2. Agenda:
OBJECTIVE: SWBAT evaluate algebraic expressions.
Language Objective: SWBAT describe the steps to evaluating expressions.
1) Warm Up
2) Launch
3) Explore- 1
4) Explore- 2
5) Practice
6) Assessment
2
Individual
Shopping with Marvin- Whole Class/Pairs
Class work: Can’t Wait to Evaluate – Groups
Exit Slip- Individual
Evaluating with Marvin- Whole Class
Practice with Formulas- Whole Class
3. Warm Up
Agenda
3
OBJECTIVE: SWBAT evaluate algebraic expressions.
Language Objective: SWBAT describe the steps to evaluating expressions.
A magic store is selling exploding pens for
$3 each plus $1 for tax.
Do you agree or disagree?
Explain.
3 10 1
Kyle thinks you can figure out the cost of 10
pens with the below.
Click to reveal next part
4. Launch- Shopping with Marvin
Agenda
4
Marvin the Math Magician has a problem for you.
How much will Marvin have to
pay for 12 wands and 7 hats?
He wants to buy some magic wands
and some magician hats.
The wands cost $8 each and $5
for each hat.
5. Agenda
5
How much will Marvin have to pay for 12 wands and 7 hats?
The wands cost $8 each and $5 for each hat.
How did you get your answer?
How can we write a
to show our answer of 131?
8 12 5 7
Click to reveal next part
Launch- Shopping with Marvin
6. Explore 1- Evaluating with Marvin
Agenda
6
How much will Marvin have to pay
for 6 wands and 3 hats?
Remember: the wands cost $8 each and $5 for each hat.
Click to reveal next part
Write an numerical expression to
find the answer.
8 6 5 3
48 15
63
7. Agenda
7
What changed in the two examples?
Sometimes it helps to represent a problem as
an
The wands cost $8
each and $5 for each
hat.
w= # of wands
h= # of hats
Click to reveal next part
12 wands
7 hats
6 wands
3 hats
8
5
12 7
8
5
6 3
12 7
6 3
Explore 1- Evaluating with Marvin
8. Agenda
8
8w 5h
8
5
10 2
80 10
90
w h
This is called
substitution!!
Click to reveal next part
We just
evaluated the
expression.
evaluate
w = 10 h = 2
How much will Marvin have to pay
for 10 wands and 2 hats?
Explore 1- Evaluating with Marvin
9. Agenda
10
w=
h=
8w 5h
8
5
9 7
72 35
107
w h
Find the cost of buying 9 wands and 7 hats.
Steps:
1. Copy the expression.
2. Substitute the value
in for the variable.
3. Evaluate using the
order of operations.
Click to reveal next part
9
7
Explore 1- Evaluating with Marvin
10. Explore 2- Formulas
Agenda
11
Flashback…
Click to reveal next part
Objective: evaluate algebraic expressions.
For example: engineers, architects and builders use geometric
formulas every day.
C d
Circumference
V lwh
Volume
Rectangular Prism
SA 2r2
dh
Surface Area
Cylinder
We can use the process of evaluating to solve problems in the real
world.
11. Explore 2- Formulas
Agenda
12
Volume is the amount of space a shape takes
up. The expression for calculating the
volume of the rectangular
prism is below.
Find the volume
5ft
l w h
36 5
180 ft3
l w h
Click to reveal next part
Steps:
1. Copy the expression.
2. Substitute the value
in for the variable.
3. Evaluate using the
order of operations.
lwh or
12. 5ft
Agenda
13
Surface Area is the total of the area of all
sides. The expression for calculating the
surface area of a rectangular
prism is below.
Find the surface area.
2lw 2lh 2wh
Click to reveal next part
Steps:
1. Copy the expression.
2. Substitute the value
in for the variable.
3. Evaluate using the
order of operations.
2lw
2lh
2wh
2
2
2
72 90 40
202 ft2
Explore 2- Formulas
13. Practice- Class work
Agenda
14
Can’t Wait To Evaluate!
Directions: Each group receives a set of Evaluation Cards along with two different colored
number cubes. Before starting, the team decides which color cube stands for which variable.
