What is measurement division

What if I have 5 on each plate? I want to put 4 cookies on each plate. How many plates do I need to hold my cookies? You can tell this is a measurement problem because it tells how many go on 1 each plate, and asks how many plates groups there are. A child could direct model to figure this out by making groups of 4 from a set of 24 counters. A child could figure this out by skip counting up by 4's until they reached 24, and keeping track of the groups as they counted up, or they could figure this out probably on paper by subtracting 4's from 24 until all were gone.

Price or cost problems are often appropriate for solving by direct modeling if the numbers are small enough. In price problems, the amount being grouped or shared is the money--the total cost, and it is grouped by the price per item.

So, if it is a problem about buying pencils, then the total cost will be grouped by the cost for each pencil, and a single group is the price of a single pencil. The cost of 36 cents must be divided among the 4 pencils. Cost per pencil is one group. The total cost is again divided among several pencils, but this time the price for one pencil is known, and the number of pencils groups in unknown.

Rate problems are a more general version of the sort of thinking involved in price problems. Whereas price problems involve a price per item cost for 1 item , general rate problems can relate a wider variety of things. Miles per hour is the most familar rate for most of us relating distance--miles, and time--hours , but there are lots of others: words per minute reading or typing , bushels per acre corn or other crops , miles per gallon.

Rate problems are usually appropriate for children at the age when they are familiar with the things being compared. In these examples, if children had experience perhaps in science with measuring distances things moved, and elapsed time with stop watches, these problems would be appropriate.

It takes a battery powered toy train 5 seconds to go 20 inches. How far does the train go in 1 second? The amount being divided up is the 20 inches travelled, and these are grouped into the distance travelled in each second.

The group in problems like this is often indicated by the sentences: "how far This uses the same type of total amout and way of grouping, but here we don't know how many groups how many seconds.

Multiplicative comparison problems use or ask for a comparison by explicitly using multiplication in the description. For these ones, it's helpful to compare not just the two kinds of division, but also compare division to multiplication. A farmer has 6 ducks. He has 3 times as many chickens as ducks. The quotient tells us the number of copies of the divisor that are in the dividend.

All rights reserved. Students enrolled in MthEd may make one 1 copy of this text for their personal use in this class. All other reproductions are expressly forbidden without the written permission of the author. In a measurement division problem ,you know how many should go in each group, and you have to figure out how many groups there will be.

A child could skip count add 3's until they got to 15, while keeping track of how many 3's were added: 3, 6, 9, 12, there were 5 groups of 3. Explain why this is harder than doing it with the measurement model thinking. A child could make a guess at how many would be in each group. So they might guess that 2 were in each group and skip count 3 groups of 2. Then they would realize that the number was too small, so they would try a bigger number, and they would keep trying numbers until they found one that worked: 5, 10, This is harder than what to do for the measurement division case because with measurement division, you know what number to skip count by and you can keep going until you get to the total.

With partition division, you know how many times to skip count, but you don't know what to skip count by, so it's harder to get started. You can put 15 into an array that is 3 down and 5 across, so if you want 3 groups you can look at the rows--then the number in each group is the number of columns, and if you want groups of 3 you can look at the columns--then the number of groups is the number of columns.

Either way, the answer is the number of columns, so of course both questions have the same answer. I have personally written rather a lot of these for Tell whether each of these word problems is a multiplication problem, a partitive division problem or a measurement division problem. Sally has 4 times as many pencils as Jan. Jan has 5 pencils. How many pencils does Sally have?