5E Lesson Plan Math
Grade Level: 4th
Lesson Title: All Operations
Subject Area: Math
Lesson Length: 14 Days
THE TEACHING PROCESS
Lesson Overview: This unit bundles student expectations that address input-output
tables, sequences, expenses, and solving one-, two-, or multistep problems using all four
operations. According to the Texas Education Agency, mathematical process standards
including application, a problem-solving model, tools and techniques, communication,
representations, relationships, and justifications should be integrated (when applicable)
with content knowledge and skills so that students are prepared to use mathematics in
everyday life, society, and the workplace..
During this unit, students apply previously learned concepts to solve one-, two-, or
multi-step problems involving addition and subtraction of whole numbers and decimals
to the hundredths place, multiplication of whole numbers up to two-digit factors and up
to four-digit factors by one-digit factors, and division of whole numbers up to four-digit
dividends by one-digit divisors with remainders in appropriate contexts. Students
examine financial literacy situations that involve calculating a profit and learn to
distinguish between fixed and variable expenses. Representations of these real-life
situations that continue to be utilized include strip diagrams and equations with a letter
standing for the unknown quantity. This unit further requires students to represent
problems using an input-output table and numerical expressions to generate a number
pattern that follows a given rule. These identified rules incorporate an algebraic
understanding of the relationship of the values in the resulting sequence and their
position in the sequence.
Unit Objectives:
Students will
 solve one-, two-, or multi-step problems involving addition and subtraction of
whole numbers and decimals to the hundredths place
 solve multiplication of whole numbers up to two-digit factors and up to fourdigit factors by one-digit factors
 perform division of whole numbers up to four-digit dividends by one-digit
divisors with remainders in appropriate contexts
 examine financial literacy situations that involve calculating a profit and learn to
distinguish between fixed and variable expenses
 represent problems using an input-output table and numerical expressions to
generate a number pattern that follows a given rule.
Standards addressed:
TEKS:
4.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
4.1B Use a problem-solving model that incorporates analyzing given information, formulating a
plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
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4.1C Select tools, including real objects, manipulatives, paper and pencil, and technology as
appropriate, and techniques, including mental math, estimation, and number sense as
appropriate, to solve problems.
4.1D Communicate mathematical ideas, reasoning, and their implications using multiple
representations, including symbols, diagrams, and language as appropriate.
4.1E Create and use representations to organize, record, and communicate mathematical ideas.
4.1F Analyze mathematical relationships to connect and communicate mathematical ideas.
4.1G Display, explain, and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
4.4A Add and subtract whole numbers and decimals to the hundredths place using the standard
algorithm.
4.4H Solve with fluency one- and two-step problems involving multiplication and division,
including interpreting remainders.
4.5A Represent multi-step problems involving the four operations with whole numbers using
strip diagrams and equations with a letter standing for the unknown quantity.
4.5B Represent problems using an input-output table and numerical expressions to generate a
number pattern that follows a given rule representing the relationship of the values in the
resulting sequence and their position in the sequence.
4.10A Distinguish between fixed and variable expenses.
4.10B Calculate profit in a given situation.
ELPS:
ELPS.c.1A use prior knowledge and experiences to understand meanings in English
ELPS.c.1C use strategic learning techniques such as concept mapping, drawing, memorizing,
comparing, contrasting, and reviewing to acquire basic and grade-level vocabulary
ELPS.c.1G demonstrate an increasing ability to distinguish between formal and informal
English and an increasing knowledge of when to use each one commensurate with grade-level
learning expectations
ELPS.c.2G understand the general meaning, main points, and important details of spoken
language ranging from situations in which topics, language, and contexts are familiar to
unfamiliar
ELPS.c.2H understand implicit ideas and information in increasingly complex spoken language
commensurate with grade-level learning expectations
ELPS.c.3D speak using grade-level content area vocabulary in context to internalize new
English words and build academic language proficiency
ELPS.c.3E share information in cooperative learning interactions
Misconceptions:
 Some students may misunderstand the distinction between fixed and variable
expenses
 Some students may attempt to solve multistep problems by using only a one-step
process.
 Some students may apply a rule for an additive numerical pattern to a
multiplicative pattern.
 Some students may misinterpret values in an input-output table by comparing
input values to other input values, or by comparing output values to other output
values, rather than interpreting the relationship between input values and
corresponding output values.