(Example: the red cube replaces a, the green cube replaces b.) One person in the group rolls
the number cubes. Students use the numbers to evaluate the expression.
a=____ b=____
a b
3a 2b
2(ab)
ab
a2
b2
3(a b)
3a 1
2b 5
a 4b
b
a a
ab
a b
14. Exit Slip
Agenda
15
Kiara was asked to evaluate the
expression . Her answer was 14.
27 p
Did she substitute 11, 13, or 15?
How do you know?
Answer : 13
27 – 13
14
15. Summary
Agenda
16
a=____ b=____
a b
3a 2b
2(ab)
ab
a2
b2
3(a b)
3a 1
2b 5
a 4b
b
a a
ab
a b
Click each problem for demonstration
Can’t Wait To Evaluate!
16. The goal of 21st Century Lessons is simple: We want to assist teachers, particularly in
urban and turnaround schools, by bringing together teams of exemplary educators
to develop units of high-quality, model lessons. These lessons are intended to:
•Support an increase in student achievement;
•Engage teachers and students;
•Align to the National Common Core Standards and the Massachusetts curriculum
frameworks;
•Embed best teaching practices, such as differentiated instruction;
•Incorporate high-quality multi-media and design (e.g., PowerPoint);
•Be delivered by exemplary teachers for videotaping to be used for professional
development and other teacher training activities;
•Be available, along with videos and supporting materials, to teachers free of charge via the
Internet.
•Serve as the basis of high-quality, teacher-led professional development, including mentoring
between experienced and novice teachers.
21st Century Lessons
The goal…
35
17. Directors:
Kathy Aldred - Co-Chair of the Boston Teachers Union Professional Issues Committee
Ted Chambers - Co-director of 21st Century Lessons
Tracy Young - Staffing Director of 21st Century Lessons
Leslie Ryan Miller - Director of the Boston Public Schools Office of
Teacher Development and Advancement
Emily Berman- Curriculum Director (Social Studies) of 21st Century Lessons
Carla Zils – Curriculum Director (Math) of 21st Century Lessons
Brian Connor – Technology Coordinator
21st Century Lessons
The people…
36
Editor's Notes
(Time on this slide – 1 min) Time passed 5 min
In-Class Notes
Preparation Notes
(Time on this slide - 4 min) Time passed 4 min
In-Class Notes
Read slide as it appears.
Click to reveal a quick discussion how this can be written as an algebraic expression.
Preparation Notes
The purpose of this warm up is to review numerical expressions and algebraic expressions, and to make a quick connection between the two. Be sure to make the connection that the variable, p, took the place of the 10. Since students will be evaluating expressions in this unit, this is quick way to prompt students for lesson.
(Time on this slide - 2 min) Time passed 7 min
In-Class Notes
Read the slide as it appears.
Click to advance.
Have students do a ‘turn and talk’ to come up with the answer.
Preparation Notes
The purpose of the launch is to familiarize students with problems they already know how to solve. Then for them to start to see the connection to algebraic expressions and evaluating them. This problem is meant to be quick- no more than five minutes. The next slide is where time is provided to discuss students’ answers and thought process. As students are discussing their answer to the problem, ask them to think about the operations they are using and the order in which they are using them. This will help with the upcoming slides.
(Time on this slide - 4 min) Time passed 11 min
In-Class Notes
Read slide as it appears
Emphasize the fact that this expression is a numerical expression versus an algebraic expression.
Preparation Notes
You can show this slide in two ways, depending on the level of your students. If your students need guided practice in writing a numerical expression for this problem, give time for students to share their results and put them on the board before advancing the slide. Questions may needed to be prompted to help students derive at the expression. For example: What operation did you use first? What as the last operation you used? How can write the math you did as one numerical expression without using an equal sign? (Advancing the slide will have the numerical expression appear). If you circulate the room and observe your students were able to write the expression, you can advance this slide as quickly as you want.
A discussion should take place that there are different ways to write the expression. For example 12(8) + 7(5) is the same expression.
(Time on this slide - 4 min) Time passed 15 min
In-Class Notes
Read slide as it appears
Preparation Notes
Based on the Launch, this slide is designed to give students individual practice to write a numerical expression without any guidance. Encourage students to find the answer by writing a numerical expressions as shown in the Launch. Again, students may write the expression differently than the one shown, and should be discussed. Be sure to point out the fact that equal signs were not used at all to derive the answer.
