Grade 6 Expressions & Properties with Variables Unit- Conceptual Lessons
Type of
Knowledge
& SBAC
Claim
C, 1, 3
C, RK- 1, 2, 3
C- 1
M, C- 1
C, RK- 1, 2
P, RK
Lesson Title and Objective/Description
Suggested
Time Frame
Math Practice
embedded
Discovering Properties with Numbers
Students use numeric expressions to investigate, discover and write
properties of operations. Students will learn that there is a commutative
property of addition and multiplication but not one of subtraction or division.
Students will summarize the properties at the end of the lesson.
Are They Equivalent I?
In this lesson, students will investigate the concept of equivalent expressions
by applying commutative, associative and distributive properties to
determine if numerical expressions are equivalent and justify their reasoning
with properties. Students will then be challenged to apply properties to write
as many equivalent expressions as possible for a given numeric expression.
Filling the N Box
Students will recall the concept of a variable by trying to figure out what is inside
the “N” box and by realizing they don’t know, and learn that it represents an
unknown. They will play with this context to understand how to write variable
expressions and what contexts might match these expressions. In Part 2, students
will come to understand the concept of evaluating an expression by placing a
given number of counters into the N box and determining physically, in a drawing,
and mathematically how to evaluate an expression for a given value.
Sorting Key Words
Students will sort words commonly found in expressions by the operation
they most often indicate.
Formulas as Expressions
Students will learn a reason for evaluating expressions by doing so with given
geometry formulas to solve for missing side lengths.
Practice & Problem Solving: Reading, Writing and Evaluating
Expressions
1-2 class
periods
2, 3, 8
1 class
period
1, 2, 3
1-2 class
periods
2
15-30
minutes
6
20-30
minutes
1, 2, 7
2-3 class
periods
EE_T1
C- 1
Distributive Property with Variables
Students will build upon their understanding of the area model of
multiplication and the distributive property of multiplication over addition
with numbers to develop the distributive property of multiplication over
addition with variables.
C, RK- 1, 3
Building Equivalent Expressions
In this lesson, students will develop an understanding of equivalent algebraic
expressions by building up a basic statement of equivalence and justifying the
steps with properties. Students will then build a set of equivalent and a set of
non-equivalent expressions and trade with another student to determine
which set of expressions is equivalent based upon the application of
properties.
C, RK- 1, 3
Are They Equivalent II?
Students will investigate the concept of equivalent algebraic expressions by
applying the associative, commutative and distributive properties to
determine if the expressions are equivalent and justify their reasoning with
properties. Students will then be challenged to apply properties to write as
many equivalent expressions as possible for a given algebraic expression.
Unit Notes: Grade 6 Standards EE 2 (some), 3, 4, 6
Time- 2 weeks
1 class
period
5, 7, 8
1 class
period
2, 3, 7
1 class
period
2, 3, 6
EE_T2
Teacher Directions
Put students into groups of 6. Within each group, students need a partner. (Note: this should be a review/summary
lesson, but if students are unfamiliar with properties, you can have each student go through each property rather than the
jigsaw directions described below)
Pass out the activity Sheet. There are sets of directions and problems for three different pairs. Have each pair select
which properties they will work on (each group of 6 needs to have one pair doing each of the three sets of problems).
Give students 20-30 minutes to work through their part. Circulate during this time to ensure students are solving their
basic arithmetic correctly.
As soon as a pair finishes, pass out the Summary Page. Have each pair complete the row(s) for the properties they
worked on. Pairs 1 and 2 should complete 4 rows. Pair 3 will only complete 1 row. It is ideal if they can create their own
example; however, if they struggle, encourage them to use problems from the section they worked on. Allow pairs about
5-10 minutes to do this.
Have the groups get back together and allow each pair 5 minutes to “teach” their properties to the rest of the group.
Make sure all group members record the summary on the activity sheet.
IMP Activity Discovering Properties with Numbers
16
EE_T3
Teacher Directions
Materials: None
Objective
In this lesson, students will investigate the concept of equivalent expressions by applying
properties to determine if numerical expressions are equivalent and justify their reasoning with
properties. Students will then be challenged to apply properties to write as many equivalent
expressions as possible for a given numeric expression.
Directions:
Pass out the activity sheet and have a student read the directions. Model the first problem as a
class. Note: it might help for students to have out their properties summary page for this lesson.
