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Things That Come in Groups Connections to the mathematics TEKS (3.4) Number, operation, and quantitative reasoning. The student recognizes and solves problems in multiplication and division situations. The student is expected to: (3.6) (A) learn and apply multiplication facts through the tens using concrete models (B) solve and record multiplication problems (one-digit multiplier) Patterns, relationships, and algebraic thinking. The student uses patterns to solve problems. The student is expected to: (A) identify and extend whole-number and geometric patterns to make predictions and solve problems (B) identify patterns in multiplication facts using concrete objects, pictorial models, or technology (3.15) Underlying processes and mathematical tools. The student applies Grade 3 mathematics to solve problems connected to everyday experiences and activities in and outside of school. The student is expected to: (A) identify the mathematics in everyday situations (B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness (C) select or develop an appropriate problem-solving strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem (D) use tools such as real objects, manipulatives, and technology to solve problems H Chapter 7 275 (3.16) Underlying processes and mathematical tools. The student communicates about Grade 3 mathematics using informal language. The student is expected to: (A) explain and record observations using objects, words, pictures, numbers, and technology (B) relate informal language to mathematical language and symbols (3.17) Underlying processes and mathematical tools. The student uses logical reasoning to make sense of his or her world. The student is expected to: (A) make generalizations from patterns or sets of examples and non examples (B) justify why an answer is reasonable and explain the solution process. Mathematics overview Students model multiplication facts using concrete materials and discover patterns in multiplication facts and properties of whole number multiplication. Lesson Overview Students make a list of real-world objects that come in sets of 2, 3, 4, and so forth. Connect these sets to multiplication equations, and use the objects to create and solve simple multiplication problems. Materials interlocking cubes large sheet of butcher paper unlined 8.5” x 11” paper glue H 276 Chapter 7 Lesson resources Suzanne Aker, What Comes in 2’s, 3’s and 4’s? Aladdin Paperbacks, 1992. Set-up (to set the stage and motivate the students to participate) Day one: 1. Choose a book that focuses on the concept of pairs. Read it to the class. (3.15A) 2. Have the students brainstorm other things that can be grouped into pairs. Make a chart on butcher paper and begin to list students’ ideas. For example, eyes, hands, ears, shoes, arms, dancing couples. (3.15A, C; 3.16A, B) 2's 3's 4's 5's 6's 7's 8's 9's 10's eyes hands Can extend to 12 depending on the group's ability 3. Have students think of things that are grouped into 3s. Record two or three responses and then put students into groups. Direct each group to continue their responses by using the unlined 8.5” x 11” paper to copy the butcher paper chart. They are to start with the 3s and continue through groups of 10. (3.15A, C; 3.16A, B) 4. Combine ideas onto the class chart. Record ideas from each group, eliminating any duplicates. Discuss and clarify answers. Talk about categories that were difficult to fill. (3.15A, C; 3.16A, B) 5. Have each group meet again and write a summary statement about what they did. Have them share statements with the class. (3.16A, B) H Chapter 7 277 Day two: 6. Review the chart and add any new ideas. Pose a problem with an example from the chart using the 2s. For example, “If I had six children, how many eyes would there be?” Draw a picture to show the answer. Write the appropriate number sentence: 6 x 2 = 12. Do a few more examples. Using the interlocking cubes, show how to “discover” the 2s facts. (3.4A, B; 3.6A, B) 1x2=2 2x2=4 7. Continue until 10 x 2 = 20. Discuss and clarify. (3.4A, B; 3.16A, B) 8. Have groups of students continue to work with the cubes and record their multiplication sentences on paper. (3.4A, B; 3.16A, B) 3's 1x3=3 10 x 3 = 30 Monitor and assist as needed. 9. Gather students together with their charts and discuss the findings. Discuss the patterns demonstrated in each number fact. Review concept of multiplication as sets of groups (4 groups of 2 is the same as 4 x 2 = 8). Assign each group of students a multiplication sentence and have them create it with interlocking cubes. Then have them show what multiplication fact will come next. Discuss the pattern. Teacher Students Next add H 278 Chapter 7 Have them show what multiplication fact would come before. Discuss the patterns again. (3.6A, B; 3.17A) Day three: 10. Review the multiplication sentences and the patterns. Tell the students that they will be writing stories using ideas from their list of multiplication sentences. Review the class chart. (3.4A, B; 3.6A, B; 3.17A) 11. Put up a story on the board that ends with a question that generates a multiplication sentence. (Example: Mrs. Jones’s third-grade class has four pairs of students who are going to the science fair. The school wants to honor all the partners with ribbons. Mrs. Jones was responsible for making the ribbons for her students going to the science fair. How many ribbons does she need to make?) Write the number sentence 4 x 2 = 8. Have students make up another story that would fit the multiplication sentence. (3.15A, B, C, D; 3.16A, B; 3.17B) 12. Tell the students that in pairs they will be making pages for a multiplication book. Each pair will make one or more pages for the book. The front of each page will have a story problem and an illustration. The back of the page will have a multiplication fact that goes with the story problem. (3.4A, B; 3.15A, B, C, D; 3.16A, B; 3.17B) Example: Front Back 10 x 4 = 40 Once there was a turtle with 10 children. She wanted to buy them shoes, but she didn't know how many shoes to buy. Help Mrs. Turtle. H Chapter 7 279 13. Assign a multiplication fact or facts to each pair of students and hand out paper. Allow time for students to complete their pages. Teacher monitoring and editing will be necessary. Have a pair of students that finishes early decorate a cover for the book. Put the book together. (3.4A, B; 3.15A, B, C, D; 3.16A, B; 3.17B) Summary Questions (to direct students’ attention to the key mathematics in the lesson) To determine to what extent students have connected multiplication to the action in the story, ask questions such as: • How did you decide what multiplication sentence to use with this story? (3.15A, B, C, D; 3.16A, B) • How do you know your answer to the problem is reasonable? (3.4A, B; 3.17B) To determine students’ general understanding of multiplication as an operation, ask questions such as: • How does each story in the book relate to multiplication? (3.4A; 3.15A; 3.17A) • What does multiplication mean? (3.4A; 3.15A; 3.17A) To focus students’ attention on strategies that they can begin to use to remember multiplication facts, ask questions such as: • What patterns did you see in the multiplication chart for groups of 2? Groups of 4? Groups of 5? (3.6A, B; 3.17A) • What other patterns did you see in the multiplication chart? (e.g., 2 x 3 = 3 x 2) (3.6A, B; 3.17A) Teacher notes (to personalize the lesson for your classroom) H 280 Chapter 7 Assessment Tasks (to identify the mathematics students have learned in the lesson) • Give students a multiplication story and have them act it out with manipulatives and write a number sentence to go with it. • Give students a multiplication sentence and have them write a story to go with it. • Have students write a summary of what they have learned about multiplication. Teacher notes (to personalize the lesson for your classroom) Extensions (to lead students to connect the mathematics learned to other situations, both within and outside the classroom) The book can be put in a center, and students can practice multiplication facts by working the problems in the book. Teacher notes (to personalize the lesson for your classroom) H Chapter 7 281