Estimate the following problems 79 / 4 418 / 4 419 / 7 237 / 2 36 * 385 This should be done as mental math with a whole class discussion. Do a few or all of the estimation problems to assess the students’ understanding of division. You can change the numbers so they will better fit the abilities in your class.

Leftover Brownies? We will review 4 ways a remainder might impact the answer to a word problem. The last one (share it equally by changing it to a fraction or decimal) is a 5th, not a 4th grade skill. However, you can introduce the idea to 4th graders so they know this can be done but not make this skill part of their assessment. If you don’t do this they will have an incomplete understanding that may cause confusion later. The numbers are the same for all brownie problems so that the class can focus on the treatment of the remainder. Please change any numbers in the latter problems so they are appropriate for your students. I change the name of the people in each problem to the names of my students that year.

Situational Context The Brownie Problem: 1 Jillian has 26 brownies which she will put onto plates that can each hold exactly 4 brownies. How many plates can be completely filled? The remainder is 2 brownies. You would ignore the remainder to give the final answer. The answer is 6 plates of 4 brownies each. What does the remainder represent? How does the remainder impact the answer? 3

The Brownie Problem 2: Julia has 26 brownies which she will put onto plates that can each hold exactly 4 brownies. How many plates will she use to hold all of the brownies? What is different about this problem? Unlike the first problem, all the brownies get put into boxes. The remainder makes you get another container. So, here the answer is 7 plates. How does the remainder impact the answer? 4

The Brownie Problem: 3 Reed has 26 brownies which he will put onto plates that can hold exactly 4 brownies. After he fills as many containers as he can, how many brownies will be left over? Still another variation. What has changed now? Now, the remainder is the answer. 2 brownies. How does the remainder impact the answer? 5

The Brownie Problem: 4 Victoria has 26 brownies. She will put 4 brownies on a plate and any remaining brownies on a plate. How many plates will be filled and what fractional part will another plate hold? 6 ½ plates. This is an awkward question but it gets at the point that we use the remainder of 2 brownies but the plate will only be ½ full. The remainder is changed to a fraction. How does the remainder impact the answer? 6

A roller coaster holds 30 people A roller coaster holds 30 people. There are 252 people waiting for a ride. How many times will the roller coaster need to run so that all 252 people get a ride? There is a remainder of 12 people. You would need to add one to the quotient so that all can ride the rollercoaster. The answer is the rollercoaster would neet 9 times. What does the remainder represent? How does the remainder impact the answer?

Colored Pencils What does the remainder represent? Mrs. Best is organizing the colored pencils. She is putting 24 pencils into a box and has 57 pencils. How many full boxes will she have? What does the remainder represent? How does the remainder impact the answer? The remainder is 9 pencils. The remainder is ignored so the answer is 2 full boxes. 8

Making sense of remainders 63 gumdrops for a class of 20 students. How many does each student get? 155 people waiting in line to ride the monorail. Each ride holds 50 people. How many rides are necessary for everyone to get a ride? 4 boxes of candy cost $5. How much does each box cost? Each gets 3 gumdrops. The remainder of 3 gumdrops is ignored. There would need to be 4 trips for the monorail to carry all 155 people. The remainder of 5 people forced the answer to increase by one. Again, this is a 5th grade problem but can be introduced to 4th graders. It is simple so they can deal with the remainder mentally. Each box cost $1 but there is $1 left. Split the $1 by the 4 boxes and you would get $.25. Each box is $1.25. The remainder was changed into a fraction. 9 9

Rebecca and her three sisters bought their mother a bread machine for her birthday. The machine cost $218, including tax. The sisters split the bill evenly. How much did each sister contribute? While this question is aligns with the 5th grade standard, it promotes strong discussion of remainders at any grade. There are 2 dollars left over. How would you split the $2 between 4 people? My 4th graders have solved this by just thinking about the $2 separately and not making it part of the algorithm. We do the division problem then discuss the remainder of 2. The remainder is shared equally between the 4 sisters. Each sister must pay another $.50 so the final answer is that each sister will pay $54.50. What does the remainder do to the answer?