Once they class understands what to do, set the timer for 10 minutes to students to work
independently. After time is up, allow students to compare answers with a partner and then use
random selection to have students share their answers and reasoning.
Next, explain Part 2- a competition to see who can write the most equivalent expressions, using
properties of operations. Show the example for #1 and make sure students understand that they
can not change the numbers used, but can only use properties to re-write the expression. They
must justify each expression with a property. Set the timer for 3-5 minutes for each expression
and at the end of each one, either have the student who found the most share or use roundtable to
have each student share one expression he/she found.
IMP Activity Are They Equivalent?
3
EE_T4
Teacher Directions
Materials
N Box- 3 per pair (template on final page)- Copy onto cardstock, but, fold, tape all but TOP.
Counters- about 20 per pair
Overview:
Students will recall the concept of a variable by trying to figure out what is inside the “N” box
and realizing they don’t know, so it represents an unknown. They will play with this context to
understand how to write variable expressions and what context might match these expressions.
In Part 2, students will come to understand the concept of evaluating an expression but placing a
given number of counters into the N box and determining physically, in a drawing and
mathematically how to evaluate and expression for a give value.
Directions
Part 1
Begin by placing a few counters into an “N” box without students seeing this. Show the class
the box and ask them what it is. Agree that it is called “N”. Ask the class how much they think
it is worth. Throw the box to a few students to let them feel and shake the box and ask each
student who catches it, “How much is N worth?” Continue this until you have at least 1 student
who says, “I don’t know.” After enough students have had opportunity to feel and predict, agree
that you don’t know, so you call it “N”.
Repeat this process, but now with a box that has approximately 8-10 counters in it. Pass it
around until most students are able to see that they “don’t know” the exact value until you open
it up.
Now show the class 3 N boxes (it does not matter what is in them) and then 2 counters. Ask
them how much this is worth. Ask a number of students until the class agrees it is worth “3N +
2”. Pass out the activity sheet and have the students record this under the first expression. Ask
them to draw this as well (three N boxes with 2 counters). Now give them 1 minute to write a
story to represent this. Give them a minute to share their idea with a partner and then another
minute to record their idea. Select a few students to share and record one of their ideas on the
page you have up at the document camera.
Repeat the above steps 3 more times showing them the following each time:
 #2- one N box and 5 counters
 #3- four “N” boxes
For #’s 4-6, the students are given one of the 3 pieces (expression, phrase or picture) and then
must now do the other two parts. Give the class about 10 minutes to complete this followed by
time to share with a partner and the class. Select students to share their stories, expression and
drawings for each problem.
Note: It should be emphasized that expressions cannot be simplified or “answered’ until the
variable value is known.
Answer Key Near End (phrases can be different)!
IMP Activity Filling The N Box
5
EE_T5
Part 2: Filling the N Box
Let students know that they will now be evaluating expressions by filling the N boxes with a
given number of tiles. Model #7 with them by first showing them one N box with 4 extra tiles
and having them write the expression and draw a picture. Then ask them to put 6 tiles into the N
box and show this in a drawing. Ask how many total tiles they now have and have them record
this under “Evaluate”. (See sample on answer key below). Once students understand, allow
them to work on the remaining problems, each time making sure they use tiles to fill the N
box(es) and then record this in the picture and mathematically. Give students 10-15 minutes to
finish and then have volunteers come up front to show how they filled the boxes and their
pictures and math.
Answer Key
1. Expression:
Drawing
3N + 2
N
N
N
Phrase: I have 3 boxes of crackers plus 2 more crackers.
2. Expression:
Drawing
N+5
N
Phrase: I have a bucket of apples and 5 more
IMP Activity Filling The N Box
6
EE_T6
3. Expression:
Drawing
4N
N
N
N
N
Phrase: I have 4 full boxes of baseball cards
4. Expression:
Drawing
N + 3 + 2N
N N
N
Phrase: I have a pack of gum plus 3 extra pieces and then get 2
more packs of gum.
5. Expression:
Drawing
4+2N + 6
N
N
Phrase: I have 2 bags of apples and 8 extra apples
IMP Activity Filling The N Box
7
EE_T7
6. Expression:
Drawing
N
5+3N
N
N
Phrase: I have 5 baseball cards in addition to 3 full boxes of
baseball cards. Write an expression to show how many baseball
cards I have.
