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Number Trail Grade 5 / Week 03 / Wednesday
3/6
Week 03 · Multiply big numbers

Wednesday

Bigger factors and estimates
// Partial products and the standard algorithm
⏱ about 15 min

Wednesday: Bigger factors and estimates

Lucy the Ladybug and Bennie the Bear count jars of berries for the summer picnic.

"There are 342 berries in each jar, and we have 25 jars," says Bennie.

Lucy blinks. "That is a three-digit number! I feel worried I will make a mistake."

"Mistakes help us learn," says Bennie kindly. "And we have a way to check."

"First we estimate. 342 is close to 300, and 300 × 25 = 7,500."

"So our answer should be a bit more than 7,500," says Lucy. "That helps me feel ready."

Learn it: the same steps for bigger numbers

Row 1: 342 × 5 = 1,710.

Row 2: 342 × 20 = 6,840.

Add: 1,710 + 6,840 = 8,550.

Check the estimate: 8,550 is a bit more than 7,500. It makes sense.

Four-digit numbers work the same way.

1,206 × 34: Row 1 is 1,206 × 4 = 4,824. Row 2 is 1,206 × 30 = 36,180.

Add: 4,824 + 36,180 = 41,004.

ESTIMATE FIRST
  • Read the question.
  • Tap your answer.
Round 342 to the nearest hundred. Then multiply by 25.
Round 412 and 38 to the nearest ten. Then multiply.
Round 1,206 to the nearest hundred. Then multiply by 34.
MULTIPLY THREE-DIGIT NUMBERS
  • Read the question.
  • Tap your answer.
342 × 25 = ?
412 × 38 = ?
205 × 47 = ?
678 × 19 = ?
MULTIPLY FOUR-DIGIT NUMBERS
  • Read the question.
  • Tap your answer.
1,206 × 34 = ?
2,315 × 12 = ?
4,008 × 25 = ?
1,750 × 46 = ?
DOES IT MAKE SENSE?
  • Read the question.
  • Tap your answer.
Riley's answer for 342 × 25 is 855. Is it reasonable?
An answer for 412 × 38 is 15,656. Is it reasonable?
SentenceTrue or false?
342 × 25 = 1,710 + 6,840?
205 × 47 = 9,635?
2,315 × 12 = 27,780?
1,206 × 34 = 4,824 + 3,618?
WHY THIS EXERCISE1,206 × 30 is 36,180, not 3,618. So 1,206 × 34 = 41,004.
Try it
Find a book with more than 100 pages.
Pretend you have 24 copies of it.
Estimate how many pages all the copies have.
Then multiply on paper and compare with your estimate.
Show 205 × 47 in two rows. Write your estimate beside it.

Strong work! Tomorrow Chris tells a story full of multiplication.

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