )
= 1 2
2 2 3
1
[This object is a pull tab]
Ans
wer
Slide 46 (Answer) / 215
21 )
= 1 2
52
Slide 47 / 215
21 )
= 1 2
52
[This object is a pull tab]
Ans
wer
Slide 47 (Answer) / 215
22 )
= 2 5
5 1 2
4
Slide 48 / 215
22 )
= 2 5
5 1 2
4
[This object is a pull tab]
Ans
wer
Slide 48 (Answer) / 215
23 )
= 1 2
2 3 8
3
Slide 49 / 215
23 )
= 1 2
2 3 8
3
[This object is a pull tab]
Ans
wer
Slide 49 (Answer) / 215
Winnie needs pieces of string for a craft project. How many 1/6 yd pieces of string can she cut from a piece that is 2/3 yd long?
16
23 ÷
23
x 61
123 == 4 pieces4
1
or
23
x 61 =
1
241
= 4 pieces
Application Problem
Slide 50 / 215
One student brings 1/2 yd of ribbon. If 3 students receive an equal length of the ribbon, how much ribbons will each student receive?
12 ÷ 3
12
x 13
16
yards of ribbon=
Application Problem
Slide 51 / 215
Kristen is making a ladder and wants to cut ladder rungs from a 6 ft board. Each rung needs to be 3/4 ft long. How many ladder rungs can she cut?
6 ÷34
61
÷ 34
61 x 4
3 = 243
81 8 rungs= =
Application Problem
Slide 52 / 215
A box weighing 9 1/3 lb contains toy robots weighing 1 1/6 lb apiece. How many toy robots are in the box?
9 13
1 16÷
283
76÷
67
283
x
1
4
1
2
= 81
8 robots=
Application Problem
Slide 53 / 215
24 Robert bought 3/4 pound of grapes and divided them into 6 equal portions. What is the weight of each portion?
A 8 pounds
B 4 1/2 pounds
C 2/5 pounds
D 1/8 pound
Slide 54 / 215
24 Robert bought 3/4 pound of grapes and divided them into 6 equal portions. What is the weight of each portion?
A 8 pounds
B 4 1/2 pounds
C 2/5 pounds
D 1/8 pound
[This object is a pull tab]
Ans
wer
D
Slide 54 (Answer) / 215
25 A car travels 83 7/10 miles on 2 1/4 gallons of fuel. Which is the best estimate of the number miles the car travels on one gallon of fuel?
A 84 miles
B 62 miles
C 42 miles
D 38 miles
Slide 55 / 215
25 A car travels 83 7/10 miles on 2 1/4 gallons of fuel. Which is the best estimate of the number miles the car travels on one gallon of fuel?
A 84 miles
B 62 miles
C 42 miles
D 38 miles
[This object is a pull tab]
Ans
wer
D
Slide 55 (Answer) / 215
26 One tablespoon is equal to 1/16 cup. It is also equal to 1/2 ounce. A recipe uses 3/4 cup of flour. How many tablespoons of flour does the recipe use?
A 48 tablespoons
B 24 tablespoons
C 12 tablespoons
D 6 tablespoons
Slide 56 / 215
26 One tablespoon is equal to 1/16 cup. It is also equal to 1/2 ounce. A recipe uses 3/4 cup of flour. How many tablespoons of flour does the recipe use?
A 48 tablespoons
B 24 tablespoons
C 12 tablespoons
D 6 tablespoons
[This object is a pull tab]
Ans
wer
C
Slide 56 (Answer) / 215
27 A bookstore packs 6 books in a box. The total weight of the books is 14 2/5 pounds. If each book has the same weight, what is the weight of one book?
A 5/12 pound
B 2 2/5 pounds
C 8 2/5 pounds
D 86 2/5 pounds
Slide 57 / 215
27 A bookstore packs 6 books in a box. The total weight of the books is 14 2/5 pounds. If each book has the same weight, what is the weight of one book?
A 5/12 pound
B 2 2/5 pounds
C 8 2/5 pounds
D 86 2/5 pounds
[This object is a pull tab]
Ans
wer
B
Slide 57 (Answer) / 215
28 There is gallon of distilled water in the
class science supplies. If each pair of
students doing an experiment uses
gallon of distilled water, there will be
gallon left in the supplies . How many
students are doing the experiments?