Part 2- Selected Answers
7. Expression: N+4
Drawing
Evaluate for N=6
N+4
6+4
10
8. Expression: 3N
Drawing
Evaluate for N=5
3N
3•5
15
IMP Activity Filling The N Box
8
EE_T8
Words To Sort
Sum
Product
Increased
Decreased
Minus
Quotient
Equal
Altogether
Total
Of
Out of
Dropped
groups
Fewer
than
Difference Less Than
Plus
Per
Both
Twice
Split
Combined
Times
Lost
Doubled
Shared
Tripled
In all
Each
Groups of
Change
IMP Activity Sorting Key Words
2
EE_T9
Teacher Directions
Materials: Scissors (optional)
Objective
Students will sort words commonly found in expressions by the operation they most often
indicate.
Directions:
Option A: Have students cut out key words and individually sort them before conferring with a
group and then gluing.
Option B: Students record each key word under the operation they indicate and then confer with
a partner.
As a class, once the sort is done, use random selection to have students share under which
operation they placed each word and explain why. Note: It will help struggling students to create
an example (sentence with this word in it). Additional Note: in some cases a word can mean
either add or subtract or multiply or divide depending on if the students is thinking about how to
solve or modeling it directly. Allow for both interpretations, so long as the explanation defends
the position.
Have the students use the final product to help them the rest of the year!
IMP Activity Sorting Key Words
3
EE_T10
Teacher Directions
Materials: None
Objective
Students will learn a reason for evaluating expressions by doing so with given geometry
formulas to solve for missing side lengths.
Directions:
Pass out the activity sheet and ensure students understand the directions. Ask them where the
formula, s2 came from in relation to the square. Model how to evaluate the formula for the side
lengths of 1 and 2 and then ensure they understand they need to do the same for the remaining
values and then try out a few more values until they find the length of s that yields an area of
289. Repeat the same process for the next two, noting that there are multiple correct answers for
#2.
IMP Activity Formulas as Expressions
3
EE_T11
Teacher Directions
Materials: Optional- Algebra Tiles (x’s one ones)
Objective
Students will build upon their understanding of the area model of multiplication and the
distributive property of multiplication over addition with numbers to develop the distributive
property of multiplication over addition with variables.
Directions:
Pass out the activity sheet and work through #1 together, ensuring students recall using an area
model to multiply. If students are unfamiliar with this model, pass out graph paper and have
students do 5-10 problems of single or double digit multiplication. Below is what # 1 should look
like when drawn out. In an area model, the factors become the dimensions of a rectangle and the
area represents to product of those two factors.
4
3
4 • 3 = 12
Once students are able to do simple single-digit problems, have them try #2, using a longer
length to represent each 10. See below for a model.
40 • 3 = 120
40 (4 tens)
3
Next move on to using variables. If you have algebra tiles, pass them out to allow students to
build each problem. If not, students will draw a length of x, which needs to be longer than 1 but
not exactly any whole number. Below is a model for #3.
x
x
x
x
3
4x • 3 = 12x
2
Once students are comfortable drawing, have them complete the rest of the problems. #4 is draw
for you below for your reference. Once students have finished up through #8, stop to have
students share their work in front of class to ensure all students have correct answers. Then give
students 5-10 minutes to individually complete the last section, Understanding the Distributive
Property of Multiplication Over Addition. Once the time is up, have students work with a
partner to share their ideas and then use random selection to have students share with the class.
x+4
2(x+4) = 2x+8
IMP Activity Distributive Property Variables
4
EE_T12
Teacher Directions
Materials: Sheet of notebook paper- 1 per student
Objective
In this lesson, students will develop an understanding of equivalent algebraic expressions by
building up a basic statement of equivalence and justifying the steps with properties. Students
will then build a set of equivalent and a set of non-equivalent expressions and trade with another
student to determine which set of expressions is equivalent based upon the application of
properties.
Directions:
Pass out the activity sheet and have a student read the overview. Model the example for the
students on the document camera (don’t pass out the page yet) and have students tell you what
you did each step and whether or not the expressions are still equivalent. Then pass out the
activity sheet and have the students read the directions under “your turn”. For students
struggling, you can allow them to work with a partner, taking turns adding building each row.
Then have pairs trade papers and verify if the expressions are still equivalent.
