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6
Lesson 3
NYS COMMON CORE MATHEMATICS CURRICULUM
Exit
Ticket
Find the quotient using a model.
1. Find
the quotient:
Problem
Set
For the following exercises, rewrite the division problem. Then be sure to draw a model to support your answer.
NYS COMMON
CORE
MATHEMATICS
1.
÷
3COMMON
NYS
CORE MATHEMATICSCURRICULUM
CURRICULUM
1.
2.
Lesson 8
6
÷
Problem Set
÷
Example 1 (10 minutes)
Calculate each quotient.
Today we will work with Partitive Division.
3. 1.
÷3
Step 1: Let’s use an example that uses partitive division: 50 ÷
1 4
4. 2. 4 3 ÷ 7
6
Lesson 2
NYS COMMON
CORE
Example
1 MATHEMATICS CURRICULUM
1
2
.
3
9
2. 3.÷ 326 ÷ 10
5.
Divide
÷
Step 4.
1: Decide
÷ 2 on an interpretation. (given: partitive model)
Problem Set
2. Rewrite each problem as a multiplication question. Model the answer.
Rewrite each problem as a multiplication question. Model the answer.
Step 2 is to draw a model. How many equal size rectangles do we need?
1.
Nicole has used 3
6 feet of ribbon. This represents
of the total amount of ribbon she started with. How much
ribbonHow
did Nicole
haveknow?
at the start?
do you
2.
The denominator of the fraction tells us we are using thirds. We need 3 rec
How many quarter hours are in 5 hours?
Draw a model.
The 50 accounts for how many of those 3 rectangles?
Two because the numerator tells us how many thirds that the 50 represents
Lesson 1:
Interpreting Division of a Whole Number by a Fraction—Visual
So the 50 must be
spread
out
evenly
between
two thirds. How much would be in e
Models
Lesson 3:
Interpreting and Computing
Division of a Fraction by a Fraction—
More Models
Date:
Date:
9/9/13
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
25
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
Draw a model.
9/17/13
S.16
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Creative
Commons
Attribution-NonC
Creative Commons Attribution-NonCommercial-ShareAlike
3.0 Unported
License.
3.
4.
5. .How much chocolate will each person get if 3 people share 1/2 lb. of chocolate
equally?
6. How many 3/4- cup servings are in 2/3 of a cup of yogurt?
NYS COMMON CORE MATHEMATICS CURRICULUM
Le
Problem Set
1.
Find each sum or difference.
a.
381
1
10
214
43
100
7. Find each sum or difference.
3
4
b.
32
c.
517
12
1
2
37
3
+ 312
50
100
NYS COMMON CORE MATHEMATICS CURRICULUM
d.
632
16
3
+ 32
25
10
3
50
Exercises
e.
421 1–4 212
8. 1.
2.
Lesson
9
10
Calculate the product.
324.56 × 54.82
Use a calculator to find each sum or difference. Round your answer to the nearest hundredth.
3
7
a.
422
b.
23 + 45
2.
1
5
367
5
9
7
8
Kevin spends $11.25 on lunch every week during the school year. If there are 35.5 weeks during the
how much does Kevin spend on lunch over the entire school year? Remember to round to the neare
Lesson 4: The Opposite of a Number
9. Xavier earns $11.50 per hour working at the nearby grocery store. Last week,
Xavier worked for 13.5 hours. How much money did Xavier earn last week?
Remember to round to the nearest penny.
Classwork
Exercise 1: Walk the Number Line
1.
Each integer has an opposite, denoted
;
and
same distance from zero on the number line.
are opposites if they are on opposite sides of zero and the
NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 14
6
10.
Problem Set
Example 1: Every Number has an Opposite
1. Asian purchased 3.5 lbs. of his favorite mixture of dried fruits to use in a trail mix. The total cost was $16.87. How
Locate
8 and
opposite
on the number line. Explain how they are related to zero.
muchthe
didnumber
the fruit
costitsper
pound?
