To add... or subtract...
Factors and Multiples
Am I multiplying? Why didn't I make a tape diagram!!??
Where is this place? What is my Value?
Multiplicative Conundrums
100

The Buffalo Zoo is tracking the number of visitors over a weekend. On Saturday, 12,450 people visited. On Sunday, 15,325 people visited.

The Question: How many people visited the zoo in total over the weekend?

Addition

12,450 + 15,325= 27,775 visitors

100

9.Which number is not a multiple of 7? 

a. 14

b. 17

c. 49

d. 70

b. 17

100

The Scenario: At a local pet store, there are 8 hamsters. The store has 4 times as many fish as it has hamsters.

The Question: How many fish are at the pet store?

8 x 4

32 Fish

100

The Scenario: In the number 57,432, what is the value of the digit 7?

  • (A) 700

  • (B) 7,000

  • (C) 70,000

  • (D) 70


(B) 7,000

100

Level 1: Basic Arrays/Area Models

The Scenario: A classroom has 4 rows of desks. Each row has 12 desks.

The Question: Which expression can be used to find the total number of desks in the classroom?

  • (A) 12 + 4

  • (B)  12 divide4  4

  • (C) 12 X 4

  • (D) 12 - 4

c. 12 X 4

200

A tech company in New York City has a warehouse with 45,800 laptops. During a massive back-to-school sale, they sold 23,150 of them.

The Question: How many laptops are left in the warehouse?

45,800 - 23,150= 22,650 laptops

200

Which numbers are multiples of 9? choose all that apply. 

a. 90

b. 27

c. 29

d. 72

a.90 & b.27

200

Level 2: Finding the Unknown Factor

The Scenario: A library has two bookshelves. The fiction shelf is 54 feet long. The non-fiction shelf is 9 feet long.

The Question: How many times longer is the fiction shelf than the non-fiction shelf?

6 times longer

54/9

200

Consider the two 4s in the number 44,125. How does the value of the 4 in the ten-thousands place compare to the value of the 4 in the thousands place?

The Question: Complete the sentence: The 4 in the ten-thousands place represents _______ times the value of the 4 in the thousands place.

10 times

200

To solve 7 x 23, Sarah broke the problem into two smaller parts:


(7 x 20) + (7 x 3)


The Question: What is the final product of 7 x 23?

  • (A) 140

  • (B) 161

  • (C) 143

  • (D) 154

140 + 21

(B) 161

300

Two apple orchards in Upstate New York are totaling their harvest. Orchard A picked 38,765 apples. Orchard B picked 46,438 apples.

The Question: What is the combined total of apples picked by both orchards?


38,765 + 46,438 = 85,203 apples

300

Jacob told Eric that 5 is a composite number is Jacob correct? 

YES

NO

NO 

300

Level 3: "Times as Many" with Multi-Digit Numbers

The Scenario: A school cafeteria sold 120 cartons of milk on Monday. On Friday, they sold 3 times as many cartons as they did on Monday.

The Question: How many cartons of milk were sold on Friday?

123 x 3 = 360 Cartons

300

Expanded Form and Word Form

The Scenario: A local park covers thirty-six thousand, eight hundred five square feet of land.

The Question: Which of the following shows this number written in expanded form?

  • (A) $30,000 + 6,000 + 80 + 5$

  • (B) $3,000 + 600 + 80 + 5$

  • (C) $30,000 + 6,000 + 800 + 5$

  • (D) $30,000 + 6,000 + 800 + 50$

(C) 30,000 + 6,000 + 800 + 5

300

A local bakery sells boxes of cookies. Each box contains 10 cookies. On Saturday, the bakery sold 6 boxes. On Sunday, they sold 8 boxes.

The Question: How many total cookies did the bakery sell over the weekend?



60 + 80 = 140


400

The Adirondack Park has two main hiking regions. Region One has an area of 60,000 acres. Region Two has an area of 42,575 acres.

The Question: Exactly how many more acres are in Region One than in Region Two?

60,000 - 42,575 = 17,425 acres

400

list all the factors of 27.

1,3,9,27

400

Level 4: Comparison with a Total (The "Tape Diagram" Challenge)

The Scenario: A baker made chocolate and vanilla cupcakes. She made 5 times as many vanilla cupcakes as chocolate cupcakes. She made 4 chocolate cupcakes.

The Question: How many cupcakes did she make in all (chocolate and vanilla combined)?

4 x 5 = 20

20+4 = 24 total cupcakes

400

The Scenario: The population of a town in New York is 77,491.

The Question: What is the relationship between the value of the 7 in the ten thousands place and the value of the 7 in the thousands place.

ten times as much

400

The Scenario: Look at the partial products used to solve the problem below:


4 x 36


  • Step 1: 4 x 30 = 120

  • Step 2: 4 x 6 = ?

The Question: What is the value of the missing partial product in Step 2, and what is the final product of 4 x 36?

Step 2: 24

Final Product: 144

500

The Scenario: A professional football stadium is tracking attendance for three games.

  • Game 1: 62,450 fans

  • Game 2: 18,300 fans

  • Game 3: 25,750 fans

The Question: Is the attendance of Game 1 greater than or less than the combined attendance of Game 2 and Game 3? By how much?

18,300 + 25,750 = 44,050

62,450 - 44,050 = 18,400

Game 1 is greater by 18,400

500

Which are a factor pair of 36?

a. 3,12

b. 6,9

c. 1,3

d. 4,18

a. 3,12

500

DAILY DOUBLE!

Level 5: The Double Comparison (Multi-Step)

The Scenario: Three friends are saving money for a trip to a New York state park.

  • Leo saved $10.

  • Maya saved 4 times as much as Leo.

  • Sam saved $20 less than Maya.

The Question: What is the total amount saved by all three friends?

Leo 10

Maya 10 x 4 = 40

Sam 40-20=20

10+40+20

Total : $70

500

The Scenario: Use the digits 4, 0, 9, 2, 7 to create the largest possible 5-digit number and the smallest possible 5-digit number (the number cannot start with 0).

The Question: Write both numbers. Then, use the symbol <, >, or = to compare the two numbers. Finally, determine how much larger the digit in the ten-thousands place of your "largest number" is compared to the digit in the ten-thousands place of your "smallest number."

Largest: 97,420; Smallest: 20,479. 

Comparison: 97,420 > 20,479. The value of the 9 is 70,000 greater than the value of the 2.

500

Two schools are collecting cans for a food drive.

  • School A collected 12

  • School B collected 3 times as many cans as School A.

The Question: How many more cans did School B collect than School A? Show your work.

12 x 3 = 36

36 - 12 = 24

24 More Cans