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Joost Mathematics Lesson Plan
Class and Date: Math 75
Bellwork:
Materials:
Vocabulary:
Monday, November 1
MSA
NO SCHOOL SIP DAY
Joost Mathematics Lesson Plan
Class and Date: Math 75
Tuesday, November 2
1.3 MSA
Bellwork: 6.7.15- 2 Multiple Choice A and B
Materials: Student notebooks, Overhead projector, Transparent grid paper or large poster paper (optional)
Vocabulary: Independent variable, Dependent variable
What I Can Statements are expected of students?
• Construct graphs and tables to model problem situations
• Translate information about linear relations given in a table, a graph, or an equation to one of the
other forms
• Informally explore the y-intercept
Which priority standards are supported in this lesson?
7IL 6.7.15, 7IL 8.7.06, 7IL 8.7.10, 7IL 8.A.3b, 7IL 8.B.3
Is there any prior learning that should be referenced or reviewed?
Use the Math Background to help you understand the mathematics being taught in this unit.
Which lesson openers or examples will be used in the modeling/guided segment of the lesson?
Start with the Getting Ready. Pose the three pledge plans of Leanne, Alana, and Gilberto.
Encourage students having trouble writing an equation to write out what the relationship is in words.
What activities will be used to provide students opportunities to work together?
Discuss Questions A and B. Ask about the variable:
• Which one is the independent variable? The dependent variable?
• How is the effect of cost per kilometer similar to a person’s walking rate in meters per second?
• How can you recognize that the patterns in both situations (the pledge plans and the walking rates)
are the same in a table, graph, or equation?
Pick two points on the table.
• What is the change between the two variables? Is it the same for two other points? What rate of
change is this?
• How does the constant rate of 0 produce a horizontal line?
• Describe another pledge plan (and give its equation) whose graph is a horizontal line.
Pick some points on the graph and tables.
• What information does this point represent?
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• Which graph does (4, 8) lie on? Explain.
• How is this point related to a corresponding table and equation for
this graph?
• What are the coordinates of the point where each graph intersects the y-axis? What information
does this point represent?
Discuss the coordinates of the intersections of the three graphs.
• Find a pledge plan whose rate is greater and one that is less than the three original pledge plans.
Compare the graph of this new pledge plan with the graphs of the original three.
How or when will you differentiate instruction?
Students will work with a partner with various understandings for discussion purposes.
How or when will students be allowed the opportunity to discuss the mathematics being taught?
Students will work in small groups and also talk openly as a class.
In what ways will students be informally assessed?
I will be assessing students understanding as I teach the lesson.
What independent work activities will be assigned?
Students will complete the ACE questions on the back of the worksheet assigned today.
Joost Mathematics Lesson Plan
Class and Date: Math 75
Wednesday, November 3
1.4 MSA
Bellwork:6.7.15- 2 Short Response A and B
Materials: Student notebooks, Overhead projector
Vocabulary:
What I Can Statements are expected of students?
• Understand negative rates of change and how they are represented in equations, tables, and
graphs
• Continue to explore y-intercept
• Describe the information the variables and numbers in an equation represent
Which priority standards are supported in this lesson?
7IL 8.7.06, 7IL 8.7.10, 7IL 8.A.3b, 7IL 8.B.3
Is there any prior learning that should be referenced or reviewed?
I will review and go over the homework assigned from the previous lesson.
Which lesson openers or examples will be used in the modeling/guided segment of the lesson?
Tell the students that they have been looking at linear relationships. Ask:
• How can you tell whether a relationship is linear?
Tell the first story of how one class is going to use the money they raised from the walkathon. Put up
Transparency 1.4A and ask:
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• What do you think the graph of this data would look like?
• Is this a linear relationship?
What activities will be used to provide students opportunities to work together?
For Question B, students may need help finding the constant rate for the graph. Suggest that they make a
table of values to help them find the constant rate. Be sure to have students share their strategies in the
summary.
Students should practice reading information from tables and graphs and using tables and graphs to
answer questions.
• For each class, how much money is being spent or withdrawn per week?
• Compare the rates of change in this Problem with other rates that we have studied so far in this
unit.
• How do the rates in this Problem show up in a table? graph? equation?
• What are the coordinates of the point where the line intersects the y-axis? What information does
this point represent?
• What are the coordinates of the point where the line intersects the x-axis? What information does
this point represent?
• Pick a pair of corresponding values in the table in Question A. What two questions could you
answer by choosing this pair of values?
• Pick a point on the graph in Question B and ask two questions you could answer by locating this
point.
• Pick a point not on the graph in Question B. Explain what this means in terms of the account.
• After how many weeks will each account be zero dollars?
• Which account has a graph that contains the points (0, 100)? (10, 24)? (12, 0)? (8, 20)?
How or when will you differentiate instruction?
Students will work with a partner with various understandings for discussion purposes.
How or when will students be allowed the opportunity to discuss the mathematics being taught?
Students will work together to complete the book questions.
In what ways will students be informally assessed?
I will check for understanding as I discuss the lesson with the class.
What independent work activities will be assigned?
Students will complete the ACE question worksheet for homework.
Students should also review all of the assignments and notes that were taken for Investigation 1 for the
quiz tomorrow.
