Download Grade 6 Answer Key

Grade 6 Answer Key
Day 1
1. D
2. For each step in the pattern, the student may see that each figure is the number of dots in the
previous figure plus the current figure number. So the rule for this pattern is to find the number
of dots in the current figure by adding the current figure number and the number of dots in the
last figure. This rule can be used to find the number of dots for any figure in the pattern.
Day 2
1. B
2. To solve this problem, students must calculate the next time both buses will leave Central
Station. There are different ways to find this time.
One method is to find the least common multiple of the two numbers, 10 and 16. The least
common multiple of two numbers is the smallest whole number that is divisible by each of the
numbers. One way to find the least common multiple is to list all the multiples of each number.
Then, look across both lists to find which multiples are multiples of both numbers. Then, choose
the smallest one. For example:
Multiples of 10 are 10, 20, 30, 40, 50, 60, 70, 80, 90,...
Multiples of 16 are 16, 32, 48, 64, 80, 96, ...
So, the least common multiple is 80, and 80 minutes from 4 p.m. is 5:20 p.m.
Another way of finding this time is to list the times the buses will leave and find the next time
both buses will leave at the same time. The bus to the stadium leaves every 10 minutes. So, this
bus will leave at the following times:
4:00
4:10
4:20
4:30
4:40
4:50
5:00
1
5:10
5:20
The bus to the zoo leaves every 16 minutes. So, this bus will leave at the following times:
4:00
4:16
4:32
4:48
5:04
5:20
The next time that both buses will leave the station at the same time is 5:20 p.m.
Day 3
1. D
2. Students must use the rate of earning and extend it over time. There are different ways to solve
this problem. One way is to extend the pattern to 6 hours:
Hours
Earnings
1½
$120
3
$240
6
$480
Another way is to calculate the hourly rate.
.
If the earning rate per hour is $80, then over 6 hours it will be $480, or
Another way students can solve the problem is to use a proportion:
2
.
Day 4
1. B
2. There are different ways to solve this problem.
Students might see that each layer has five more blocks than the layer before it. They can make a
table to show the pattern of blocks in each layer and extend the pattern to the tenth layer to find
there are 50 blocks.
Layer
1 2
Number of Blocks
3
4
5
6
7
8
9
10
5 10 15 20 25 30 35 40 45 50
Or, students might see that the number of blocks in each layer is 5 times the layer number. Then
they could use this formula (5 x layer number) to find the number of blocks in the tenth layer: 5
blocks x layer 10 = 50 blocks.
Day 5
1. C
2. The first step is to find the amount of money Jared will have saved each week. He saves $8,
but his mother contributes $2 (8 × 0.25 = 2). The next step is to find how long it will take Jared
to get to the $100 goal if he saves $10 a week. The answer is 10 weeks because 10 × $10 = $100.
Day 6
1. B
2. Using the order of operations means doing the operations in a specific order: first solve
expressions in parentheses, then use exponents, then multiply or divide, and finally add or
subtract. Because there are no parentheses or exponents in this expression, the first step is to
divide, 4  0.5  8. The expression becomes 10  8  4 . In the order of operations, next comes
addition or subtraction. Because there is an addition and a subtraction, the correct order is to
solve from left to right. So, 10  8  2 and 2  4  6 .
Therefore, the answer is 6.
Day 7
1. C
3
2. To find the rule, students should see that the second number (4) is found by multiplying the
first number (1) by 3 and by adding 1 to the answer: 4 = 1(3) + 1.
Then, students should test this rule on the third number (13) of the pattern. Can 13 be found by
multiplying 4 by 3 and by adding 1 to the result? The answer is yes: 13 = 4(3) + 1. Students
should test a few more numbers to make sure that the rule works for all numbers in the pattern.
The rule for the pattern is “multiply the previous number (the number before) by 3 and add 1.”
To find the next term, students need to apply the rule to 121, like this: 121(4) + 1 = 364.
Day 8
1. B
2. There are 6 grams of fiber in 1 cup of oatmeal because every 3 grams of fiber have cup of
1 1
1
oatmeal. So, 6 grams of fiber would have 1 cup of oatmeal (   1) . Because 1 cups of
2 2
8
oatmeal remain, this totals to about 7 grams of fiber.
Day 9
1. C
2. Divide the input by 2 and add 4; For example, when the input = 2, students get: 2 ÷ 2 = 1.
Adding 4 to this answer gives 1 + 4 = 5. So, for an input of 2, the correct output is 5.
Day 10
1. A
2. To calculate Joan’s savings, students need to determine the discount of each product she is
purchasing.
For the shampoo and toothpaste discounts, students can multiply the regular price by the fraction
discount to determine the amount of the discount:
Shampoo discount:
$7.50 
Toothpaste discount:
1
 $2.50
3
$4.50 
1
 $2.25
2
For the hair gel discount, they should express the percent discount as a decimal (25% becomes
0.25) and multiply it by the regular price to determine the amount of the discount:
$6.00  0.25  $1.50
By adding up all three discounts, students determine that Joan will save a total of $6.25.
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