Section 1.8 Patterns and Variables: Justifying Patterns with Algebra
Subsection 1.8.1 Number Talk: 96 + 29
Mentally solve 96 + 29 in as many ways as you can.
Raise a thumb when you have a solution. Raise a finger for each additional solution process you find.
How does this number talk relate to your work with patterns in the Table 1.6.3.1?
Will your process work for adding any two numbers? Why or why not?
Activity 3. Sharing Rectangle Patterns in the 100s Chart.
Share your justifications of patterns you found for homework with your group. As a group, decide which two patterns to justify in words and algebraically for the class. For your algebraic justification, label your rectangle as generally as you can, with
Homework 1.8.2 Homework
1.
Go back to the How To Learn Math For Students Directions. Complete How to Learn Math for Students Exercise 1.1.1.9. You will hand in your written reflections for How to Learn Math for Students Exercise 1.1.1.9 in class.
2.
(a)
Draw a 3 by 3 box around 9 numbers in the October 2020 calendar. An example is shown in Figure 1.8.2.1.
Use the example or draw your own 3 by 3 box.
(b)
Find two different patterns among the numbers in the 3 by 3 box. Describe each pattern carefully.
(c)
Use algebra to justify one of the patterns you found in Task 1.8.2.2.b. Indicate which pattern you are justifying.
3.
A famous pattern called Pascal's Triangle is shown in Figure 1.8.2.2.
(a)
Study the pattern. How are the numbers from one row related to the numbers in the next row?
(b)
Fill-in the missing numbers in the last row. Extend the pattern at least one additional row.
(c)
Describe 2 patterns that you see in this arrangement of numbers.
4.
(a)
Using only mental arithmetic, solve each problem in Table 1.8.2.3 below. Record how you thought about the numbers to help you add them mentally.
| Simplify | Solution | How did you solve the problem? |
|---|---|---|
(b)
Write the sum
(c)
What other problems did you solve using the same strategy you used to solve
(d)
Did you use the same strategy to mentally solve all of the problems? If you used more than one strategy, color code problems you solved using the same strategy. Do this for each strategy you used. Describe each strategy.