Slide 58 / 215
28 There is gallon of distilled water in the
class science supplies. If each pair of
students doing an experiment uses
gallon of distilled water, there will be
gallon left in the supplies . How many
students are doing the experiments?
[This object is a pull tab]
Ans
wer
Slide 58 (Answer) / 215
29 Carol makes cups of snack mix. She
puts all the snack mix into plastic bags. She
puts cup of the snack mix in each bag.
How many plastic bags does Carol need?
Enter your answer in the box.
bags
From PARCC EOY sample test non-calculator #9
Slide 59 / 215
29 Carol makes cups of snack mix. She
puts all the snack mix into plastic bags. She
puts cup of the snack mix in each bag.
How many plastic bags does Carol need?
Enter your answer in the box.
bags
From PARCC EOY sample test non-calculator #9
[This object is a pull tab]
Ans
wer
& M
ath
Prac
tice
14 bags
MP 4
Word problems allow students to recognize math in everyday like and use the math they know to solve problems.
30 Part AA group of hikers buy 8 bags of trail mix.
Each bag contains cups of trail mix. The
trail mix is shared evenly among 12 hikers.
How many cups of trail mix will each hiker
receive? Show your work or explain your
answer.
From PARCC PBA sample test calculator #10
Slide 60 / 215
30 Part AA group of hikers buy 8 bags of trail mix.
Each bag contains cups of trail mix. The
trail mix is shared evenly among 12 hikers.
How many cups of trail mix will each hiker
receive? Show your work or explain your
answer.
From PARCC PBA sample test calculator #10
[This object is a pull tab]
Ans
wer
Slide 60 (Answer) / 215
31 Part BThe hikers plan to visit a scenic lookout. They will rest after they hike 2 miles. Then they will hike the remaining miles to the lookout. The trail the hikers will use to return from the lookout is mile shorter than the trail they will use to go to the lookout. Each hiker will bring gallon of water for each mile to and from the lookout.· Determine the total distance each hiker
31 Part BThe hikers plan to visit a scenic lookout. They will rest after they hike 2 miles. Then they will hike the remaining miles to the lookout. The trail the hikers will use to return from the lookout is mile shorter than the trail they will use to go to the lookout. Each hiker will bring gallon of water for each mile to and from the lookout.· Determine the total distance each hiker
will hike. Show your work or explain your answer.
From PARCC PBA sample test calculator #10
[This object is a pull tab]
Ans
wer
Slide 61 (Answer) / 215
32 Part B (continued)· Determine the total number of gallons of
water each hiker will bring. Show your work or explain your answer.
From PARCC PBA sample test calculator #10
Slide 62 / 215
32 Part B (continued)· Determine the total number of gallons of
water each hiker will bring. Show your work or explain your answer.
James has a board that is 3/4 foot long. He wants to cut the board into pieces that are each 1/8 foot long. How many pieces can James cut from the board? Explain how James can use the number line diagram to determine the number of pieces he can cut from the board.
From PARCC PBA sample test calculator #8
Slide 63 / 215
33 This diagram shows a number line.
Part A
James has a board that is 3/4 foot long. He wants to cut the board into pieces that are each 1/8 foot long. How many pieces can James cut from the board? Explain how James can use the number line diagram to determine the number of pieces he can cut from the board.
From PARCC PBA sample test calculator #8
[This object is a pull tab]
Ans
wer
The number line diagram show segments marked that are spaces 1/8 unit apart. I know James' board is 3/4 foot long. I counted the number of 1/8 units until I got to 3/4 on the number line. There are 6 of these. So James can cut a total of 6 pieces from the board.
Slide 63 (Answer) / 215
34 Part B
Write an equation using division that represents how James can find the number of pieces he can cut from the board.
When we are dividing, we are breaking apart into equal groups
EXAMPLE 1
Find 132 3
Step 1: Can 3 go into 1, no so can 3 go into 13, yes
4
- 12 1
3 x 4 = 1213 - 12 = 1Compare 1 < 3
3 132
3 x 4 = 1212 - 12 = 0Compare 0 < 3
- 12 0
Step 2: Bring down the 2. Can 3 go into 12, yes
2
4
Click for step 1
Click for step 2
Slide 67 / 215
Step 3: Check your answer.