Next, direct the class’ attention to part 2. Give them 1-2 minutes to study the steps to try to
determine why the expressions are not equivalent or which step involved something that made
the expressions not equivalent. Once the students understand this, have each student now build
two more expressions, intentionally making one equivalent, like was done before, and then one
non equivalent (showing the steps). Set the timer for 8 minutes to allow them to complete this.
Once students are done, pass out a sheet of paper and have each student write out the two pairs of
expressions on the paper. Strategically trade the papers with another student and give each
student 5 minutes to determine which pair of expressions is and which is not equivalent. Have
the students write to justify why a pair of expressions is or is not equivalent.
Note: You can also select a few examples to put on the document camera and have the whole
class try to determine which of those were and were not equivalent.
IMP Activity Building Equivalent Expressions
3
EE_T13
Teacher Directions
Materials: None
Objective
In this lesson, students will investigate the concept of equivalent algebraic expressions by
applying properties to determine if the expressions are equivalent and justify their reasoning with
properties. Students will then be challenged to apply properties to write as many equivalent
expressions as possible for a given algebraic expression.
Directions:
Pass out the activity sheet and have a student read the directions. Model the first problem as a
class. Note: it might help for students to have their properties summary page out for this lesson.
Once the class understands what to do, set the timer for 10 minutes for students to work
independently. After time is up, allow students to compare answers with a partner and then use
random selection to have students share their answers and reasoning. If students are struggling,
encourage them to use numbers to check as they originally did in Are They Equivalent.
Next, explain Part 2- a competition to see who can write the most equivalent expressions, using
properties of operations. Show the example for #1 and make sure students understand that they
can not change the numbers used, but can only use properties to re-write the expression. They
must justify each expression with a property. Set the timer for 3-5 minutes for each expression
and at the end of each one, either have the student who found the most share or use roundtable to
have each student share one expression he/she found.
IMP Activity Are They Equivalent-II?
3
EE_T14
Type of
Knowledge
& SBAC
Claim
C- 1
C, RK 1, 3
C, RK, 1, 3
P- 1
C, RK- 1, 2, 3
Grade 6 Equations and Inequalities Unit- Conceptual Lessons
Lesson Title and Objective/Description
Hook Lesson
What’s Inside the N Box?
Students will be told how many total tiles were used in creating an expression
with the N box and then determine how many tiles must be in the box. They
will draw the tiles (substitute/evaluate) to check. After doing this a number of
times, students will try to define what it means to solve an equation. Students
will then compare and contrast expressions and equations and finally write the
equation for each N box scenario as well as the solution.
Cover- Up
Students will use mental math to solve equations by “covering-up” the variable
and figuring out what number must be hidden to make the equation true. This
connects to the “solving” students have been doing since Kinder. Students will
also substitute the solution to prove or check that the answer was a solution.
Solving Equations with Inverse Operations
Students will continue to solve equations by determining the value of the
variable using methods from earlier grades and then will be asked to
determine a different operation that would allow them to solve the same
equation. Students will analyze the different operations used to conclude that
they could also use the inverse operation to solve if they cannot figure out the
answer easily.
Practice Solving one-step linear equations with whole numbers and with
positive rational numbers (fractions and decimals).
From Bar Models to Equations
Students should have learned how to create bar models and tape diagrams in
prior grades. This lesson connects the drawing of the model with the writing of
an equation and then subsequent solving of that equation. Students are first
shown how to draw each bar model, assuming most have not had much
experience with this.
Suggested
Time
Frame
Math Practice
embedded
1 class
period
1, 2, 3
1 class
period
1, 2
1 class
period
2, 7, 8
3-5 class
periods
2 class
periods
2, 6
1, 2, 4, 6
EE_T15
P- 1
Practice writing equations from words
RK- 2
Problem Solving- Writing and solving one-step equations in context
C, RK- 1, 2, 3
What Number Could it Be?
Students will use real life contexts to determine solutions of what they will
eventually call inequalities. By listing all possible answers and then graphing
them, students will demonstrate conceptual understanding of an inequality.
Then, students will be told the meaning of the symbols and language used to
write and graph inequalities. Students will practice writing and graphing
single-variable inequalities on a number line.
Practice writing and graphing single variable inequalities
P- 1
C, RK- 1, 2, 3, Drop and Catch
4
Students will investigate the relationship between drop height and rebound
height for a ball. After collecting data, students will graph the data, look for
patterns and write an equation to model the data. Students will analyze and
discuss which variable is dependent and which is independent as well as if the
data are discrete or continuous.
