The final picture is this:
Putting counters 1 at a time into groups is a partitive strategy. Counting the amount in 1 group is how you find the answer to a partitive problem.
1. Tell whether each of these word problems is a multiplication problem, a partitive division problem or a measurement division problem.
a. Three children can ride in each car. How many cars will we need to take 18 children to the zoo?
18 children in groups of 3. Total split into groups of a known size. The unknown is how many groups are needed. Measurement division.
b. Each box of crayons has 8 crayons in it. How many crayons are in 3 boxes?
8 crayons in each group. 3 groups. Total unknown. Multiplication.
c. Each person left 2 shoes at the door. There are 12 shoes at the door. How many people left shoes?
12 total shoes. Known number in each group. Unknown numberof groups. Measurement division.
d. There are 4 colors of cups in the cupboard. There are the same number of each color of cup. There are 20 cups in all. How many cups are there of each color?
Each color is a group--4 groups. 20 total. Unknown amount in each group. Partitive division.
e. Erin has 36 Pokemon cards. She can fit 9 cards on each page of her card collecting book. How many pages will she need to hold all of her Pokemon cards?
36 total. 9 in each group. Unknown number of groups. Measurement division.
f. Julia's mom made 24 cookies. She wants to put them on 3 plates, so each plate will have the same number of cookies. How many cookies should she put on each plate?
24 total. 3 groups. Unknown amount in each group. Partitive division,
g. Kyle has 3 bags of marbles. There are 12 marbles in each bag. How many marbles does he have?
3 groups. 12 in each group. Unknown total. Multiplication.
h. There are 40 books to put on shelves. Eight books will fit on each shelf. How many shelves do I need to hold the books?
40 total. 8 in each group. Unknown number of groups. Measurement division.
i. I am making 12 cupcakes. I want to put 4 M&M's on each cupcake. How many M&M's do I need.
12 cupcakes. 4 for each of the 12. 12 groups of 4. Unknown total. Multiplication.
2. Direct modeling. Tell what kind of problem (multiplication, measurement division or partitive division) fits with the direct modeling strategy.
a. Place 3 counters to represent groups. Count out 18 counters. Put counters 1 at a time next to the counters representing the groups. Count the amount in a group for the answer.
The final picture is this:
Putting counters 1 at a time into groups is a partitive strategy. Counting the amount in 1 group is how you find the answer to a partitive problem.
b. Place 5 counters to represent groups. Put 3 counters next to each of the group counters. Count the total amount in all of the groups (not including the 5 that represent the groups) to find the answer.
The final picture is this:
Putting a known number of counters into groups is either a multiplication or a measurement division action. Finding the total number of counters is how to find the answer to a multiplication problem. This is multiplication.
c. Count out 24 counters. Using the 24 counters, make groups of 4 counters. Count the number of groups for the answer.
Counting out the total to start with is a division strategy. Making groups of a known size is a measurement division strategy. Counting the number of groups is how you find the answer to a measurement division problem.
d. Count out 30 counters. Put 2 counters into each of 5 groups. Add 2 counters to each group. Add 1 counter to each group. Add another counter to each group. Count the amount in a group to find the answer.
Counting out the total to start with is a division strategy. Putting equal amounts into a known number of groups is a partition division strategy. Counting the amount in 1 group is the way to find the answer to a partition division problem. Partition division.
e. Make 5 groups of 4 counters. Count the total number of counters, and add another group of 4 counters. Count the total number of groups for the answer.
Known number of groups and known numbe of counters in each group is multiplication givens. Counting the total number of groups is how you find a multiplication answer. Multiplication.
3. Rewrite each of these problems so that they stay as close as you can to being the same problem, but there is an action to be acted out that you have introduced (turn each from a harder to an easier problem--without changing the numbers or the type of items):
a. There are 4 pencil holders in the room, and each pencil holder has the same number of pencils. There are 20 pencils total. How many pencils are in each pencil holder?
Ms Triangle has 20 pencils, and 4 pencil holders. She wants to put the same number of pencils in each pencil holder. How many pencils will be in each pencil holder?
b. Ms. Cupcake used 6 apples to make each pie. In all, she used 18 apples. How many pies did she make?
Ms Cupcake has 18 apples. It takes 6 apples to make a pie. How many pies can she make?
c. Janet's collection of 24 rocks is in some small boxes. Each box has 6 rocks in it. How many boxes of rocks does she have?
Janet has 24 rocks in her rock collection. She wants to put her collection into some small boxes. Each box can hold 6 rocks. How many boxes will she need to hold all of her rocks?
d. Kyle has 5 boxes of toy animals. There are the same number of animals in each box. In all, he has 30 toy animals. How many animals are in each box?
Kyle has 30 toy animals. He wants to put them into 5 boxes, so that each box will have the same number of animals. How many animals will be in each box?