44 x 3 132
click
Slide 68 / 215
Estimating Your AnswerBefore any calculations, estimate your answer to make sure you are on the right track.
What place value should we round to?
Round to the largest place value.
357 rounds to ____
15 rounds to ____
Our answer should approximately be ...
20
357 ÷ 15
click
click
Slide 69 / 215
EXAMPLE 2(change pages to see each step)
Step 1: Can 15 go into 3, no so can 15 go into 35, yes
2
-30 5
15 x 2 = 3035 - 30 = 5Compare 5 < 15
15 357
Slide 70 / 215
2
-30 5
15 35715 x 3 = 4557 - 45 =12Compare 12 < 15
7 - 45 12
Step 2 : Bring down the 7. Can 25 go into 207, yes
3
EXAMPLE 2(change pages to see each step)
Slide 71 / 215
2
-30 5
15 357.0
7 - 45 120 - 120 0
3
Step 3: You need to add a decimal and a zero since the division is not complete. Bring the zero down and continue the long division.
15 x 8 = 120120 - 120 = 0Compare 0 < 15
.8
EXAMPLE 2(change pages to see each step)
Is our answer close to our estimate?
Slide 72 / 215
Check your answer.
23.8 x 15
357click
Slide 73 / 215
Estimate the following problems. Discuss your answers with your group.
35 300
15 20
click
clickclick
click
Slide 74 / 215
Now solve the following problems. Discuss your answers with your group.
41 324
19.5 23.2
click
click click
click
Slide 75 / 215
35 Estimate the quotient.
779 ÷ 19
Slide 76 / 215
35 Estimate the quotient.
779 ÷ 19
[This object is a pull tab]
Ans
wer
40
Slide 76 (Answer) / 215
36 Compute.
779 ÷ 19 =
Slide 77 / 215
36 Compute.
779 ÷ 19 =
[This object is a pull tab]
Ans
wer
41
Slide 77 (Answer) / 215
37 Estimate the quotient.
1,551 ÷ 55
Slide 78 / 215
37 Estimate the quotient.
1,551 ÷ 55
[This object is a pull tab]
Ans
wer
Approximately 33
Slide 78 (Answer) / 215
38 Compute.
1,551 ÷ 55 =
Slide 79 / 215
38 Compute.
1,551 ÷ 55 =
[This object is a pull tab]
Ans
wer
28.2
Slide 79 (Answer) / 215
39 Estimate the quotient.
1,288 ÷ 35
Slide 80 / 215
39 Estimate the quotient.
1,288 ÷ 35
[This object is a pull tab]
Ans
wer
25
Slide 80 (Answer) / 215
40 Compute.
1,288 ÷ 35 =
Slide 81 / 215
40 Compute.
1,288 ÷ 35 =
[This object is a pull tab]
Ans
wer
36.8
Slide 81 (Answer) / 215
41 The school concert hall contains 312 chairs in 12 rows. Estimate how many chairs are in each row.
Slide 82 / 215
41 The school concert hall contains 312 chairs in 12 rows. Estimate how many chairs are in each row.
[This object is a pull tab]
Ans
wer
30
Slide 82 (Answer) / 215
42 The school concert hall contains 312 chairs in 12 rows. How many chairs are in each row?
Slide 83 / 215
42 The school concert hall contains 312 chairs in 12 rows. How many chairs are in each row?
[This object is a pull tab]
Ans
wer
26
Slide 83 (Answer) / 215
43 Compute.
4706 ÷ 104 =
Slide 84 / 215
43 Compute.
4706 ÷ 104 =
[This object is a pull tab]
Ans
wer
45.25
Slide 84 (Answer) / 215
44 The local Italian restaurant receives the same number of visitors every day. If 343 people visit the restaurant over the course of one week, how many visitors visit each day?
Slide 85 / 215
44 The local Italian restaurant receives the same number of visitors every day. If 343 people visit the restaurant over the course of one week, how many visitors visit each day?
If you know how to add whole numbers then you can add decimals. Just follow these few steps.
Step 1: Put the numbers in a vertical column, aligning the decimal points.
