Mathematics Alignment Lesson Grade 5 Quarter 2 Day 87

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1 Mathematics Alignment Lesson Grade 5 Quarter 2 Day 87 Common Core State Standard(s) 5.OA.3 Generate two numerical patterns using two given rules. Identify apparent relationship between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns and graph the ordered pairs on a coordinate plane. For example, given the rule Add 3 and the starting number 0, and given the rule Add 6 and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Standards for Mathematical Practice Standard 7 Look for and make use of structure Materials Needed: From Day 85- Transparency/Blackline Master- Instructions for 5 th Grade Committees Spring Carnival Planning Transparencies/Blackline Masters- Fibonacci Sequence, Presentation Requirements Posterboard Index cards Markers Rulers Alignment Lesson Planning a Spring Carnival (Day 3 of 4) 1. Display Transparency Fibonacci Sequence and allow students to work on determining the pattern with a partner or in a small group. When students have had time to discover the pattern, select a student leader to explain the pattern and show how to determine the next three numbers in the sequence. 2. Have students take out their graphs from yesterday as well as the Describe the Graph sheet. Most committees will likely need more time to complete their graphs and describing the graphs (following the model from yesterday). 3. Explain to students that when they ve completed graphing and analyzing, they should move on to planning their presentation. 4. Display Transparency Presentation Requirements and read it with students so that each committee is familiar with what should be included in their presentation. 5. Have students complete Blackline Master- Which Representation Journal Prompt for homework. Assessment Ask students What are some other real world situations in which you could use numerical patterns to answer questions? Homework Blackline Master, Which Representation? Journal Prompt Source: Teacher Created Vocabulary

2 Transparency/Blackline Master Grade 5 Day 87 Fibonacci Sequence Standard 5.OA.3 Directions: Examine the sequence below to determine the pattern. Once you have discovered the pattern, find the next 3 numbers in the sequence The pattern is: The next 3 terms are:

3 Answer Key Grade 5 Day 87 Standard 5.OA.3 Fibonacci Sequence Answer Key Directions: Examine the sequence below to determine the pattern. Once you have discovered the pattern, find the next 3 numbers in the sequence The pattern is: To generate the next number in the pattern, you add the two previous numbers together. For example, = 3; 2 +3 = 5; = 8 and so on. The sequence begins with two 1s since you would add the first 1 plus 0 (since there was nothing before it) to generate the second number. The next 3 numbers are: 55, 89, 123

4 Transparency/Blackline Master Grade 5 Day 87 Presentation Requirements Standard 5.OA.3 Include the following on your poster (or other presentation tool): Data Tables: The data table for each item should be visible. The data table for each item should be clearly labeled. Each table should have a sentence with it that summarizes the pattern. Graphs: The graphs for each pair of data should be visible. The graphs for each pair of data should be clearly labeled. Each group should have a sentence with it to summarize the pattern. Other: Your committee name should be included. You should make your presentation as visually appealing as possible (other drawings, etc would be helpful). You should have the details of the relationships between the PTA s cost last year and your proposed cost for each item written down on index cards to use during your presentation. Each member of the group must actively participate in the presentation (holding the poster, etc) is not actively participating, You will have about 5 minutes to give your presentation and answer questions from the audience. All of your work, including the index cards used during your presentation will be turned in at the end of your presentation.

5 Blackline Master Grade 5 Day 87 Standard 5.OA.3 Name: Date: Which Representation? Journal Prompt Which of the following is the easiest way for you to compare two numerical patterns? Making tables, creating graphs or a different strategy? Why do you think so?