Joost Mathematics Lesson Plan
Class and Date: Math 75
Thursday, November 4
Quiz/ 2.1 MSA
Bellwork: 6.7.15- 2 Extended Response
Materials: Student notebooks, Grid paper or blank sheets of transparency, Large sheets of paper
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Vocabulary: x-intercept
What I Can Statements are expected of students?
I can do well on the Investigation 1 quiz
• Find solutions to a problem using a table or graph
Which priority standards are supported in this lesson?
7IL 8.7.06, 7IL 8.B.3
Is there any prior learning that should be referenced or reviewed?
I will review and go over the homework assigned from the previous lesson, and answer any last questions
before the quiz.
Which lesson openers or examples will be used in the modeling/guided segment of the lesson?
Students will first take the Investigation 1 Quiz.
Tell the story of the race between Emile and his younger brother, Henri. This problem is just for students
to explore the race, so let students use whatever method makes sense to them. Problem 2.2 will serve as
a summary. Because the problem asks “how long” the race should be, some students will choose to focus
on length and some on time. Ask students for some preliminary thinking:
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•
•
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What should Emile do?
So what head start should he give his brother and how many meters long should the race be?
Is giving a head start sufficient to guarantee that the little brother will win?
So what strategy do we need to ensure that the little brother is still ahead at the end of the race?
Let the class work in groups of 2 to 3.
What activities will be used to provide students opportunities to work together?
Circulate and ask groups to explain their thinking. Encourage all groups to listen to each member and
reach a consensus on a single answer or to agree that more than one choice is reasonable and why.
Look for interesting strategies. You could have the groups present their solutions and arguments on
poster paper or transparencies.
Collect some strategies from the class.
• How did your group interpret the problem? What strategy did you use?
Mathematically, we would probably find the intersection of the two lines for the equations and choose a
race length less than the length at which Emile overtakes Henri. Students will have more informal ways of
thinking about the problem. Transition to more formal means should proceed slowly so students can
develop their intuitions. See the extended teacher’s edition for possible student explanations. For each
suggestion ask:
• How did you determine what the length (time) of the race should be?
• Why is that length (time) reasonable? Will Henri win the race?
Use this summary to launch the next problem. If someone has used a table, use the table as a lead into
the next problem. Problem 2.2 is a good summary for this problem. It looks at the table, graph, and
equations for each brother and asks students to look at the patterns of change in all three representations
and to use these representations to answer questions about the race.
How or when will you differentiate instruction?
Students will work in small groups with various understandings for discussion purposes.
How or when will students be allowed the opportunity to discuss the mathematics being taught?
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In what ways will students be informally assessed?
I will be assessing students understanding as I teach the lesson.
What independent work activities will be assigned?
There will be no assignment for tonight.
Joost Mathematics Lesson Plan
Class and Date: Math 75
Friday, November 5
2.1/2.2 MSA
Bellwork: 6.7.15 Bellwork Quiz
Materials: Student notebooks, Grid paper or blank sheets of transparency, Large sheets of paper
Vocabulary:
What I Can Statements are expected of students?
•
Understand the connections between linear equations and patterns in the tables and graphs of
those relations, including rate of change, and the x- and y-intercepts
• Translate information about linear relations given in a table, a graph, or an equation to one of the
other forms
• Find solutions to a problem using a table or graph
• Connect solutions in graphs and tables to solutions of equations
Which priority standards are supported in this lesson?
7IL 8.7.06, 7IL 8.7.08, 7IL 10.A.3a, 7IL 10.C.3b, 7IL 8.B.3
Is there any prior learning that should be referenced or reviewed?
I will finish going over 2.1 and answer and questions pertaining to this section.
Which lesson openers or examples will be used in the modeling/guided segment of the lesson?
Use the summary of Problem 2.1 to launch this problem. If your students did not use a table, graph, or
equation to do the above problem, discuss with them that it is sometimes useful to look at other ways to
solve the problem.
• Let’s see if we can use a table, graph, or equation to answer the question posed in Problem 2.1.
Once you have tables, graphs, and equations, you can answer other questions about the race.
Students should make their own table, graph, and equation, but discuss the strategies for using them to
find information with the group.
What activities will be used to provide students opportunities to work together?
As you circulate, ask additional questions about features of the graph or table. For example,
• Why are the y-intercepts (the places where the line crosses the y-axis) different on the two
brother’s graphs?
• What does the vertical difference between the graph lines tell you?
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Can you tell from the table how far Henri is from the start line in the first 7 seconds? If so,
how?
Ask students:
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• How can you tell how long the race should be from the graph and from the table?
• What information does the point (20, 50) represent in the problem? Would this be a data point for
Henri or for Emile? How does it relate to a table of values, a graph or an equation for this situation?
• How does the pair of values, (10, 55), from the table show up on the graph? How is it related to the
equation?
Pick a point on the graph of one of the brothers and ask a question that can be answered with this point.
The questions in Question B are a preliminary introduction to solving equations. Students can answer
them using a table, graph, or reasoning about the situation.
How or when will you differentiate instruction?
Students will work in small groups with various understandings for discussion purposes.
How or when will students be allowed the opportunity to discuss the mathematics being taught?
In what ways will students be informally assessed?
I will be assessing students understanding as I teach the lesson.
What independent work activities will be assigned?
There will be no assignment for tonight.