Lesson Questions: How can I use my deductive reasoning skills and my understanding of numbers and variables to solve problems?

Transcription

1 Name of Lesson: Triplet Topic: Algebraic Puzzle Lesson Gifted Standard and element(s): G1CG1. Students will reason logically using induction, deduction, and abduction. a. Explore critical thinking skills through the process of convergent thinking. d. Solve problems using logical reasoning. f. Develop verbal and nonverbal communication skills to convey logical reasoning. Supports CCGPS: 1.OA.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. 1.OA.8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. Standards for Mathematical Practice: 2. Reason abstractly and quantitatively. 6. Attend to precision. 7. Look for and make use of structure. Essential Question(s): How can I use the mathematical meaning of equivalence to solve problems? *How can I use variables to solve problems? *How can I use patterns, rules, and relationships to solve problems? Lesson Questions: How can I use my deductive reasoning skills and my understanding of numbers and variables to solve problems? Lesson Summary: Students will be introduced to an activity where they match variables and their values with operations and possible solutions to create a group of Triplets. Key idea: Solving algebraic puzzles is easier if students employ strategies based on properties of numbers. Assessment Description/Performance Task: Constructed response Informal assessment Performance task Selected response Brief Description of Assessment: Students will solve one Triplet puzzle by matching variables and their values with operations and possible solutions to create a group of Triplets. The teacher will rate each child as he/she solves the assessment puzzle, explaining his/her thinking. Instructional Methods: Hook/Activator: Tell students that they are going to learn how to solve a kind of algebraic puzzle that involves Triplets. Show them numerous Triplet cards. Teaching Strategy: Note: This part will be easier to do if you have cards made ahead of time with each Triplet part (Ex. m = 4 or m + 3 or = 6 ) written on one card. (A printable set of the cards needed in this lesson is provided.) The cards can then be moved around during the lesson. They could be used with an ELMO, have magnets attached for use on a dry erase board, or be created for an interactive whiteboard.

2 Show students the following Triplet cards in this order, pointing out how they are organized by category. value for the variable operation solution m = 4 m + 3 = 6 m = 2 m + 2 = 5 Explain that a Triplet is a group of three cards one of each category, that together, make a true statement. Ask students to create a Triplet by choosing one value for the variable, one operation, and one solution. Ask the students to explain their thinking as they work. Discuss the fact that there are two Triplets that could be made simultaneously. (m = 4, m + 2, = 6 AND m = 2, m + 3, = 5) Show students the following: value for the variable operation solution h = 2 h + 2 = 4 h = 3 h 1 = 5 h = 5 h + 5 = 7 Ask them to choose one value for the variable, one operation, and one solution to create a Triplet. Offer to start them off by choosing: h = 2 h + 2 = 4 Since solving the puzzle means that all cards must be used simultaneously in Triplets, ask students to make another Triplet from the remaining values, operations, and solutions. When they can t, ask what would happen if they started off with a different Triplet. Suggest: h = 5 h + 2 = 7 Ask students to use the remaining cards to create another Triplet. When they can t, ask what would happen if they started off with a different Triplet. Suggest: h = 3 h + 2 = 5 Ask students to use the remaining cards to create another Triplet. This time, they should be able to create two other Triplets. h = 2 h + 5 = 7 h = 5 h 1 = 4 Explain to students that they will now be given several sets of cards (puzzles) to solve. There will be four cards with values for variables, four operations cards, and four cards with solutions. In order to solve each puzzle, they are to arrange all the cards to create four Triplets. Students need

3 to begin with Puzzle 1 and work through Puzzle 6 with a partner. As they work, they must talk with their partners, sharing strategies, including those that do not work. Model thinking aloud. As students work on this, observe them and listen to as much conversation as you can. Help those who need it, and frequently ask for reasons if students do not ask each other. Watch for those who use mathematical reasoning as opposed to random trial and error. Assessment: Have each student complete the as you observe. Use the provided rating sheet to record your observations. Be sure to ask students to think aloud as they solve the puzzle. Summary by the Learner: Each pair will discuss strategies with another pair, using specific puzzles as needed to demonstrate. Differentiation: More capable: Use Puzzle 7, which has 5 Triplets to create rather than 4. OR Have students create a puzzle of their own. Challenge them to make one that has only one correct solution. Less capable: Use Puzzles 1 or 2 with one whole row removed. (Recommend remove last row on Puzzle 1, first row on Puzzle 2.) Materials for this Lesson: Triplet cards from lesson for demonstration (made ahead of time- see below) Triplet Puzzle cards (Puzzles 1-6) per pair of children; recommend copying all Puzzle 1 s on one color, all Puzzle 2 s on another, etc. Note: the uncut puzzles in the lesson plan are the key. It is suggested that you solve them before teaching this lesson so that you are familiar with the kind of reasoning that you will be looking for in your students work. cards (optional- for differentiation) Blank cards (optional- for differentiation if students are creating their own puzzles) Assessment Puzzle cards (number of sets will depend on how you assess) Vocabulary for this Lesson: Triplet variable operation solution

4 Lesson Puzzle 1 Lesson Puzzle 1 Lesson Puzzle 1 m = 2 m + 3 = 5 Lesson Puzzle 1 Lesson Puzzle 1 Lesson Puzzle 1 m = 4 m + 2 = 6

5 h = 2 h + 5 = 7 h = 3 h + 2 = 5 h = 5 h 1 =4

6 = = 3 = = 7 = 7-5 = 2 = 10-6 = 4

7 = 5 - = 0 = = 6 = 2 + = 4 = = 8

8 ? = 5? + 3 = 8? = 4? - 2 = 2? = 2 5 +? = 7? = 7? - 4 = 3

9 5 = b b + b = 10 b = 4 b - b = 0 8 = b b - 5 = 3 b = b = 9

10 = 0 + = 0 = = 6 = = 5 = 3-1 = 2

11 e = 1 e + e = 2 e = 6 e 5 = 1 7 = e 5 + e = = e e - 4 = 6

12 k = k = 4 2 = k k - 2 = 0 k = 3 k + 0 = 3 4 = k k + k = 8 k = 7 k - 1 = 6

13 p = 1 p + p = 2 p = 3 4 p = 1 2 = p 1 + p = 3 5 = p p + 0 = 5

14 Scoring guide for assessment of Triplet Puzzles Name Rating Comments Rating Description 4 Solves puzzle and can explain thinking processes 3 Solves puzzle, but give minimal, if any, explanation 2 Creates more than one Triplet, but not solve puzzle; gives minimal explanation, if any 1 Creates 1 Triplet 0 Does not create a Triplet