Grade 6 Unit 1: Patterns

Lesson 1 - Review

Lesson 2 – Question 1

Activation:

We looked at patterns in the world. We did a silly math trick to “read their minds”.

Question 1

Most students used charts to find the answer (very efficient), and used a bar graph to represent the data:

Some students used a line graph to represent the data:

Consolidation:

We focused our conversation around the idea that if we put the data on a chart, we would end up with coordinates, and if we used those coordinates on a line graph, we could plot the number pattern.

We focused on some new vocabulary:

Lesson 3 - Question 2

Activation: Review

Question 2 – Graph the total amount of tiles used by both students.

Some students made a chart of all the tiles (not very efficient)

Some students made a chart of only the pertinent information:

Some students included number pattern rules of chart (going down):

Some students saw the pattern going across (the slope)

Consolidation: Focus on comparison between slopes – the importance of the x and y axis going up by equal increments in order to compare data.

Lesson 4 – Worksheets with one and two step t-charts

Focus on t-charts being coordinates for graphs, but also on comparing slopes (and formula for slope being y = mx + b). What happens when you change “m” and what happens when you change “b”.

Lesson 5 – Question 3

Activation: review

Question:

Some students only got to the chart, but were able to find an equation (formula) for the pattern across:

(T x 6) + 2 = P which is reflects the slope y = (X x 6) + 2:

+

Some students got the chart (coordinates) and made the line graph:

Some students got the graph and attempted a formula (but they were focused on the number pattern in the chart going down, instead of across. They wrote y = (X + 8) – 2. The pattern going down is +6 each time, but in the question you are adding a table, which fits 8 people (+ 8), but not putting anyone on the ends of the table (-2):

Some students found the chart, the coordinates, and the formula for the slope: y = (X x 6) + 2

Consolidation: We had an interesting conversation as about the connection between the pattern going down (+6 each time) and the pattern across (x 6), the multiples of 6 going across relating to the repetitive adding of 6 going down. Cool!

Lesson 6 – Question 4

Activation: Review

Question:

Some students used “probability” strategy to find answer – slope going down:

Some students added the number of handshakes each time to come up with a line going up:

Consolidation: We had a discussion about which answer better represents the question and answer. The students chose the slope going up (even though it is not linear)

Lesson 7 – Question 5

Activation: reviewQuestion:

A common error was the idea that once you get the answer to term 1 (one cup of coffee), the answer just keeps going up by multiples of 5:

Another common error was forcing the line to go down to “0”:

Most students found the correct coordinates and graphed them:

Some students worked on the bonus question, noticing that if you change the number of treats added, the slope remains parallel, but slides up (or down) the graph, but if you change the number you are multiplying, then you change the gradient of the line:

Consolidation: The bonus questions review the formula for the slope and the meaning of “m” and “b”.The formula for line equation is y = mx + bBut for the purposes of our class we flip the m and x around to make y = (X x m) + b

In this case it demonstrates that changing the “m” changes the slope of the line (the steepness); in this case we changed “doubling the treats” to “Tripling the treats” (we changed the “m” from a 2 to a 3 – or:y = (X x 2) + 3 to y = (X x 3) + 3

We also demonstrate that the changing of the “b” changes where the line meets the y-axis (the intercept). In other words the lines are parallel, they just slide up or down the y-axis. This we see when

we change the number of treats Mr. Wendler adds from +3 to +5.So the equation changes from:y = (X x 2) + 3 to y = (X x 2) + 5

So in summary, the “m” represents the slope of the line, and the “B” represents the y-axis intercept.

Lesson 8 – Question 6

The next questions in the unit simply reinforce these ideas, and give practice to finding the correct coordinates and graphing the data.

Explore the idea of following a pattern to discover the “Y =” formulas of given sets of data

Lesson 9 - Evaluation

Then we have our quiz.