Step 2: Add each column of digits, starting on the right and working to the left.
Step 3: Place the decimal point in the answer directly below the decimal points that you lined up in Step 1.
Adding Decimals
Slide 90 / 215
When adding or subtracting decimals, always remember to align the decimals vertically...
0.250.250.250.251.00+
Adding Decimals
Slide 91 / 215
When adding or subtracting decimals, always remember to align the decimals vertically...
0.250.250.250.251.00+
Adding Decimals
[This object is a pull tab]
Mat
h Pr
actic
e
MP 5
Students who struggle to line up the digits correctly for an addition of decimals problem may find it useful to line them up using graph paper. This will help them to choose to use graph paper as a tool to help them solve problems.
Remind students to compare their estimates to their exact answers to see if their exact answers make sense.
Slide 95 (Answer) / 215
48 Add the following:
0.6 + 0.55 =
A 6.1
B 0.115
C 1.15
D 0.16
Slide 96 / 215
48 Add the following:
0.6 + 0.55 =
A 6.1
B 0.115
C 1.15
D 0.16[This object is a pull tab]
Ans
wer
C
Slide 96 (Answer) / 215
49 Joanne and Peter are working together to solve the problem 0.6 + 0.55. Joanne says that the sum should be approximately 2. Peter disagrees and says the sum should be approximately 0. Who is correct? Why?
A JoanneB Peter
Slide 97 / 215
49 Joanne and Peter are working together to solve the problem 0.6 + 0.55. Joanne says that the sum should be approximately 2. Peter disagrees and says the sum should be approximately 0. Who is correct? Why?
A JoanneB Peter
[This object is a pull tab]
Ans
wer
Joanne is correct because 0.6 rounds to 1 and 0.55 rounds to 1. So the estimation is 2. Peter only looked at the whole number and did not round the decimals.
Slide 97 (Answer) / 215
50 Find the sum.
1.025 + 0.03 + 14.0001 =
Slide 98 / 215
50 Find the sum.
1.025 + 0.03 + 14.0001 =
[This object is a pull tab]
Ans
wer
15.0551
Slide 98 (Answer) / 215
51 Franco went to buy new video games. He bought MaxRush for $19.95, Duplo Race for $23.95 and Garage Mate for $21.95. Estimate how much Franco spent on the video games.
Slide 99 / 215
51 Franco went to buy new video games. He bought MaxRush for $19.95, Duplo Race for $23.95 and Garage Mate for $21.95. Estimate how much Franco spent on the video games.
[This object is a pull tab]
Ans
wer
$66
Slide 99 (Answer) / 215
52 Franco went to buy new video games. He bought MaxRush for $19.95, Duplo Race for $23.95 and Garage Mate for $21.95. How much did he spend on video games?
Slide 100 / 215
52 Franco went to buy new video games. He bought MaxRush for $19.95, Duplo Race for $23.95 and Garage Mate for $21.95. How much did he spend on video games?
[This object is a pull tab]
Ans
wer
$65.85
Slide 100 (Answer) / 215
53 What is the sum of
12.034 and 0.0104?
A 12.1344
B 12.0444
C 12.138
D 1.20444
Slide 101 / 215
53 What is the sum of
12.034 and 0.0104?
A 12.1344
B 12.0444
C 12.138
D 1.20444 [This object is a pull tab]
Ans
wer
B
Slide 101 (Answer) / 215
54 Estimate the sum.
8.5 + 0.042 + 12.31
A 20B 21C 22D 23
Slide 102 / 215
54 Estimate the sum.
8.5 + 0.042 + 12.31
A 20B 21C 22D 23
[This object is a pull tab]
Ans
wer
B
Slide 102 (Answer) / 215
55 Find the sum.
8.5 + 0.042 + 12.31 =
A 13.58
B 21.23
C 20.852
D 20.14
Slide 103 / 215
55 Find the sum.
8.5 + 0.042 + 12.31 =
A 13.58
B 21.23
C 20.852
D 20.14
[This object is a pull tab]
Ans
wer
C
Slide 103 (Answer) / 215
56 Five students collected paper to be recycled. Shelly's stack was .008 cm. thick; Ken's stack was .125 cm. thick; Joe's stack was .150 cm. thick; Betty's stack was .185 cm. thick; Mary's stack was .005 cm. thick. What was the thickness of the papers collected to be recycled?
