1.
Represent and describe patterns and relationships, using graphs and tables.
- Students need to be able to notice patterns in real life and represent them using graphs and tables.
- For instance a student might observe that while boiling water the temperature increases by 20 degrees for every 30 seconds it boils, the following graph could be used to represent this pattern.
The same information could be represented in a table with time going in the x column and temperature going in the y
x y
0 20
30 40
60 60
90 80
x y
0 20
30 40
60 60
90 80
2. Demonstrate an understanding of the relationships within tables of values to solve problems.
- A table of values is often used to represent a pattern, each table has a "rule" written as an equation that helps you solve for an unknown within the pattern. The example below shows that the value of Y is always equal to the value of x times 2 plus 7. Knowing the rule is helpful because it allows you to solve for the next number in the pattern. In this case when x=10 y=27 because 10x2+7=27.
- The rule can be written as Y=2x+7
3. Represent generalizations arising from number relationships, using equations with letter variables.
4. Express a given problem as an equation in which a letter variable is used to represent an unknown number.
5. Demonstrate and explain the meaning of preservation of equality, concretely and pictorially.
- It is common in math to use a letter in an equation to represent an unknown. This was seen earlier in our work with the table of values. Using letters is also a common way of communicating a formula that remains the same regardless of what number is substituted in for the letter. For example the formula for the area of a rectangle is length times width or a= LxW. It is written like this every time weather the length is 20cm or 40cm the formula is always a=LxW.
4. Express a given problem as an equation in which a letter variable is used to represent an unknown number.
- Every math equation has an unknown. FOr instance even something as simple as 1+1 has an unknown and can be written as 1+1=y
- A similar equation could be written as 1+x=2
- The letter simply represents the portion of the equation that you are trying to find the value of. It does not matte what side of the = sign it is on.
5. Demonstrate and explain the meaning of preservation of equality, concretely and pictorially.
- The preservation of equality means that an answer will remain the same regardless of what order the equation is written in.
- For instance 2+3=5 and 3+2=5 or 2x4=8 and 4x2=8
- This only works for addition and multiplication
- For instance 3-2=1 and 2-3=-1 or 4/2=2 and 2/4=0.5