(Time on this slide – 3 min) Time passed 18 min
In-Class Notes
Read the slide as it appears
Be sure students understand why the numbers change from the two expressions. Make the connection that wands and hats are the variables since they changed in both problems.
When the prompt appears for the algebraic expression, remind students what an algebraic expression is.
Explain quantities that keep changing (variables), they are assigned a letter, which will become the variable in the expression.
Before advancing the slide where the algebraic expression will appear, ask students what they think the algebraic expression is.
Preparation Notes
This slide is where students will make the connections between the two problems. The problem from the Launch and the Explore. As the slide advances, remind the students that the first expression came from when the expression was evaluated with 12 wands and 7 hats. The second expression was evaluated with 6 wands and 3 hats. Ask the students what changed in both expressions. Do not continue with the slide until students understand what changed from the first problem compared to the second problem. Advance the slide to prompt the class that we are going to use an algebraic expression that models this situation. Ask the class, what is meant by algebraic expression? Emphasize again that the number of wands and hats kept changing. Then as the variables appear to represent the wands and hats, explain why we chose the letters w and h. In this unit, students have not been exposed to this, so be sure to discuss naming variables. Give students a few minutes to see if they can derive the algebraic expression before advancing the slide.
(Time on this slide – 4 min) Time passed 22 min
In-Class Notes
Read slide as it appears
Scaffold this problem with the students.
Have them copy down the expression before they start figuring out the answer.
Prompt with questions asking what step should take place next.
Continue this process until the expression has been evaluated.
Be sure to read the prompt that appear at the right of the screen.
Click on the word evaluate at the bottom of the screen for the definition to appear.
Preparation Notes
The goal here is to scaffold the process of evaluating expressions. Students can copy this problem into their notebooks or you can just have a discussion with them. (There is another problem for them to work on without any guidance). Ask students how they would solve this problem using the algebraic expression. If students are struggling, remind students the w and h keeps changing as seen in the previous problems. Have a quick discussion on why the first step is called substitution. Once the numbers are substituted in, make the connection that the students are familiar with the rest of the process because they just have to use the order of operations. Make sure they understand why this process is called evaluating expressions. Click on the word evaluate at the bottom of the screen for the definition to appear. Again, be sure to point out the fact that equal signs were not used at all to derive the answer.
(Time on this slide - min) Time passed
This is a hidden slide.
(Time on this slide - 5 min) Time passed 27 min
In-Class Notes
Read the slide as it appears
Prompt students with questions as the slide advances.
This slide is for students to have a set of steps to follow.
Teacher discretion to have students copy the steps in their notebook.
Preparation Notes
The goal of this slide is for students to have a concrete strategy to evaluating expressions and to attempt the problem on their own. Ask what number should take the place of the w? For the h? At this point give students about 2 minutes to evaluate the expression. Ask students what answered they obtained. Then advance the slide to show the process and have the steps appear. The teacher can use their discretion if they want the students to copy them into their notebook. This is designed to scaffold the process of evaluating expressions, therefore, it is recommend to have students copy steps so they have a process to follow when students are working individually. Again, point out the fact that equal signs were not used to derive the answer.
(Time on this slide -1 min) Time passed 30 min
In-Class Notes
Read the objective again to the class.
Continue to read the slide as it appears.
Make the connection that students can evaluate geometric formulas (students may or may not have seen before) using the same process they just learned.
Quickly discuss the shapes that appear and mention the formulas provided.
Preparation Notes
This slide is designed to be discussed quickly. The goal of the slide is to transition into the next two slides since students will be asked to evaluate two problems involving geometric formulas. These are just random examples of formulas connected to the shapes provided. If time is not an issue, you can take this discussion to a deeper level discussing other formulas related with these shapes. Read the slide as it appears making sure to make the connection that formulas can be easily evaluated just as expressions using the same process.
NOTE: When presented with the next two slides, the formulas provided are written as expressions versus equations. This was done to keep the focus of the lesson using only expressions.
(Time on this slide - 3 min) Time passed 30 min
In-Class Notes
In class practice.
Can be done individually or with a partner.
Encourage students to follow the steps to evaluate the expression.
Give students about 5 minutes to complete.
Depending on the level of your students, an explanation of more than one variable next to each other means to multiply.
Advance the slide to show the process in obtaining the answer.
