Using Cognitively Guided Instruction for Teaching and Assessment
By conducting a series of basic math assessment exercises using multiplication word problems with your students, you can easily determine what skills they posses, what skills they have mastered and what difficulties they might be having. All of this information gives you baseline data for tailoring instruction to meet the specific needs of each student in your classroom.
Grouping and Partitioning problems involve three distinct quantities. The following scenario is used for illustration:
Sarah has 6 bags of marbles. There are 10 marbles in each bag. Altogether, Sarah has 60 marbles.
The three quantities in the problem are the number of bags, the number of marbles in each bag and the total number of marbles. In a problem, any one of these three quantities can be the unknown. For Multiplication problems, both the number of objects in each group and the number of groups is given. What is unknown, however, is the total number of objects.
Below you will find a number of multiplication word problems which may be used as a basic math assessment in your classroom. These problems demonstrate an identified continuum of knowledge as first detailed in the published findings of Fennema, Carpenter, et all.
Sample Problems for Basic Math Assessment of Multiplication
These multiplication word problems are to be used as examples, only. They can be changed to include familiar names and actions. For instance, you might use the names of students in your class, or their family members. You might also use situations that are familiar - like a child handing out a birthday treat or playing with popular objects. Be creative! The numbers in the problems may also be altered, depending on the mathematical abilities of the child or children you are working with.
- Mrs. Slipper has 4 boxes of candy. There are 10 pieces of candy in each box. How many pieces of candy does she have all together?
- Tommy has 4 packages of Sponge Bob lollipops. There are 7 lollipops in each package. How many lollipops does Tommy have all together?
- Our classroom has 6 jars. There are 8 butterflies in each jar. How many butterflies are in our room all together?
- Farmer Ted has 10 hens. There are 6 eggs under each hen. How many eggs are there all together?
Multiplication Solution Strategies
When solving multiplication problems, children typically begin by using direct modeling to show the action as described in the problem. Called Grouping, a student will construct each of the groups as specified in the problem and then count the total number of objects.
With time and additional practice, students will replace this direct modeling strategy with skip counting or repeated addition. Take a look at the following problem:
Joe has 5 bags of cookies. There are 3 cookies in each bag. How many cookies does Joe have all together?
To find the solution, a student might count: 3,6,9,12,15. Or, s/he might use repeated addition like this: 3+3+3+3+3=15.
Eventually, these counting strategies give way to derived facts (like doubling numbers) and known facts which have been memorized.
Other Problem Types
As is the case with division, there are other problem types that involve multiplication principles. These include:
- rate problems
- grouping problems
- partitioning problems
- price problems
- Scaler Multiple problems
Unique to multiplication are the following related problem types:
- array problems
- area problems
- combination problems
Planning for Instruction
By using these multiplication word problems for a basic math assessment you are better able to plan instruction on an individual basis, which is one of the cornerstone beliefs of the Congnitively Guided Instruction approach.
For more information about Cognitively Guided Instruction, or for basic math assessment problems for other skills, please take time to read the other articles in this series.