A .561 cm.B .452 cm.
C .480 cm.
D .473 cm.
Slide 104 / 215
56 Five students collected paper to be recycled. Shelly's stack was .008 cm. thick; Ken's stack was .125 cm. thick; Joe's stack was .150 cm. thick; Betty's stack was .185 cm. thick; Mary's stack was .005 cm. thick. What was the thickness of the papers collected to be recycled?
64 The Johnson twins raced each other in the 200-meter dash. Jordan finished in 23.48 seconds, and Max finished in 26.13 seconds. How much faster was Jordan than Max?
Slide 119 / 215
64 The Johnson twins raced each other in the 200-meter dash. Jordan finished in 23.48 seconds, and Max finished in 26.13 seconds. How much faster was Jordan than Max?
[This object is a pull tab]
Ans
wer
2.65 seconds
Slide 119 (Answer) / 215
65 Timothy is working on the problem 4.1 - 0.094. He estimates his answer before solving and rounds the numbers to the nearest tenths. He uses 4.1 and 0.1 to estimate the answer. Is he correct in doing so? Why or why not?YesNo
Slide 120 / 215
65 Timothy is working on the problem 4.1 - 0.094. He estimates his answer before solving and rounds the numbers to the nearest tenths. He uses 4.1 and 0.1 to estimate the answer. Is he correct in doing so? Why or why not?YesNo
[This object is a pull tab]
Ans
wer
Timothy is correct but he still has to use decimals instead of whole numbers. He would get the same
estimate for this problem if he rounded to the nearest whole
number.
Slide 120 (Answer) / 215
66 ) 4.1 - 0.094 =
Slide 121 / 215
66 ) 4.1 - 0.094 =
[This object is a pull tab]
Ans
wer
4.006
Slide 121 (Answer) / 215
67 ) 17 - 13.008 =
Slide 122 / 215
67 ) 17 - 13.008 =
[This object is a pull tab]
Ans
wer
3.992
Slide 122 (Answer) / 215
68 Which problem below would give you two different estimates when you either round to the nearest whole or round to the nearest tenths?
Try These!What place value will the last digit be in for the following problems? Don't forget to convert them to fractions first.
Fractions Product Place Value
1) 0.3 x 0.7
2) 0.2 x 0.13
3) 0.08 x 0.231
Slide 140 / 215
Do you notice a pattern for multiplying decimals?
3.5 x 1.72
3 510 1 72
100x
3510
x 172100
60201000
Where does the decimal point go? Drag the decimal point.
6 0 2 0
Multiplication
Slide 141 / 215
If you know how to multiply whole numbers then you can multiply decimals. Just follow these few steps.
Step 1: Ignore the decimal points.
Step 2: Multiply the numbers using the same rules as whole numbers.
Step 3: Count the total number of digits to the right of the decimal points in both numbers. Put that many digits to the right of the decimal point in your answer.
Multiplication
Slide 142 / 215
3.21x .04
.1284
There are a total of four digits to the right of the decimal points.
There must be four digits to the right of the decimal point in the answer.
} 2 digits
Multiplication
} 2 digits
Slide 143 / 215
Estimate Your AnswerBefore any calculations, estimate your answer to make sure you are on the right track.
23.2 x 4.04
What place value should we round to?
Round to the nearest whole number.
23.2 rounds to ____
4.04 rounds to ____
Our answer should approximately be ...
92click
click
Slide 144 / 215
23.2x 4.04
928
92800 0000
93.728
} 1 digit
There are a total of three digits to the right of the decimal points.
There must be three digits to the right of the decimal point in the answer.
Estimating helps us recognize where the decimal point belongs!
Exact Answer
} 2 digits
Slide 145 / 215
Estimate your answer for the following problem by rounding the numbers to the nearest whole number.
9.5 x 0.05
9.5 rounds to _____
0.05 rounds to _____
What is your estimate?
For problems like these, use your number sense!
You are multiplying 9.5 by 0.05 which means you are taking a part (fraction) of 9.5.
