Partial Products
The partial products of
126 x 3 are
What is
300 + 60 + 18?
Select the expressions that have a product of 640:
(6x100) + (4x10)
9 x 54
60 x 40 x 1
160 x 4
(6x100) + (4x10)
160 x 4
How would you use the Area Model to find 6 x 132?
100 x 6
30 x 6
2 x 6
A museum has 4 display cases. There are 118 coins in each case. How many coins are there in all the display cases?
4 x 118 =
= 400 + 40 + 32
= 472 coins in all
Round 98,732 to the ten thousands place.
99,000
The Mississippi River is about 8 times the length of the Hudson River. If the Hudson River is about 300 miles long, about how many miles long is the Mississippi River?
8 x 300 = Mississippi River length
The Mississippi River is about 2,400 miles long.
Estimate the product:
9 x 62
Round 62 to 60:
9 x 60 = 540
How would you use the Area Model to find 5 x 811?
= (5 x 800) + (5 x 10) + (5 x 1)
= 4,000 + 50 + 5
= 4,055
A large fish tank can hold 245 gallons of water and a small fish tank can hold 130 gallons of water. A pet store buys 3 large fish tanks and 6 small fish tanks. How much water will they need to fill all 3 large fish tanks and 6 small fish tanks?
245 x 3 = 130 x 6 =
= 600 + 120 + 15 600 + 180 + 0 =
= 735 = 780
735 + 780 = 1,515
A total of 103,985 fans attended the baseball game on Saturday, and a total of 103,667 fans attended the game on Sunday. Use > or < to compare the attendances. Which day had more fans attend the game? Which place value should you use to compare?
103,985 > 103,667
Use the hundreds place to compare.
What are the partial products for 8 x 4,367?
8x4,000
8x300
8x60
8x7
Sarah earns $48 a week babysitting. She saves all of her earnings for 6 weeks. Estimate to determine about how much money Sarah saves.
Round $48 to $50
50 x 6 = 300
Sarah earns about $300 babysitting.
There are 731 students at Mrs. Z School. Each student is getting a box of pencils that holds 4 pencils. How many pencils will the entire population of Mrs. Z school get?
= (4 x 700) + (4 x 30) + (4 x 1)
= 2,800 + 120 + 4
= 2,924
A red tree frog can jump up to 150 times its body length. If it is 5 cm long, how far can the frog jump?
150 x 5cm =
= 500 + 250
= 750 cm
There are 17,000 people registered for a dance marathon. Only 10,730 people registered to volunteer. How many people registered to dance?
17,000 – 10,730 = 6,270
6,270 people registered to dance.
Mrs. Z has candy in bags of 15 and in bags of 30. If she gives 3 bags of 15 to one class and 8 bags of 30 to another class, how many pieces of candy did Mrs. Z give out?
3 x 15 = 45
8 x 30 = 240
240 + 45 = 285
Ellie estimates the product of 211 and 6 is 1,800. Is this estimate reasonable? Explain.
No it is not reasonable. I know this because 211 should be rounded to 200, then multiplied by 6 to get 1,200 not 1,800.
How is the area model different than the bar diagram?
The area model is an algorithm. A bar model is another way to represent an equation.
A small bag of marbles has 15 marbles. A large bag of marbles has 80 marbles. How many marbles are in 3 large bags and 4 small bags?
Small bag total: 15 x 4 = 60 marbles
Large bag total: 80 x 3 = 240 marbles
Total = 300 marbles
What are the first 5 multiples of 20?
20, 40, 60, 80, 100
Amusement Park tickets cost $40 for each adult and $30 for each child. If 9 girls and 4 adults visit the park, how much will the trip cost?
Girl’s Cost: 9 x $30 = $270
Adult’s Cost: 4 x $40 = $160
Total Cost: $270 + $160 = $430
Sam and his two brothers want to fly to Boston. The plane trip costs $319. About how much will the trip to Boston cost in total for Sam and his two brothers?
Round $319 to $300.
$300 x 3 = $900
Which of the numbers below can be used to solve this problem using the area model: 6 x 1,842?
(6 x 1,000) 5,000 4,800 40 x 6
(6+6)
= (6 x 1,000) + (6 x 800) + (6 x 40) + (6 x 2)
= 6,000 + 4,800 + 240 + 12
= 11,052
Tony says to multiple 219 x 3, you multiply 2 x 3, 1 x 3, and 9 x 3 and then add the partial products. Explain Tony’s error. How would you help Tony understand how to correctly multiply 219 x 3?
Tony did not use the correct place value for each digit when he expanded 219. He would need to do 200 x 3, 10 x 3, and 9 x 3. I could use place value blocks to show Tony how to use place value.
What are the factors of 36?
1, 2, 3, 6, 12, 18, 36