Math Strategy: Trial & Error - Multiplication
Math Strand: Number sense and numerationFrench Video:
English Video:
Overview
Trial and Error is a strategy that can be used when students are solving partitive division problems. In a partitive division situation students begin with the whole (for example 20 cookies) and the number of groups (for example 4 friends) and have to determine how many units would be in each group. Students who view this as a fair sharing problem will divvy up the total into each group, either one by one or in small quantities until the total is used up. When a student looks to use a multiplication strategy; making a prediction about the quantity in each group and then checking to see if they are correct, they are using the trial and error strategy. Students will often predict the number of items in each group is the same as the number of groups.
How this supports student learning
A student using trial and error to solve the cookie problem will try out composites of different sizes. They may begin with 4 in each group, finding they have only accounted for 16 of their cookies. In trial and error, their guesses are systematic, not random. The next guess will be a direct reflection of the outcome of their first guess. Knowing 4 was too small they will select a new composite just slightly larger. Through this process, they are demonstrating and strengthening their ability to make reasonable predictions. The student is also reinforcing their ability to unitize, as they count each set of composite units (5 cookies) they understand that this represents one group (or unit).
The student begins by trying groups of 4. When they realize that they haven't accounted for all 20 cookies they will adjust their guess.
The student knew they were close, with 4 in each group, so they decide to try one higher. They count to find that 4 groups with 5 in each equals 20.
Where to next
When playing card games, such as Go Fish to Ten begin with a set number of cards (for example 12) and ask students to predict how many cards each player will have. Activities like "Mystery Number" are another way to practice the trial and error strategy.
An example of Mystery Number:
I see 32 horse legs in a field. How many horses could there be?
The student recognizes that there are 4 legs on each horse
The student could begin with a known fact:
4 x 10 = 40.
Realizing this is too high they would go to another known fact, that is "nearby":
4 x 7 = 28
This time they are too low. They reason that the number of groups must fall between 7 and 10 and it must be 8, as they reason that 32 is closer to 28 than 40 and that 8 is closer to 7 than 9 would be. The student may also rely on a concrete or pictorial model to solve an unknown fact.
4 x 8 = 32
No comments:
Post a Comment