- The goal of this activity is to develop an understanding of compensation. Compensation is the underlying math concept behind the “Make it Friendly” strategy. Students will use cubes to create combinations that have a total of 30. The students should observe that the most efficient strategy is to remove one boy cube as they add one girl cube, as a result, the sum of 30 does not change.
- The teacher will open Google Slides presentation Explore: Developing the Make it Friendly Strategy.
- The students will read the learning targets (Slide 2).
- The teacher will review the vocabulary (efficient and strategy) used within the lesson (Slides 3 and 4).
The teacher will present a word problem. The teacher will follow these steps: First, ask the students to close their eyes and visualize the story as the teacher reads the problem aloud. Second, ask the students to open their eyes and read the problem chorally with you. Third, ask the students, “What information in this problem is necessary to solving the problem?” It is important to use the language of part-part-whole with students. Restate their responses using the terms. For example, If a student says, "We know there are boys and girls in the lunchroom." The teacher would say, "Yes, we know the two parts in the problem are labeled boys and girls. In the problem, where would we find the whole or the total number of boys and girls?" Students should say, "lunchroom." The teacher would then ask, "What is the whole amount or the total number of boys and girls in the lunchroom?" (Slide 5)
The teacher will introduce the part-part-whole model. The model includes the word problem decomposed. The teacher may say, “It shows what we know and what we don’t know. If I add the two parts together, I will get the whole. As the graphic organizer shows, I need to determine what combination of boys and girls will total 30.” (Slide 6).
The teacher will show the students a bag of cubes and explain that the cubes will help them develop combinations. The teacher will then ask the students to independently think of a strategy they could use with the cubes to help them create combinations of 30. After an adequate wait time, the teacher will ask the students to turn and share their strategies with their neighbors. (Slide 7).
The teacher will explain to the students that they will work with a partner to generate as many solutions as possible in the time provided. Before they begin working, the partners need to decide who will be the recorder or writer and who will be the speaker for their group. They will write their roles at the top of their paper before they begin working. The teacher will provide each group with 30 cubes of one color and 30 cubes of another color. Students should only work with two different colors to help with understanding. The teacher will then distribute graphic organizers to students to use in order to organize their cubes. (If possible, the teacher should copy the graphic organizer on 8.5 x 14 paper.) The teacher could also draw the graphic organizer on a large sheet of construction paper or on the desk or table with an Expo marker. The students will record their combinations on notebook paper or on a printed copy of the problem (Slide 8).
The teacher will provide the students with either notebook paper, blank paper, or the doc with the word problem printed on it. As the students work, the teacher will monitor the students by asking some of the following questions: “What is your strategy?” “How are you using the cubes to help you create the most combinations?” “What pattern(s) are you noticing?” “How might you use what you have learned (the pattern) to solve a basic addition problem like 18 + 13=?” After monitoring the students, the teacher should choose students to share their strategies. (Slide 9).
- The teacher will need to decide whether to leave Slide 10 (the word problem) or Slide 8 (the directions) projected during the activity.
The teacher will choose three different examples of student work. If possible, choose one from each method of recording (T-chart, equations, and drawings). The goal will be to highlight the difference between using compensation versus using random combinations. If possible show compensation in all recording methods. If you do not get the student work you need to further the discussion, use Slide 12 to aid your discussion (Slide 11).
The teacher will ask the students, "How could we use what we just learned to make these numbers friendly to work with? 36 + 29 = "The students should think about the question independently first. After an adequate wait time, the teacher will ask the students to turn and tell their neighbors what they think. The teacher will listen to the conversation and choose a student who says something similar to, “ Take one from 36 and add it to 29. Now you have 30 plus 35 which is easier to add.” The goal of this is not to actually solve 29 + 36, but to develop a strategy to make the numbers friendly to work with. The teacher may want to solve the problem with the students. If so, the teacher may draw a number line to show starting at 36 and counting on 30. The teacher will want to model counting on by three tens as well as one hop of 30. The teacher may also want to model breaking apart 36 by place value, then adding the tens and the ones (Slide 13).
- Prior to the lesson, determine who will work together as partners. Partnerships should be homogenous, meaning a similar skill level. Differentiate the magnitude of the number as needed to meet the needs of each pair of students.
- The teacher will need to print the following materials: Graphic Organizer, Word Problem, and the Checklist.
- The teacher will need to create bags with 60 linking cubes (30 of one color and 30 of a different color). Each partnership will need a bag.
- The teacher will need to make sure teachers have Math Journals, paper, or a printed version of the word problem.
|Variation Tips (optional):
If students are learning online, the students can be sent to breakout rooms in Google Meet or Zoom to complete the activity. They can use virtual manipulatives.
The problem can be differentiated by lowering the number from 30 to either 15, 10, or 5. The goal of developing an understanding of the practice of compensation, the underlying concept behind the “Making it Friendly” strategy can be developed with smaller numbers.