C, RK- 1, 2, 3, Hopping Along
4
In this lesson, students will investigate the relationship between number of
hops and distance from the start. After collecting data, students will graph the
data, look for patterns and write an equation to model the data. Students will
analyze and discuss which variable is dependent and which is independent as
well as if the data are discrete or continuous.
RK- 2, 4
Problem Solving- scenarios from which students can make a table and graph
data which is linear and write an equation for the line (e.g., number of movie
tickets and cost).
P, RK- 1, 2
Practice - data, graph, table, equation and determining if data is discrete or
continuous, and which variable is independent.
Unit Notes: Grade 6 Standards EE 5, 6, 7, 8, 9
Time- 4 weeks
1 class
period
2 class
periods
1-2 class
periods
6
1-2 class
periods
1-2 class
periods
6
1-2 class
periods
1, 3, 4, 7
2 class
periods
1, 4
2 class
periods
1, 2
1, 3
1, 2, 6, 7
1, 3, 4, 7
EE_T16
Teacher Directions
Materials: Optional- N Boxes with tiles/counters
Overview: Students will be told how many total tiles were used in creating and expression
with the N box and then determine how many tiles must be in the box. They will draw the
tiles (substitute/evaluate) to check. After doing this a number of times, students will try to
define what it means to solve an equation. Students will then compare and contrast
expressions and equations and finally write the equation for each N box scenario as well as
the solution.
Note: If students do better with hands-on learning, provide the N boxes and tiles to use for
this lesson.
Begin by showing the class a single N box and 3 tiles or counters. Ask them what the
expression represented by this would be and have them chorale reply. Then tell them you
used 10 total tiles to make this expression and give them 30 seconds to silently think about
how many tiles must be inside the N box. Have them share their idea with a neighbor and
then use random selection to have students share their answer and reasoning with the
class.
Pass out the activity sheet and have the students complete # 1a and 1b. Show them how to
draw the tiles to evaluate/substitute to prove their answer is correct (See below). Once
they understand, give them about 10 minutes to complete the rest of page 1. Have a few
students read their summary of what it means to solve an equation aloud to the class.
Next, have students look at the top of page 2 and read the textbox. It is important that
students understand the difference between expressions and equations and understand
that we can not SOLVE an expression, but we can only manipulate it and evaluate it.
Have each student work on their Venn diagram for a few minutes and then complete one
together as a class.
Finally, have the students complete part 2.
Checking solution for 1b.
N
IMP Activity What’s Inside the N Box?
3
EE_T17
Teacher Directions
Materials:
 Mini-white boards, pens and erasers- 1 per student.
 Optional- post-it notes or slips of paper to cover the variable
Overview: Students will use mental math to solve equations by “covering-up” the variable and
figuring out what number must be hidden to make the equation true. This connects to the
“solving” students have been doing since Kinder. Students will also substitute the solution to
prove or check that the answer was a solution.
Begin by writing the equation 5x = 35 on the board and then use your hand to cover the variable.
Ask the class to think silently for 10 seconds about what number must be hiding under your hand
and then have them choral reply the answer. Pass out the activity sheet and have students read
the directions and the example. Show them how to substitute to check their answer. Pass out
post-it notes if you are choosing to use these. Give the class about 10-15 minutes to complete
page 1 and then call on students to share their answers with the class.
Once all students understand that solving equations can be as simple as it was in the primary
grades, have them turn to part 2. Make sure students understand the directions that they must
write TRUE equations using only numbers. Pair up students with someone of equal ability for
this part. Once both students are done, have them take turns writing out an equation from their
list and choosing any number (not just a digit but an entire number) to cover up so that their
partner can try to figure out the “solution”. If this is not working as well as you would like, you
can play this game as a class.
IMP Activity Cover-Up
3
EE_T18
Teacher Directions
Materials:
 None
Overview: Students will continue to solve equations by determining the value of the variable using methods from earlier grades and
then will be asked to determine a different operation that would allow them to solve the same equation. Students will analyze the
different operations used to conclude that they could also use the inverse operation to solve if they cannot figure out the answer easily.
Pass out the activity sheet and have students read the directions. Model the example with the students. Let them know they should be
able to figure out the solution by just using mental math and once they do, you want them to record the solution and check/prove that
the solution does work. Then ask them to consider what other operation they could have used if they did not know the answer. Note:
it is okay if some think of things other than the inverse operations (such as repeated addition). Once they get to the more challenging
problems, most students to come up with the inverse (especially as they had a major focus on inverse operations in the earlier grades).
