In this series of lessons, students learn to analyze and solve a second basic type of word problem based on a single operation of addition or subtraction. These problems are all based on situations that can be described as “increase” or “decrease” situations. In this type of problem the situation described is based on two independent groups of things that make up a third, larger group. They are different from “combination” problems covered in an earlier lesson in that the feature that differentiates the two subgroups is some action that results in an increase or decrease in the size of an original group. In other words, they also represent a part-part-whole situation. In increase problems, the sum is the group that results from the putting together two subgroups. In decrease problems, the sum is the initial number before two subgroups are formed from the larger group.

Students learn a systematic strategy for identifying the elements described in the problem as the whole and it’s parts. They then match the elements in the problem to the addends and sum of an addition number sentence. When the unknown number is the sum, they learn to add the known addends. When the unknown number is one of the addends, they learn to subtract to find the unknown addend.

In the first lesson in this series, students learn to determine whether the “whole”, the larger group made up of two smaller groups, is the group that exists before the action occurs or the group that results after the action occurs.

In this lesson, students learn to use what they have learned previously about the relationship among groups in increase/decrease situations to write an addition number sentence in words. They are given a word problem and must write an addition sentence that represents the relationship between the groups described in the problem. They do this using a systematic strategy based on first identifying the group that represents the group that contains both of the other groups and labeling that group “all” – either the group that exists before an action occurs, or the group that exists after the action occurs. They then identify the two groups that make up that group - either the beginning group and the decrease group or the increase group and the ending group - and complete an addition number sentence with the names of these groups.

In this lesson, students write a number sentence in words as they did in the lesson before, then they fill in the numbers given in the problem that correspond to two of the groups. The other group is identified as the unknown group with the letter x. They then solve the number sentence to find the solution.

In this lesson, students solve the same kind of problems as they solved in the lesson before, but they don’t write a number sentence in words or numbers. They solve the problem on paper and enter their final answer on screen.

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