CAHSEE Math Problem of the Day -- Week 16
Teacher Notes & Answers
Week & Day Week 16 – Day 1
Concept/Skill Estimating addition
Standard 7 MR: 2.1
Use estimation to verify the reasonableness of calculated results.
Materials CAHSEE Math Released Item # 139
Overview for Week
All of the problems this week deal with making an estimate to find the correct answer.
This means students will not need to find the exact answer. They will need to round the numbers to simplify the calculations. In these questions they should also eliminate the obviously wrong answers.
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Have students review how to round numbers:
Note: Since the CAHSEE gives the answers to choose from students will be able to tell to what place they need to round the answers.
1.
Look at the answers to see what place to round off to.
2.
A number that is 5 or more should be rounded up; a number that is 4 or less should be rounded down.
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Have students do the guided practice on Day 1 of the student CAHSEE Math
Problem of the Day -- Week 16 worksheet.
Example:
Write an expression that would give the BEST estimate for the following expression to the nearest hundred:
239 + 687 + 355
239 will be rounded to _200___
687 will be rounded to _700___
355 will be rounded to _400___
The expression that gives the BEST estimate is
A 200 + 600 + 300
B 200 + 700 + 300
C 200 + 700 + 400
D 300 + 700 + 400
Day 1 continued on next page.
Laura Westermeier, Ed.D.
SAUSD, Educational Services
Fall 2007
Week 16 – Teacher - Page 1 of 6

CAHSEE Math Problem of the Day -- Week 16
Teacher Notes & Answers
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Have students do the CAHSEE released test item on Day 1 of the student CAHSEE
Math Problem of the Day -- Week 16 worksheet.
(CAHSEE Math Released Item # 139)
139. The table below shows the number of visitors to a natural history museum during a 4-day period.
Students need to round the numbers to
Day Number of Visitors
Which expression would give the BEST estimate of the total number of visitors during this period?
A 500 + 1100 + 1300 + 300
B 600 + 1100 + 1300 + 300
C 600 + 1100 + 1300 + 400
D 600 + 1100 + 1400 + 400
Laura Westermeier, Ed.D.
SAUSD, Educational Services
Fall 2007
Week 16 – Teacher - Page 2 of 6

CAHSEE Math Problem of the Day -- Week 16
Teacher Notes & Answers
Week Week 16 – Day 2
Concept/Skill Estimating multiplication
Standard 7 MR: 2.1
Use estimation to verify the reasonableness of calculated results.
Materials CAHSEE Math Released Item # 140
Review that when doing estimates for multiplication, look at the answers provided to determine which place the problem needs to be rounded to. For example, if there is only one digit in the answer besides 0 then the numbers multiplied need to be rounded so they only have one digit.
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Have students do the guided practice on Day 2 of the student CAHSEE Math
Problem of the Day -- Week 16 worksheet.
Example:
Which is the best estimate of 189 x 32?
A 600
B 6,000
C 60,000
D 600,000
First, look at the answers. How many digits besides 0 are in the answer: __1__
The 189 should be rounded to _200____
The 32 should be rounded to __30___
200 x 30 = 600
The correct ANSWER is _600__.
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Have students do the CAHSEE released test item on Day 2 of the student CAHSEE
Math Problem of the Day -- Week 16 worksheet.
Day 2 POD
(CAHSEE Math Released Item # 140)
140. Which is the best estimate of 326 x 279?
A 900
B 9,000
First round the numbers in the expression to
300 x 300.
Multiple the rounded numbers to get 90,000.
C 90,000
D 900,000
Laura Westermeier, Ed.D.
SAUSD, Educational Services
Fall 2007
Week 16 – Teacher - Page 3 of 6

CAHSEE Math Problem of the Day -- Week 16
Teacher Notes & Answers
Week Week 16 – Day 3
Concept/Skill Estimating division
Standard 7 MR: 2.1
Use estimation to verify the reasonableness of calculated results.
Materials CAHSEE Math Released Item # 143
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Have students do the CAHSEE released test item on Day 3 of the student CAHSEE
Math Problem of the Day -- Week 16 worksheet.
Day 3 POD
(CAHSEE Math Released Item # 143 )
143. Sally paid $1.89 for 5 plums. About how many plums would she get for $10?
A 4
B 5
C 10
D 25
Here is an example where students should begin by eliminating the obviously wrong answers.
A is wrong because it is less than the number of plums Sally got for $1.89.
B is wrong because it is the same as the number of plums Sally got for $1.89.
That leaves C and D.
Do an estimate: Sally paid about $2 for 5 plums so for $10 she should get 5 times as many plums or 5 x 5 = 25. The correct answer is D.
Laura Westermeier, Ed.D.
SAUSD, Educational Services
Fall 2007
Week 16 – Teacher - Page 4 of 6

CAHSEE Math Problem of the Day -- Week 16
Teacher Notes & Answers
Week Week 16 – Day 4
Concept/Skill Estimating percent
Standard 7 MR: 2.1
Use estimation to verify the reasonableness of calculated results.
Materials CAHSEE Math Released Item # 141
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Have students do the guided practice test item on Day 4 of the student CAHSEE
Math Problem of the Day -- Week 16 worksheet.
(CAHSEE Math Released Item # 142 )
142. The temperature on a mountain peak was 7 degrees Fahrenheit (°F) at 6:00 p.m. By 8:00 p.m., the temperature had dropped to 0°F. If the temperature continued to drop at about the same rate, which is the BEST estimate of the temperature at 11:00 p.m.?
A
-
20°F
B
-
14°F
C
-
10°F
D
-
9°F
Start by drawing a number line to show the time and the drop in temperature:
6:00 7:00 8:00 9:00 10:00 11:00
7 0 -3.5 -7 -10.5
At 11:00 the temperature should be about -10.5 which is closest to C -10°F
Laura Westermeier, Ed.D.
SAUSD, Educational Services
Fall 2007
Week 16 – Teacher - Page 5 of 6

CAHSEE Math Problem of the Day -- Week 16
Teacher Notes & Answers
Week Week 16 – Day 5
Concept/Skill Estimating rate
Standard 7 MR: 2.1
Use estimation to verify the reasonableness of calculated results.
Materials CAHSEE Math Released Item # 142
Day 5
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Have students do the CAHSEE released test item on Day 5 of the student CAHSEE
Math Problem of the Day -- Week 16 worksheet.
(CAHSEE Math Released Item # 141 )
141. Marcus plans to buy a CD that has a regular price of $13.99. It is on sale for
10% off, but Marcus will have to pay 7% sales tax. Which is the MOST reasonable estimate of the total cost of the CD including tax?
A $12.50
B $13.50
C $14.50
D $15.50
First estimate that the price of the CD is $14.
If it is 10% off then you need to subtract 14 -1.40 to get a cost of $12.60.
You then need to add the tax so multiply the new cost of the CD (rounded to the nearest 1)
13 x .07 to get a tax of .91 which is close to $1.00.
To find the total cost add $12.60 and $1.00 to get $13.60 which is closest to B $13.50
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At the end of the week remind students to keep the student CAHSEE Math
Problem of the Day -- Week 1 worksheet to use as a study guide as they continue to prepare for the CAHSEE.
Laura Westermeier, Ed.D.
SAUSD, Educational Services
Fall 2007
Week 16 – Teacher - Page 6 of 6