Once students have completed the table, have the class share which different operation they used for each problem and record tally
marks by who also wrote that. Then have the class look at part 2 and complete the sentence frames. The goal here is to officially see
the use of inverse operations.
Go through the summary section as a class, allowing students to define inverse operations as well as explain how they can use them to
solve an equation. Call on students to share what they wrote. Finally, do the last section, which method would you use, as a class.
Show the equation and give 10 seconds of silent think time and then have students show you thumbs up for mental math, sideways
thumb for not sure and thumbs down for inverse operations. Ask a few students to explain why and guide the discussion so that
students realize easy or friendly equations can just be solved mentally or through cover-up whereas more difficult equations need
inverse operations with pencil and paper.
IMP Activity Solving Equations with Inverse Operations
4
EE_T19
Teacher Directions
Materials: None
Overview: Students should have learned how to create bar models and tape diagrams in prior
grades. This lesson connects the drawing of the model with the writing or an equation and then
subsequent solving of that equation. In the case of this lesson, students are first shown how to
draw each bar model, assuming most have not had much experience with this.
Directions:
Explain that today students will learn how to use algebra to solve the word problems they have
been working on since Kindergarten. Ask how many students have drawn bar models to solve
word problems. Pass out the activity sheet and go through the example together. Let the class
try problem #1 and select a student to come show his/her work and explain at the front. If most
students are doing okay with this allow them to work alone or with a partner for 15-20 minutes
and then come back together as a class and have volunteers show their work. As someone shows
their work, ask the class if anyone thought about it differently and if so, have that person also
share (there is one than one correct way to set up and solve each problem). If the class needs
more guidance, go through one problem at a time, giving the students a few minutes to solve
followed by someone sharing.
When you get to page 6, you can assign problems to teams to work our and share on a poster
gallery style or students can solve all 10 problems.
IMP From Bar Models to Equations
8
EE_T20
Teacher Directions
Materials: None
Overview: Students will use real life contexts to determine solutions to what they will
eventually call inequalities. By listing all possible answers and then graphing them, students will
demonstrate conceptual understanding of an inequality. Then, students will be told the meaning
of the symbols and language used to write and graph inequalities. Students will then practice
writing and graphing single-variable inequalities on a number line.
Part 1: Give the students 5 minutes to complete part 1. Encourage them to write down any and
all answers they think could work.
Part 2: Without giving any direct instruction, ask the students to use the number lines provided
to show all the answers they thought of or could think of from part 1 on the number line below.
Choose a few students at random to show how they represented all the possible answers and
make sure other students can understand the thinking. Ask a few probing questions, such as,
“Could it also be ___?” “What about a number between 4 and 5?”
Part 3: Begin by asking the students “How many answers are there to each of these problems?”
“Do you think we could represent the answer with an equation, such as x = 3?” “Why or why
not?” After the class agrees that there is a whole group of possible answers, direct their attention
to the reading at the top of page 2. Ask the class if they recall seeing these symbols in
elementary school and what they might mean. Then allow them to work alone or with a partner
to write in inequality for each of the 4 scenarios.
Part 4: Direct the students’ attention to the box on the right of part 4. Go over the math
conventions for noting if a point is or is not included and discuss the concept of a “boundary”
point by asking them, for each of the scenarios, what was the largest or smallest number it could
have been. Ask the students to try to represent scenario 1 using the correct notation and check
the work as a class. Finally, have them graph the other 3 scenarios and choose students at
random to present their solutions.
Part 5: Allow the students 5-10 minutes to try to complete the chart on their own, explaining
that they need all three representations for each row. The second row may pose a challenge and
is there to help them be aware that not all inequalities are single. After most students are
finished, have them work in a group of 4 and use roundtable to share (begin with 1 member of
the group and go in a circle, having each student share their work on each problem). While they
are sharing, circulate to see how well they are understanding and provide additional explicit
instruction and practice, if necessary.
Part 6: End class by having the students try to summarize or explain what in inequality is by
comparing it with an equation. Question students to ensure they understand that an equation with
a single variable has a single solution; whereas an inequality has a set of numbers that represent
the solution.
IMP Activity What Number Could it Be?
