Factors and Multiples
Prime Factorization, GCF, and LCM
Integers
Fractions
Arithmetic on Fractions
What Went Wrong?
100
What is a composite number?
Composite numbers have more than two factors.
100
What is the prime factorization of 525?
3\cdot 5^2 \cdot 7
100
What is a zero pair?
A pair of integers is called a zero pair if their sum is zero.
100
Consider the diagram below where one shape is considered the unit. What improper fraction is represented?
\frac{8}{3}
100
It is harvest season at Joe’s Farm. He has two pumpkin fields and the total area of the two pumpkin fields is 3 2/5 acres. The big field yield 3 2/5 tons of pumpkins and the small 2 1/12 tons of pumpkins. What is the total yield of pumpkins?
Write the answer as a mixed number and be sure to answer with the appropriate units.
5 \quad \frac{29}{60} \text{ tons}
100
What is wrong with this student's work? Find the correct answer.
6\times 3 \ne 24
The correct answer is
40
200
Rewrite the statement in the form a|b.
16 is a multiple of 4
4 | 16
200
Form a number bond diagram for addition and subtraction using 4, 6, and 10.
200
Use colored chips to compute the sum.
-8+5
200
Which fraction is larger?
\frac{2}{3} \text{ or } \frac{5}{7}?
\frac{5}{7}
200
For the following subtraction problem, use the comparison perspective. The results must come from your diagram.
\frac{7}{8}-\frac{3}{4}
200
A student is asked to give the minimal collection as his final answer. He draws the following.
What is wrong with this student's work? Find the correct answer.
He has too many units.
300
Use the rectangular model to show that 15 is a multiple of 3.
300
Using the list method, find
\text{GCF}(12, 18).
\text{GCF}(12, 18)=6
300
Using the chip model, compute the difference.
3-8
300
If the triangle shown has a value of 1 1/3, draw a picture that shows 1.
300
According to a recipe, 9/20 oz of sugar is needed to make 6 cookies. Ashley decided to use only a third of the sugar to make it healthier. How much sugar did Ashley use?
Be sure to answer with the appropriate units.
\frac{3}{20} \text{ ounces}
300
What is wrong with this student's work? Find the correct answer.
The student did not regroup when they could not take 9 from 7.
The correct answer is
400
Use the linear model to illustrate that 8 is a factor of 24.
400
Using the prime factorization of each number, find
\text{LCM}(24, 32).
You can leave your answer in terms of exponents.
\text{LCM}(24, 32)=2^5 \times 3 = 96
400
Using the number line model, find
-3\times 4
400
If the diagram represents 3/5, draw a diagram that represents 1.
400
Use fraction bars and the measurement (repeated subtraction) perspective to find the quotient.
\frac{5}{6} \div \frac{1}{3}
400
Given the problem 8 x 3, a student produced the following picture. What is wrong with the answer and what is the correct answer?
The second number repeats. The student should have added 3 repeatedly, not 8.
500
Complete the sentence below.
a is a factor of b if and only if there is a whole number c such that _________.
ac=b
500
Using the prime factorization of each number, find
\text{GCF}(16,25).
\text{GCF}(16, 25)=1
500
As you left your last class of the day at 4:30 pm, the temperature was 45 degrees. At dinner time, 6:30 pm, the temperature is 29 degrees. Assuming the temperature changes at a steady rate, what is the change in temperature each hour?
-8^{\text{o}}
500
If the diagram shown represents 1/8, draw a diagram that represents 3/4.
500
Name the perspective illustrated with the word problem below.
An airplane covers 50 miles in 1/5 of an hour. How many miles can the airplane cover in one hour?
Sharing or partitive perspective
500
Given
a=2^3 \cdot 7^2 \cdot 11
and
b=5^2 \cdot 7^3 \cdot 13^2
the student claims
\text{LCM}(a,b)=2 \cdot 7 \cdot 11 \cdot 5 \cdot 13
What is wrong and what is the correct answer?
The student did not take the maximum occurrence of each prime number in the factorizations.
\text{LCM}(a,b)=2^3 \cdot 5^2 \cdot 7^3 \cdot 11 \cdot 13^2