So your answer must be smaller than 9.5!click
Estimate Your Answer
Slide 146 / 215
smallerthan 3.214
TRY THESE.Estimate the following products in your notebook then check with the rest of your group.
1) 14.512 2) 8.31 x 4.21 x 1.008
3) 7.0045 4) 3.214 x 5.2 x 0.0034
15 x 4 = 60 8 x 1 = 8
7 x 5 = 35
click
clickclick
click
Slide 147 / 215
TRY THESE.Complete in your notebook then check with the rest of your group.
1) 14.512 2) 8.31 x 4.21 x 1.008 14512 290240 5804800 61.09552
3) 7.0045 4) 3.214 x 5.2 x 0.0034 140090 3502250 36.42340
66480000
00000831000
8.37648
1285696420
0.0109276
click
click
click
click
Slide 148 / 215
TRY THESE.Complete in your notebook then check with the rest of your group.
1) 14.512 2) 8.31 x 4.21 x 1.008 14512 290240 5804800 61.09552
3) 7.0045 4) 3.214 x 5.2 x 0.0034 140090 3502250 36.42340
66480000
00000831000
8.37648
1285696420
0.0109276
click
click
click
click
[This object is a pull tab]
Mat
h Pr
actic
e MP 1
Remind students to compare their estimates to their exact answers to see if their exact answers make sense.
Slide 148 (Answer) / 215
77 Estimate the product.
0.42 x 0.032
A The product will be less than 1B The product will be equal to 1C The product will be greater than 1
Slide 149 / 215
77 Estimate the product.
0.42 x 0.032
A The product will be less than 1B The product will be equal to 1C The product will be greater than 1
[This object is a pull tab]
Ans
wer
A
Slide 149 (Answer) / 215
78 The product of 0.42 x 0.032 will have 4 digits to the right of the decimal point.
TrueFalse
Slide 150 / 215
78 The product of 0.42 x 0.032 will have 4 digits to the right of the decimal point.
TrueFalse
[This object is a pull tab]
Ans
wer
False
Slide 150 (Answer) / 215
79 Multiply 0.42 x 0.032
Slide 151 / 215
79 Multiply 0.42 x 0.032
[This object is a pull tab]
Ans
wer
0.1344
Slide 151 (Answer) / 215
80 Multiply 3.452 x 2.1
Slide 152 / 215
80 Multiply 3.452 x 2.1
[This object is a pull tab]
Ans
wer
7.2492
Slide 152 (Answer) / 215
81 You need to buy 6 notebooks that cost $0.87 each. If you have $5, do you have enough money?
Estimate to determine your answer. Do not solve.
YesNo
Slide 153 / 215
81 You need to buy 6 notebooks that cost $0.87 each. If you have $5, do you have enough money?
Estimate to determine your answer. Do not solve.
YesNo
[This object is a pull tab]
Ans
wer
NO
Slide 153 (Answer) / 215
82 You need to buy 6 notebooks that cost $0.87 each. How much will this cost?
Slide 154 / 215
82 You need to buy 6 notebooks that cost $0.87 each. How much will this cost?
[This object is a pull tab]
Ans
wer
$5.22
Slide 154 (Answer) / 215
83 Multiply 53.24 x 0.089
Slide 155 / 215
83 Multiply 53.24 x 0.089
[This object is a pull tab]
Ans
wer
4.73836
Slide 155 (Answer) / 215
84 The regular price of a pair of jeans is $29.99. Mrs. Jones has four children for whom she must buy new jeans. The jeans are on sale for $22.50.
What would the total cost be of four pairs
of jeans on sale?
A $119.96B $90.00
C $86.00
D $52.49
Slide 156 / 215
84 The regular price of a pair of jeans is $29.99. Mrs. Jones has four children for whom she must buy new jeans. The jeans are on sale for $22.50.
What would the total cost be of four pairs
of jeans on sale?
A $119.96B $90.00
C $86.00
D $52.49
[This object is a pull tab]
Ans
wer
B
Slide 156 (Answer) / 215
85 How many digits will be to the right of decimal point in the product for the problem 4.0156 x 7.8?
A 2B 3C 4D 5
Slide 157 / 215
85 How many digits will be to the right of decimal point in the product for the problem 4.0156 x 7.8?
89 Thomas buys a case of bottled water. A case contains 36 bottles of water and costs $4.69. Thomas will sell each bottle of water for $0.75 at a school event.