Students may need reassurance that formulas can be evaluated as well following the steps/process.
Preparation Notes
The practice is designed for students to work individually or with a partner. There are two problems provided. These are optional problems depending on the level of your students. A group work assignment is provided for students after these problems.
If these slides are chosen to be used, reassure the students that formulas are expressions that are evaluated. If they have not been exposed to these formulas yet, explain that in their upcoming units, a complete understanding of the formulas will take place. Otherwise, make the connection that they have seen these formulas before. An explanation of more than one variable next to each other means to multiply. Point out the dimensions of the prism leading the students to decided which number takes the place of which variable.
These types of problems were chosen because the standards reference formulas. Give students about 5 minutes to work on the problems. Depending on the level of your students, an explanation of more than one variable next to each other means to multiply. Advancing the slide will show the process to obtaining the answer.
(Time on this slide - 3 min) Time passed 33 min
In-Class Notes
This is another problem for students to practice with.
Can be done individually or with a partner.
Encourage students to follow the steps to evaluate the expression.
Give students about 5 minutes to complete.
Advance the slide to show the process in obtaining the answer.
Students may need reassurance that formulas can be evaluated as well following the steps/process.
Preparation Notes
The practice is designed for students to work individually or with a partner. This is the last of guided practice problems. These are optional problems depending on the level of your students. A group work assignment is provided for students after these problems.
If these slides are chosen to be used, reassure the students that formulas are expressions that are evaluated. If they have not been exposed to these formulas yet, explain that in their upcoming units, a complete understanding of the formulas will take place. Otherwise, make the connection that they have seen these formulas before. Remind students again, that more than one variable next to each other means to multiply. Point out the dimensions of the prism leading the students to decided which number takes the place of which variable.
These types of problems were chosen because the standards reference formulas. Give students about 5 minutes to work on the problems. Advancing the slide will show the process to obtaining the answer.
(Time on this slide – 20 min) Time passed 53 min
In-Class Notes
Have students in groups of 3-4.
Each group needs a set of cards and two different color numbered cubes. (See below for alternate suggestions if do not have number cubes).
Read the directions and/or model a problem to the class.
Circulate the room making sure students are using the process that was modeled.
Preparation Notes
Preparation for the activity:
Copy the following expressions onto index cards. Make enough so that each group has a set of cards. Each group will also need two different colored number cubes. The group decides which colored cube represents the variable a and b before starting. Students place all cards face down on their desk. One student in the group turns over a card. Another student rolls the dice. They evaluate the expression on the card using the numbers that appeared on the cubes. Student work should be in their notebook. Modeling one example may be helpful for the students.
Some changes: You can use a spinner instead of number cubes. Either have two spinners or just have the students spin one spinner twice. Have the first spin represent variable a and the second spin represent variable b. This will also give you the opportunity to choose numbers higher than 6 and/or negative numbers. Also, students do not necessarily need a set of index cards; the worksheet is sufficient enough. NOTE: This activity will NOT generate negative numbers. A set of problems are also provided for an enrichment level class if you want students to work with negative numbers.
While students are in their groups, provide them with a set of cards and two numbered cubes. Explain how to play and may need to model one example. As students start to play, circulate the room, making sure students are using the process discussed in the lesson. There is an opportunity to explain/discuss to the whole class any one of the expressions using the next slide.
(Time on this slide - 3 min) Time passed 60
In-Class Notes
Have students individually answer the following question.
Either go over the question or just collect before students leave for the period.
Preparation Notes
This exit slip is designed to quickly assess students individually to see if they have gained an understanding from the lesson. The answer is provided if decide to go over as a whole class or can just collect as students leave.
(Time on this slide – 4 min) Time passed 57 min
In-Class Notes
This slide is only needed if decide to discuss any of the expressions.
If choose to go over the problems, click on the card and a screen will appear for work to be shown. (Work is not provided since the number to substitute are dependant on the cube.)
Preparation Notes
This slide is used if decide to demonstrate any of the expressions. If there is time in your class period, you may designate certain groups to put their work up on the board; assigning two problems per group, depending how many groups your have. Just click on the problem of choice, and a slide will appear for work to be done. The work was not provided since the numbers to substitute change. Although, this lesson and activity is not designed to discuss every expression, but if time permits it is a great way to show students work to the class.
