This 4th grade student wondered how many small bottles of ketchup would be needed to fill up the large bottle.
Although this can be thought of as a division problem, the context of pouring in caused her to think of it as a multiplication problem. Her diagram mimicked the real ketchup bottle. She kept track of the ounces of ketchup in red and the number of small bottles used in black.She then solved the problem a second way, using a place value strategy to multiply 6*64.
from Tomato Tomato by Graham Fletcher
This 6th grade student wondered how long will it take for the bucket to be filled up with water?
He created a ratio table to calculate how many 21.6 in3 measuring cups would fill the 590 in3 bucket. The ratio table helped him to efficiently work this out.
He then multiplied the 27 measuring cups by the 26 seconds it took to fill each cup and found the total time to fill the bucket. Keeping the convention of how we mark time, he converted the 702 seconds into minutes and seconds.
from Water Bucket by Asher Gittel
In this problem, the students wondered how long the jumbo paper clip was when it was straightened out.
This 4th grader recognized that the unfamiliar 3.5*9 was similar to the very familiar 35*9. She then transferred the strategies she knew for multiplying two digit numbers to the new problem with decimal numbers.
She decomposed 3.5 into 3 and 0.5. She knew 3*9=27. She reasoned that 0.5*9 meant one half of 9 or half of a group of 9. She knew that would 4.5. Just as with a whole number problem, she added the two products together 27 and 4.5 and came up with her solution.
from Straighten Up by Graham Fletcher
This 3rd grader wanted to know how many bins were on the is this gigantic Pic-a-Bric wall at the Lego Store in the Mall of America?
Taking a moment to think before crunching the numbers, the student found an efficient solution path. She multiplied to calculate how many bins were in the large array boxed in blue(30*12). Then she subtracted the 6 bins missing because of the sign (green box). Finally, she added the partial rows boxed in red to get the total.
Her strategy of breaking the bins up into smaller groups made this problem much easier to solve accurately.
From Lego Wall by Yummy Math
This student wondered how many blocks weighed as much as the nectarine.
He applied his prior knowledge of how doubling works with whole numbers to this new problem with fractions. Without someone modeling for him, he invented how to multiply fractions by whole numbers because his curiosity was sparked; he understood the context; and he recognized this as a similar problem to doubling whole numbers.
from The Nectarine by Graham Fletcher
This 3rd grade student wondered how many toy cars were in this parking lot. He constructed the distributive property to solve the problem with mental math. Instead of multiplying 17 columns by 4 rows, he broke it down into math facts that he already knew, 10×4 and 7×4.
The teacher then extended the learning by asking, “What other parking lots could hold 68 cars?”. The student quickly knew that he could make 1 long row of 68 cars. From there, he found solutions with 2 rows and 4 rows. The student invented his own method for finding the factors of 68.