Unit 6, Lesson 12
Solve Problems Involving Multiplication
Grade 4
Activity 1
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A baby elephant was born exactly 48 weeks ago. How many days old is the elephant?
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A leap year has 366 days. A non-leap year has 365 days. How many days are in 3 leap years?
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In our calendar system, some months are 31 days long, some are 30 days long, and one month (February) is either 28 or 29 days long.
What if the calendar system changed so that each month has 31 days? How many more days would there be in a year?
Student Section Summary
We learned to multiply factors whose products are greater than 100, using different representations and strategies.
When working with multi-digit factors, it helps to decompose them by place value before multiplying. For example, to find the value of , we can decompose the 5,342 into its expanded form, , and then use a diagram or an algorithm to help us multiply.
multiply. 5 thousand 3 hundred 42 times 4. 7 rows. First row: 5 thousand 3 hundred 42. Second row: multiplication symbol, 4. Horizontal line. Third row: 8. Fourth row: 1 hundred 60. Fifth row: 1 thousand 2 hundred. Sixth row: plus 20 thousand. Horizontal line. Seventh row: 21 thousand 3 hundred 68
In both the diagram and the algorithm, the 20,000, 1,200, 160, and 8 are called the partial products. They are the result of multiplying each decomposed part of 5,342 by 4.
We can do the same to multiply a two-digit number by another two-digit number.
For example, here are two ways to find the value of . The 31 is decomposed into and 15 is decomposed into .
multiply. 31 times 15. 7 rows. First row: 31. Second row: multiplication symbol, 15. Horizontal line. Third row: 5. Fourth row: 1 hundred fifty. Fifth row: 10. Sixth row: plus 3 hundred. Horizontal line. Seventh row: four hundred sixty 5.
Diagram, rectangle partitioned vertically and horizontally into 4 rectangles. Top left rectangle, vertical side, 10, horizontal side, 30, area, 10 times 30 equals three hundred. Top right rectangle, horizontal side, 1, area, 10 times 1 equals 10. Bottom left rectangle, vertical side, 5, area 5 times 30 equals one hundred fifty. Bottom right rectangle, area, 5 times 1 equals 5.