2. Divide: 994.14 ÷ 18.9
8
7
6
5
4
3
2
1
0
1
2
3
1
2
3
4
5
6
7
8
11.
Exercises 2–3
2.
Locate the opposites of the numbers on the number line.
a.
9
2
b.
c.
d.
4
7
10
9
8
7
6
5
Lesson 4:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
4
3
2
1
0
4
5
6
7
8
9
10
The Opposite of a Number
10/8/13
S.11
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Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
$73.45 Gas and Electric
Lesson$45.00
Summary
Cell phone
The order of numbers in an ordered pair is important because the ordered pair should describe one
location in the coordinate plane.
12.
The first number (called the first coordinate) describes a location using the horizontal direction.
6.
1
3
1
5
1
8
Arrange
the following
rational
numbers
in order
from greatest
to least:
, 0 , using
, the
. vertical direction.
The second
number
(called
the second
coordinate)
describes
a location
Problem Set
13.
1.
Use the set of ordered pairs below to answer each question:
{(4,20), (8,4), (2,3), (15,3),
(6,15), (6,30),
(1,5), (6,18), (0,3)}
Lesson 8:
Ordering Integers and Other Rational Numbers
a.
Date:
10/15/13
Write the ordered pair(s) whose first and second coordinate have a greatest common factor of 3.
b.
Lesson
11 6 3 3.0 Unpor
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Attribution-NonCommercial-ShareAlike
Write the ordered pair(s) whose first coordinate is a factor of its
second
coordinate.
c.
Write the ordered pair(s) whose second coordinate is a prime number.
COMMON
CORE
MATHEMATICS
CURRICULUM
©NYS
2013 Common
Core, Inc.
Some rights
reserved. commoncore.org
2.
This work is licensed under a
Problem14.
Set
Write ordered pairs that represent the location of points A, B, C, and D, where the
first coordinate represents the horizontal direction, and the second coordinate
For
each of thethe
following
twodirection.
quantities in problems 1–4, which has the greater magnitude? (Use absolute value to
represents
vertical
defend your answers.)
1. 33 dollars and 52 dollars
2.
14 feet and 23 feet
3.
24.6 pounds and 24.58 pounds
1
3. 4.Extension:
11 degrees and 11 degrees
4
Write ordered pairs of integers that satisfy the criteria in each part below. Remember that the origin is the
whose coordinates are (0,0). When possible, give ordered pairs such that: (i) both coordinates are positiv
For problems 5–7, answer true or false. If false, explain why.
both coordinates are negative; and (iii) the coordinates have opposite signs in either order.
5. The absolute value of a negative number will always be a positive number.
a.
These points’ vertical distance from the origin is twice their horizontal distance.
6.b. TheThese
absolute
value of
any number
will always
be athe
positive
number.
points’
horizontal
distance
from
origin
is two units more than the vertical distance.
c.
These points’ horizontal and vertical distances from the origin are equal but only one coordinate is po
7. Positive numbers will always have a higher absolute value than negative numbers.
8. Write a word problem whose solution is: |20| = 20.
9. Write a word problem whose solution is: |
70| = 70.
15.
16.
17.
NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson
Lesson Summary
The axes of the coordinate plane must be drawn using a straight edge and labeled (horizont
(vertical axis).
Before assigning a scale to the axes it is important to assess the range of values found in a set
well as the number of grid lines available. This will allow you to determine if the number of un
line should be increased or decreased so that all points can be represented on the coordinate
you construct.
Problem Set
18.
1. Label the coordinate plane then locate and label the set of points below.
(0.3,0.9), ( 0.1,0.7), ( 0.5, 0.1),
( 0.9, 0.3), (0, 0.4)
2. Label the coordinate plane then locate and label the set of points below.
(90,9), ( 110, 11), (40, 4),
( 60, 6), ( 80, 8)