Students will be working on a problem that requires them to do multiple steps to solve. I chose this problem to help stimulate their minds and get them thinking about math.
Possible solution: Students will use multiplication to try and solve the problem. They will do 25 x 4 to get to 100 and then add $50 to get to $150. Once they get this, the students can do a guess and check to estimate their solutions.
For example:
Number of watches |
Amount she earns |
25 |
$150 |
50 |
$150 + $150 = $300 |
75 |
$300 + $150 = $450 |
100 |
$450 + $150 = $600 |
Students can estimate that she will need to sell more than 75 watches to earn $506.
Then, they could say that Sarah had to sell 75 watches to earn $450. Next, they will subtract $506 - $450(amount sold for 75 watches) to get $56(Remaining dollar amount) . Students should divide to 56 by 4(How much she earns for each watch) to get 14.
Finally, they can use the guess and check estimation of 75 and add it to the 14 to get 89 watches sold.
To help students out with this problem, you could ask them about the important information:
How much does she earn per watch?
How much does she earn for a bonus?
What earns her the bonus?
Is there a tool that can be use to help us organize our data?
This problem attends to SMP 2 by understanding what the numbers mean and SMP 5 by using an appropriate tool to organize our information.
Tools: Do now problem
I chose Numbered Heads Together because it is my favorite and also because it allows students time to work independently and check solutions with a group. Each problem represents a similar problem for their assessment. Students will be writing and solving inequalities and using the coordinate grid to graph their solutions.
For questions 1 – 3 the students will be writing equations. If needed, remind students to circle key words and identify both expressions. Question 2: the students may want to use 2 variables. “If both coefficients relate to firefighters, do we need to have 2 variables?” Once they see that they do not need two variables, they can combine like terms to write a simplified equation.
Questions 4 and 5 deal with inequalities. Students will need to write and graph the inequality. For the word problem, if students get stuck with what symbol to use say to them “if you have $20 to spend, think about the amounts you can spend?”
Questions 6 and 7 are asking the students to identify the independent and dependent variable. If students get stuck ask them to draw a table. Remember that what gets substituted “in” for the variable is the independent variable, and what comes out is the dependent variable. Students could use made up information and a table to model this mathematics (SMP4 and 5).
Question 8 is asking the students to write an equation to represent the information in the table. For students to use precision in their equation, they should use the recommended variables from the problem. (SMP 6)
Question 9 is asking the students to use the equation to complete the information from table. They are finding both the independent and dependent variable given one of them. Students may have trouble when the dependent variable is given. If this happens, ask the student to say to themselves “what number times 3 makes 24”?
Questions 10 and 11 are asking students to write an equation, complete a table and graph the information in a grid. Students will need to create their own table and grid. If students have trouble with creating a grid, it might be a good idea to have some available for them. In question 11, the word function is used. Students may be confused by this as we have yet to cover this word. Explain to students that a function is an algebraic term to describe the table and the equation.
Question 12 is asking the students to write the equation given the points on a line. If students are having difficulty, encourage them to write the ordered pairs in a table so they can see the pattern. Students will understand the pattern and write it as an equation. (SMP 7 and 8)
Numbered Heads Together supports mathematical practices:
SMP1: making sense of problems
SMP2: understanding what the numbers mean.
SMP3: constructing viable arguments to prove their solution is correct.
Tools: NHT power point, whiteboards, markers, coordinate grids.
The students will receive their study guides for the test. The problems on the study guide are similar to NHT and are helpful for practicing problems for the assessment. Allow students time to look over their study guide and ask any questions they may have. We will go over the study guide before the assessment the next day. Any extra time can be used to start the study guide.
Tools: Study Guide for Equations.