December 18, 2012
“Teachers are thus free to provide students with
whatever tools and knowledge their professional
judgment and experience identify as most helpful
for meeting the goals set out in the Standards.”
~ Introduction to the CCSS
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Describe the overview of 6-8 math
curriculum
Identify properties of the RDW
modeling technique for application
problems
Describe and apply tape diagrams
Evaluate foundational and challenging
problems from gr. 6-8
 State
Overview of scope and sequence
and modules
 Tape Diagram Problems
 Grade Level Problems
 Assessment Problems (PARCC)
Grades
Modules
Lessons
PK-5
Common Core
Inc
6-12
CCI with Support
from EdutTron
Tape diagrams are best used to model
ratios when the two quantities have the
same units.

1. David and Jason have marbles in a ratio of 2:3.
Together, they have a total of 35 marbles. How many
marbles does each boy have?
 2. The
ratio of boys to girls in the class
is 5:7. There are 36 children in the
class. How many more girls than boys
are there in the class?
Lisa, Megan and Mary were paid $120
for babysitting in a ratio of 2: 3: 5. How
much less did Lisa make than Mary?
The ratio of Patrick’s M & M’s to Evan’s
is 2: 1 and the ratio of Evan’s M & M’s to
Michael’s is 4: 5. Find the ratio of
Patrick’s M & M’s to Michael’s.
The ratio of Abby’s money to Daniel’s is
2: 9. Daniel has $45. If Daniel gives
Abby $15, what will be the new ratio of
Abby’s money to Daniel’s?
Double number line diagrams are best used when the quantities
have different units. Double number line diagrams can help make
visible that there are many, even infinitely many, pairs of numbers in
the same ratio—including those with rational number entries. As in
tables, unit rates (R) appear in the pair (R, 1).

It took Megan 2 hours to complete 3 pages of math
homework. Assuming she works at a constant rate, if she
works for 8 hours, how many pages of math homework will
she complete? What is the average rate at which she works?
 Read
(2x)
 Draw a model
 Write an equation or number sentence
 Write and answer statement
• Unit
• Object
• Context
2
boxes of salt and a box of sugar cost
$6.60. A box of salt is $1.20 less than a
box of sugar. What is the cost of a box of
sugar?
Salt
Salt
$6.60
3 parts = $6.60- $1.20
Sugar
$1.20+$1.80= $3.00
$1.20
3 parts = $5.40
1 part = $5.40 ÷ 3
= $1.80

The students in Mr. Hill’s class played games at recess.
•
•
•
•
6 boys played soccer
Mika Said: “Four more girls
4 girls played soccer
jumped rope than played
2 boys jumped rope
soccer.”
8 girls jumped rope
Chaska Said: “For every girl that
played soccer, two girls jumped
rope.”
Mr Hill Said: “Mika compared girls by looking at the difference and Chaska
compared the girls using a ratio”

1) Compare the number of boys who played soccer and jumped rope
using the difference. Write your answer as a sentence as Mika did.

2) Compare the number of boys who played soccer and jumped rope
using a ratio. Write your answer as a sentence as Chaska did.

3) Compare the number of girls who played soccer to the number of
boys who played soccer using a ratio. Write your answer as a
sentence as Chaska did.
 Compare
these fractions:
3
4
and
3+1
4+1
Which one is bigger than the other? Why?
 Using
Grade level packets, explain the
exemplar solution of problems.
Thanks for coming!
Links
 www.btboces2.org/mathpd
 http://www.parcconline.org/samples/ma
thematics/grade-6-slider-ruler
 http://www.parcconline.org/samples/ma
thematics/grade-7-mathematics
 www.Engageny.org