How much profit, in dollars, will Thomas earn if he sells all the bottles of water?
Enter your answer in the box.
$
From PARCC EOY sample test non-calculator #17
Slide 161 / 215
89 Thomas buys a case of bottled water. A case contains 36 bottles of water and costs $4.69. Thomas will sell each bottle of water for $0.75 at a school event.
How much profit, in dollars, will Thomas earn if he sells all the bottles of water?
Enter your answer in the box.
$
From PARCC EOY sample test non-calculator #17
[This object is a pull tab]
Ans
wer
& M
ath
Prac
tice
$22.31
MP 2
Make sure to also check that the students have used good reasoning habits and can show an understandable representation of the problem solved.
108 Heather has 5.5 lbs of jelly beans. She will put them in 8.5 bags. How much will be in each bag?
Slide 194 / 215
108 Heather has 5.5 lbs of jelly beans. She will put them in 8.5 bags. How much will be in each bag?
[This object is a pull tab]
Ans
wer
0.647 lbs
Slide 194 (Answer) / 215
109
Slide 195 / 215
109
[This object is a pull tab]
Ans
wer
Slide 195 (Answer) / 215
110 ) 91.84 ÷ 4.8 =
Slide 196 / 215
110 ) 91.84 ÷ 4.8 =
[This object is a pull tab]
Ans
wer
Slide 196 (Answer) / 215
111 Texas suffered through a heat wave in August 2011. The highest four temperatures (in degrees Fahrenheit) were 103.4, 102.8, 101.9 and 102.5. What was the average temperature for those four days?
Slide 197 / 215
111 Texas suffered through a heat wave in August 2011. The highest four temperatures (in degrees Fahrenheit) were 103.4, 102.8, 101.9 and 102.5. What was the average temperature for those four days?
[This object is a pull tab]
Ans
wer
102.65o F
Slide 197 (Answer) / 215
112 For your sewing project at school, you need to purchase 3.5 yards of fabric. You spend $9.10 on one pattern and $8.40 on another. How much does one yard cost?
Slide 198 / 215
112 For your sewing project at school, you need to purchase 3.5 yards of fabric. You spend $9.10 on one pattern and $8.40 on another. How much does one yard cost?
[This object is a pull tab]
Ans
wer
$5.00
Slide 198 (Answer) / 215
113 ) 9 ÷ 0.22
A 40.9B 40.90C 40.91D 40.9
Slide 199 / 215
113 ) 9 ÷ 0.22
A 40.9B 40.90C 40.91D 40.9
[This object is a pull tab]
Ans
wer
B
Slide 199 (Answer) / 215
Glossary & Standards
Return to Table of Contents
Slide 200 / 215
Glossary & Standards
Return to Table of Contents
[This object is a pull tab]
Teac
her N
otes Vocabulary Words are bolded
in the presentation. The text box the word is in is then linked to the page at the end of the presentation with the word defined on it.
MP1: Making sense of problems & persevere in solving them.MP2: Reason abstractly & quantitatively.MP3: Construct viable arguments and critique the reasoning of others. MP4: Model with mathematics.MP5: Use appropriate tools strategically.MP6: Attend to precision.MP7: Look for & make use of structure.MP8: Look for & express regularity in repeated reasoning.
Additional questions are included on the slides using the "Math Practice" Pull-tabs (e.g. a blank one is shown to the right on this slide) with a reference to the standards used.
If questions already exist on a slide, then the specific MPs that the questions address are listed in the Pull-tab.
Slide 215 / 215
Standards for Mathematical Practice
MP1: Making sense of problems & persevere in solving them.MP2: Reason abstractly & quantitatively.MP3: Construct viable arguments and critique the reasoning of others. MP4: Model with mathematics.MP5: Use appropriate tools strategically.MP6: Attend to precision.MP7: Look for & make use of structure.MP8: Look for & express regularity in repeated reasoning.
Additional questions are included on the slides using the "Math Practice" Pull-tabs (e.g. a blank one is shown to the right on this slide) with a reference to the standards used.
If questions already exist on a slide, then the specific MPs that the questions address are listed in the Pull-tab.