### Effective Math Instruction 6

```October 2, 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

Describe how Math Sprints:




diagnose fluency gaps
build fluency
Create Math Sprints
Identify strategies to teach ratio and
proportion problems
 Fluency
in 6-8
 Transition
Units (Gap Analysis)
 Teaching
Ratios and Proportional
Relationships
 Module
Unit alignment
6
7
A
bananas are 6 for \$1.50, and a sign by the
oranges indicates that they are 5 for
\$3.00. Find the total cost of buying 2
bananas and 2 oranges.
 A \$0.85
 B \$1.70
 C \$2.25
 D \$4.50
 Jeremy
has two 7-foot-long boards. He
needs to cut pieces that are 15 inches
long from the boards. What is the greatest
number of 15-inch pieces he can cut from
the two boards?
A 15
B 10
C 11
D 12


A comparison of 8 black circles to 4 white circles can
be written as the ratio of 8:4 and can be regrouped
into 4 black circles to 2 white circles (4:2) and 2
black circles to 1 white circle (2:1).
Students should be able to identify all these ratios
and describe them using “For every…., there are …”
A
clothing store offers a 30% discount on
all items in the store.
Part A: If the original price of a sweater is \$40, how much will it cost
after the discount?
A
clothing store offers a 30% discount on
all items in the store.
Part B: A shopper bought three of the same shirt and paid \$63 after the
30% discount. What was the original price of one of the shirts?
A
clothing store offers a 30% discount on
all items in the store.
Part C: Every store employee gets an additional 10% off the already
discounted price. If an employee buys an item with an original price of
\$40, how much will the employee pay?
The new floor in the school cafeteria is going to be constructed of square tiles
that are either gray or white and in the pattern that appears below:
Part A: What is the ratio of gray tiles to
white tiles?
Part B: What is the ratio of white tiles to
the total number of tiles in the pattern?
The new floor in the school cafeteria is going to be constructed of square tiles
that are either gray or white and in the pattern that appears below:
Part C: If the total cost of the white tiles is
\$12, what is the unit cost per white tile?
Part A: 10 to 8, 5:4, or other equivalent ratio
Part B: 8 to 18, 4:9, or other equivalent ratio
Part C: \$1.50 per white tile

On a bicycle you can travel 20 miles in 4 hours. What are the unit rates in this
situation, (the distance you can travel in 1 hour and the amount of time
required to travel 1 mile)?

Last summer, a family took a trip to a beach that was
about 200 miles away from their home. The graph
below shows the distance driven, in miles, and the time,
in hours, taken for the trip.


While on vacation, a group can rent bicycles and scooters by the week.
They get a reduced rental rate if they rent 5 bicycles for every 2 scooters
rented. The reduced rate per bicycle is \$15.50 per week and the reduced
rate per scooter is \$160 per week. The sales tax on each rental is 12%.
The group has \$1600 available to spend on bicycle and scooter rentals.
What is the greatest number of bicycles and the greatest number of
scooters the group can rent if the ratio of bicycles to scooters is 5:2?


While on vacation, a group can rent bicycles and scooters by the week. They get a reduced rental
rate if they rent 5 bicycles for every 2 scooters rented. The reduced rate per bicycle is \$15.50 per
week and the reduced rate per scooter is \$160 per week. The sales tax on each rental is 12%.
The group has \$1600 available to spend on bicycle and scooter rentals. What is the greatest
number of bicycles and the greatest number of scooters the group can rent if the ratio of bicycles
to scooters is 5:2?
Number
# Bikes
5
10
15
20
# Scooters 2
4
6
8
Value
Bikes
77.5
155
232.50
310
Value
Scooters
\$320
\$640
\$960
\$1280
Value of
both
\$397.5
\$795
\$1192.50 \$1590
Cost with
Tax
\$445.20 \$890.40
\$1335.60 \$ 1780


David is making his own strawberry yogurt. In David’s mixture, the
number of strawberries is proportional to the amount of milk, in
cups. David uses 4 cups of milk for every 14 strawberries in his
mixture.
Which equation represents the relationship between s, the number
of strawberries, and m, the number of cups of milk he uses?

Jill walks 3 meters every 2 seconds. Let d be the number of meters Jill has
walked after t seconds. d and t are in a proportional relationship.
If 2 pounds of beans cost \$5, how much will 15 pounds
of beans cost?
 Based
on the Sample Questions
• What are the skills most students have to be
successful
• What are the skills students don’t have
 Part
1: Fluency Work (10 minutes)
 Part
2: Problem Solving (6 minutes)
 Part
3: Content Lesson and Debrief (34
min)
 Gr
6 R.P.
Effective Teaching: Feedback
Engagement
&
7th
Grade Exemplar and the intro to
the Shifts
CCLS
Shifts and (8) Math Practices
Progressions, Illustrative
Mathematics and Math Discussions



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
Contingent
•
•
The praise is based on something you really did
You earned it
•
•
I state specifically what it is you’re being praised for
“You included a diagram in every word problem!”
•
•
I really mean it
I’m not just saying it
•
•
It’s matched to you- your level
Matched to the person you are
•
Different all the time
Specific
Genuine
Appropriate
Varied
Attributed to performance and effort
The tone of the praise statement suggests that obviously the student has the ability to do
well, and that it is the effort the student exerted that made the performance turn out so well
• “You worked hard on math-facts and it paid off on the quiz.”
•
Thanks for coming!