4
EE_T21
Teacher Directions
Materials:
◊ Meter stick- 1 per group
◊ Bouncy ball (racquet ball or tennis ball work well)- 1 per group
◊ Graph Paper- 1 sheet per student
◊ Rulers- 1 per student
Objective
In this lesson, students will investigate the relationship between drop height and rebound height
for a ball. After collecting data, students will graph the data, look for patterns and write an
equation to model the data. Students will analyze and discuss which variable is dependent and
independent as well as if the data are discrete or continuous.
Directions:
Pass out the activity sheet and have a student read the directions. Model a drop and catch for the
students, making sure to point out what part of the ball you are looking at in terms of measuring
height. Once students understand the directions, have a person from each group come get a
meter stick and ball for their group. If you allow the use of cell phones, you can have students
video the bounce and pause the video to get an exact rebound height.
Give the groups 10 minutes to collect the most accurate data possible. Once a group is done,
give them graph paper (1 sheet per student) and a ruler. Encourage the students to think about
and discuss how to label their graph, question #1. Once the class has graphed the data, bring
them back together for a discussion about which variable was dependent and which was
independent. To help, ask the following question, “Did the rebound affect how high you
dropped the ball Or did the height from which you dropped the ball affect the rebound?” Use
think-pair-share to have them discuss with selected students explaining. Guide the class to
understand that the rebound was dependent upon the height. The height was independent as it
was arbitrary and they can choose this. Next have a discussion about whether or not the points
on the graph should be connected. If students are unsure, show a graph where the line is drawn
and point to where a drop height of 27 cm would be (or some height they did not choose) and ask
what the meaning of that point would be and if this makes sense. They should agree that any
point along the line makes sense and therefore they can connect the points: the data is
continuous. Give the students about 10 minutes to complete questions 3-8 in their groups.
Circulate and ask questions to help guide them in their thinking. Once groups have completed
up through question 7, use inside outside line to have them share their responses to questions 1, 2
4 & 7. Close out the lesson by having a discussion about the equations they wrote and how they
can use their equation to solve for a rebound height of 80 cm. Below is an example; note that the
coefficient in each group’s equation can vary slightly.
r = .66d
80 = .66d
80
=d
.66
121.21 = d
IMP Activity Drop and Catch
3
EE_T22
Teacher Directions
Materials:
◊ Meter stick or measure tape- 1 per group
◊ Sidewalk Chalk- 2 per group
◊ Graph Paper- 1 sheet per student
◊ Rulers- 1 per student
Objective
In this lesson, students will investigate the relationship between number of hops and distance
from the start. After collecting data, students will graph the data, look for patterns and write an
equation to model the data. Students will analyze and discuss which variable is dependent and
which is independent as well as if the data are discrete or continuous.
Directions:
Pass out the activity sheet and have a student read the directions. Model a two-footed hop and
then show the class two-three consecutive hops. Once students understand the directions, have a
person from each group come get a meter stick or measure tape and chalk for their group. Make
sure the groups have decided who will perform each role and let them know if they are quick,
they can all take turns being the hopper.
Give the groups 10 minutes to collect the most accurate data possible. Once a group is done,
give them graph paper (1 sheet per student) and a ruler. Encourage the students to think about
and discuss how to label their graph, question #1. Once the class has graphed the data, bring
them back together for a discussion about which variable was dependent and which was
independent. To help, ask the following question, “Did the number of hops affect the distance
you went or did the distance affect the number of hops you did?” Use think-pair-share to have
them discuss with selected students explaining. Guide the class to understand that the distance
was dependent upon the number of hops. The number of hops was independent as it was
arbitrary and they can choose this. Next have a discussion about whether or not the points on the
graph should be connected. If students are unsure, show a graph where the line is drawn and
point to where the # of hops would be 4.3 and ask what the meaning of that point would be and if
this makes sense. They should agree that the data only makes sense for whole number hops: the
data are discrete. So, we do not “connect” the points. It is okay to draw a line to model the
function that best represent the data if they want to use this to predict, but they need to see that
the data are not continuous. Give the students about 10 minutes to complete questions 3-8 in
their groups. Circulate and ask questions to help guide them in their thinking. Once groups have
completed up through question 7, use inside outside line to have them share their responses to
questions 1, 2 4 & 7. Close out the lesson by having a discussion about the equations they wrote
and how they can use their equation to solve for a distance of 800 cm.
IMP Activity Hopping Along
3
EE_T23