Tens in Action
Solve: 6 x 30
180
6 x 3 tens = 18 tens = 180
Which expression equals 6 x 40?
A. 6 x (10 x 10 x 10 x 10)
B. 6 x (10 + 10 + 10 + 10)
C. 4 x (10 + 10 + 10)
D. 6 + 40
B
40 is 10 + 10 + 10 + 10
Which partial-product expression equals 3 x 16?
A. (3 + 10) + (3 + 6)
B. (3 x 10) + (3 x 6)
C. (3 x 10) x (3 x 6)
D. (3 + 10) x (3 + 6)
B
Split 16 into 10 + 6 and multiply both parts by 3.
A rectangular patio is 3 units tall and 20 units wide. It is split into two 10-unit-wide sections. Choose TWO expressions for its total area.
A. 3 + 10 + 10
B. (3 x 10) + (3 x 10)
C. 3 x 10
D. (3 + 10) + (3 + 10)
E. 3 x 20
B and E
Both find 60 square units. Add the areas of the two sections.
Mia says 6 x 40 is 24 because 6 x 4 = 24.
Explain exactly what she missed.
Use tens to prove your answer.
She counted tens as ones. The answer is 240.
Full credit: explain that 40 is 4 tens, so 6 x 4 tens = 24 tens = 240. A bare answer is not enough.
How many TENS are in the product of 70 x 3?
A. 21 tens
B. 210 tens
C. 10 tens
D. 73 tens
A. 21 tens
7 tens x 3 = 21 tens, which is 210
Which TWO expressions can be used to solve 4 x 70?
A. 4 x (7 + 10)
B. 4 x (7 x 10)
C. 28 x 10
D. 28 + 10
E. 4 + (7 + 10)
B and C
4 x (7 x 10) = (4 x 7) x 10 = 28 x 10
Solve: 3 x 16.
48
(3 x 10) + (3 x 6) = 30 + 18 = 48.
A rectangle is 5 units tall and 17 units wide. Its width is split into 10 and 7 units. The 7-unit section has area 35 square units. What area belongs in the 10-unit section?
A. 5
B. 15
C. 17
D. 50
D. 50 square units
The missing partial area is 5 x 10 = 50.
Leo says 3 x 18 = (3 x 10) + 8. Find his error, correct the expression, and prove your correction with equal groups or a drawing.
He must multiply the 8 by 3 too: (3 x 10) + (3 x 8) = 54.
Full credit: three groups each contain 10 AND 8. Therefore there are three groups of 8, not just one.
Solve: 8 x 40
320
8 x 4 tens = 32 tens = 320
Which expression equals (5 x 10) + (5 x 3)?
A. 10 + 13
B. 5 + 13
C. 10 x 13
D. 5 x 13
D. 5 x 13
The common factor is 5; 10 + 3 = 13
Solve 4 x 23 using partial products. Name both partial products.
92; partial products 80 and 12
(4 x 20) + (4 x 3) = 80 + 12 = 92.
Other factors may be used, as long as the final product is 92 and partial products were used.
A rectangle is 5 units tall and 17 units wide. Split its width into 10 and 7. What is its TOTAL area?
85 square units
50 + 35 = 85 square units.
Sam splits 4 x 15 into (4 x 10) + (4 x 5). Jo splits it into (4 x 7) + (4 x 8).
Decide whether each method works. Defend your decision, then choose the method you would use and explain why.
Both work and give 60. A justified preference may vary.
Full credit: 10 + 5 and 7 + 8 both equal 15, and both parts are multiplied by 4. Explain the choice, for example that tens and fives are easier facts.
Complete 5 x 60 = (___ x ___) x 10 using two one-digit factors. Then solve.
(5 x 6) x 10 = 300
Regroup the factors: 5 x (6 x 10) = (5 x 6) x 10. Either order in the blanks is acceptable.
Ava practices piano 3 days each week for 20 minutes each day. She does this for 4 weeks. Choose THREE expressions that find the total minutes.
A. (3 + 20) x 4
B. (3 x 20) x 4
C. (3 x 4) x 20
D. (3 x 20) + 4
E. (20 x 4) x 3
B, C, and E; 240 minutes
Each correct expression multiplies days per week, minutes per day, and weeks: 3 x 20 x 4.
There are 6 packs with 12 pencils in each pack. Use partial products to find the total.
72 pencils
(6 x 10) + (6 x 2) = 60 + 12 = 72.
A base-ten model has 4 equal rows. EACH row has one ten rod and 3 single cubes. Choose THREE expressions for the model.
A. (4 x 10) + (4 x 3)
B. 40 x 12
C. (4 x 10) x (4 x 3)
D. 40 + 12
E. 4 x 13
A, D, and E
4 tens and 12 ones make 52. Multiplying the partial products does not represent the model.
A 5-by-18 rectangle has area 90 square units.
Eli splits the width into 10 and 8 and says the partial areas are 50 and 8.
Is the total of 90 enough to show his model is correct? Explain and repair the model.
No. The partial areas must be 50 and 40 square units.
Full credit: the 8-unit section is still 5 units tall, so its area is 5 x 8 = 40. The incorrect partial areas sum to 58, not 90; a correct total alone does not validate the model.
There are 9 boxes with 20 markers in each box. How many markers are there? Explain using tens.
180 markers
9 x 2 tens = 18 tens = 180 markers
Write TWO different equivalent expressions for 7 x 30. Use addition inside parentheses in one and multiplication inside parentheses in the other.
Examples: 7 x (10 + 10 + 10) and 7 x (3 x 10)
Both expressions keep 7 groups of 30; the product is 210. Accept other valid expressions meeting both requirements.
Solve 3 x 24 in TWO ways: split 24 into 20 + 4, then split it into 12 + 12.
72 in both methods
3 x 20 + 3 x 4
= 60 + 12
= 72
Also, 3 x 12 + 3 x 12
= 36 + 36
= 72.
A rectangle is 4 units tall and 26 units wide. Split its width into 20 and 6 units. Find both partial areas and the total area.
80 and 24 square units; total 104 square units
4 x 20 = 80 4 x 6 = 24
80 + 24 = 104.
A student says, "Every whole-number multiplication expression with a product of 120 must have a factor that ends in zero." Decide whether this is always true. Use TWO examples to support your decision and explain how tens can still help solve them.
False. Examples: 8 x 15 = 120 and 5 x 24 = 120. Neither has a factor ending in zero.
Full credit: provide two valid counterexamples and explain a tens strategy, such as 8 x 10 + 8 x 5 = 80 + 40 or 5 x 20 + 5 x 4 = 100 + 20. Other valid examples accepted.