A three-lesson teacher plan that connects a stated rule and term position to ordered coordinates, then to corresponding terms from two supplied rules. It reuses three existing 40-minute investigations.
Anonymous group code: __________ Date: __________
Before the sequence
Work independently. Write a number with its unit, and record the explanation requested. Your teacher will record the answer and the reasoning separately.
pre1. Explicit-rule check: term 1 is 2, and the rule is add 5 each time. Enter term 6. On paper, label the first six term positions, write the values and show how many additions connect term 1 to term 6.
pre2. Explicit-rule explanation: term 1 is 9, and the rule is add 4 each time. Enter term 8. Explain whether every term under this stated rule is odd or even, using the starting value and increment rather than only the first few values.
pre3. Coordinate-position check: use axes with origin (0, 0), x increasing right, y increasing up and one-unit intervals. From the origin, move right 4 and up 7. Enter the first coordinate, then write and plot the complete ordered pair and explain its order.
pre4. Coordinate repair: on one-unit axes with x right and y up, start at (1, 8), move right 5 and then down 3. A helper records the endpoint as (5, 6). Enter the correct second coordinate, write the corrected pair and explain which coordinate each movement changed.
pre5. Paired-pattern check: A starts at 0 and adds 2 each time; B starts at 0 and adds 6 each time. Generate the starting pair and the next three pairs in the order (A, B). Plot A horizontally and B vertically with one grid interval for 2 units on both axes. Enter the B term after three additions and explain how B compares with A at corresponding stages.
pre6. Paired-pattern explanation: A starts at 3 and adds 2 each time; B starts at 3 and adds 4 each time. Write the starting pair and the next two pairs. After two additions, how much greater is B than A? Enter the difference and test the claim that B is twice A at that stage.
After the sequence
Use this set after the lessons. Work without a partner first. Explain your method; a correct number alone does not show every part of your reasoning.
post1. Explicit-rule check: term 1 is 1, and the rule is add 3 each time. Enter term 7. On paper, label the first seven term positions, write the values and show how many additions connect term 1 to term 7.
post2. Explicit-rule explanation: term 1 is 8, and the rule is add 6 each time. Enter term 9. Explain whether every term under this stated rule is odd or even, using the starting value and increment rather than only the first few values.
post3. Coordinate-position check: use axes with origin (0, 0), x increasing right, y increasing up and one-unit intervals. From the origin, move right 6 and up 2. Enter the first coordinate, then write and plot the complete ordered pair and explain its order.
post4. Coordinate repair: on one-unit axes with x right and y up, start at (2, 9), move right 6 and then down 5. A helper records the endpoint as (4, 8). Enter the correct second coordinate, write the corrected pair and explain which coordinate each movement changed.
post5. Paired-pattern check: A starts at 0 and adds 4 each time; B starts at 0 and adds 8 each time. Generate the starting pair and the next four pairs in the order (A, B). Plot A horizontally and B vertically with one grid interval for 4 units on both axes. Enter the B term after four additions and explain how B compares with A at corresponding stages.
post6. Paired-pattern explanation: A starts at 4 and adds 3 each time; B starts at 4 and adds 9 each time. Write the starting pair and the next two pairs. After two additions, how much greater is B than A? Enter the difference and test the claim that B is three times A at that stage.
Transfer the reasoning
transfer. Pattern A has term 1 equal to 2 and adds 3 each time. Pattern B has term 1 equal to 5 and adds 6 each time. On a graph, A is horizontal and B is vertical. A helper records the term-4 pair as (23, 11) and says B is twice A. Enter the correct B coordinate for term 4. Write the repaired pair, explain how many additions were used and test the helper's relationship claim.