Vocabulary:
Additive numerical pattern – a pattern that occurs when a constant non-zero value is added
to an input value to determine the output value
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Counting (natural) numbers – the set of positive numbers that begins at one and increases
by increments of one each time {1, 2, 3, ..., n}
Decimal number – a number in the base-10 place value system used to represent a quantity
that may include part of a whole and is recorded with a decimal point separating the whole
from the part
Dividend – the number that is being divided
Divisor– the number the dividend is being divided by
Equation – a mathematical statement composed of algebraic and/or numeric expressions
set equal to each other
Expense – payment for goods and services
Expression – a mathematical phrase, with no equal sign, that may contain a number(s), an
unknown(s), and/or an operator(s)
Factor– a number multiplied by another number to find a product
Fixed expenses – expenses that occur regularly and do not vary month to month
Fluency – efficient application of procedures with accuracy
Income – money earned or received
Input – position in the sequence
Input-output table – a table which represents how the application of a rule on a value,
input, results in a different value, output
Multiplicative numerical pattern – a pattern that occurs when a constant non-zero value is
multiplied by an input value to determine the output value
Output – value in the sequence
Product– the total when two or more factors are multiplied
Profit – money that is made in a business after all the costs and expenses are paid
Quotient– the size or measure of each group or the number of groups when the dividend is
divided by the divisor
Sequence – an ordered list of numbers, usually set apart by commas, such as {2, 4, 6, 8, 10,
12, …}
Strip diagram – a linear model used to illustrate number relationships
Trailing zeros – a sequence of zeros in the decimal part of a number that follow the last
non-zero digit, and whether recorded or deleted, does not change the value of the number
Variable expenses – expenses that occur regularly but vary month to month and can
usually be controlled by an individual
Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
Related Vocabulary:
Difference
Position
Rule
Sequential
Place Value
Remainder
Standard algorithm Sum
Unknown Value
List of Materials:
Premade Input output robot machine
Index cards with number for input/output machine
Input Output Intro Table Lesson PDF
Input Output Robot PDF
Alexander Who Used to Be Rich Last Sunday by Judith Viorst (link to online book
included)
Sample Budget for Kids
Blank Budget Sheet
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Fixed and Variable Expenses PP
Alex and the Amazing Lemonade Stand by Liz Scott
Profit, Income and Expenses Index Cards
Fourth Grade Grocer WS
Personal Financial Literacy Task Cards
You Can Toucan Math by David Adler or Greg Tang book
Multistep word problem practice WS
Solving problems using strip diagrams resource cards
Multiplication and Division strip diagram resource cards
INSTRUCTIONAL SEQUENCE
Phase One/Two Engage/Explore
Day One Activity: Teacher should have a box premade and decorated to look like a
robot/machine. There should be a cut at the top/left and a cut at the bottom/right.
Example:
Ask students to describe the box. What do they think it’s used for? What do the openings
do? Lead students to a discussion of the difference between input and output. What do
you think happens in the machine? Give a student a number to put into the input and tell
them a number that would come out. Do this a couple of times and then ask what happens
to the numbers inside the box. As a class, play the online game:
http://www.mathplayground.com/functionmachine.html
Give students input/output function worksheets for independent practice.
Reflection Journal: What did you learn today about input output tables and how numbers
can be changed? What operations do you use to increase or decrease a number and how
do you know?
What’s the teacher doing?
What are the students doing?
Leading discussion on input output
machines/tables.
Participating in discussion about input output
machine.
Helping students to see that numbers increase
when you add or multiply and decrease when
you subtract or divide.
Answering questions from the function machine
online game.
Working independently on input output table
Guiding practice with the students with the
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online math game.
practice.
Monitoring students as they work independently
and write in their reflection journal.
Reflecting in journal over lessons learned.
Phase 3 Explain
Day Two Activity: Teacher should model for students making an input/output table page
in math journal. Example follows:
Next go through the study jams lesson
http://studyjams.scholastic.com/studyjams/jams/math/algebra/function-tables.htm
Use the Input/Output table intro lesson to go through the watermelon and shell tables and
create the rule using unknown variables. Model how to show what happens to the input to
get the output or output to get the input. When finished, have the students work
cooperatively in pairs or groups to do the next three table problems. Review to check and
reteach where necessary.
Reflection Journal: Create an input output table and write an expression that can be used
to figure out the rule.
What’s the teacher doing?
What are the student’s doing?
Modeling in math journal the input output table
procedure.
Completing math journal entry for input output
tables.
Using Study Jams lesson to show students how
to discover the rule for input output tables and
represent it with unknown variables.
Contributing to discussion during study jams
lesson.
Monitoring while students practice
cooperatively and reteaching when necessary.
Addressing misconceptions about input tables
relating input to input and output to output.
Working cooperatively with group deciphering
rules for input and output tables.
Reflecting on learning for the day.
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Phase Four Elaborate/Evaluate
Day Three Activity: Using page 3 of the resource from yesterday, teacher will model for
students creating their own input output tables and rules. Ask students to give teacher a
number for input side and teacher will put number on output side. Do this three times,
filling in input output table, then see if students can figure out the rule teacher in applying.
Create an expression representing the rule for finding the unknown value. Repeat this
process for all three blank tables.
Input
Student says 15
Student says 40
Students says 100
What’s the rule?
Output
Teacher says 30
Teacher says 55
Teacher says 115
X+15=Y or Input +15=Output
Now students will practice cooperatively. Student 1 will give a number to Student 2.
Student 2 will apply some rule to it, then give the output back to Student 1. Student 1 will
give another number and Student 2 will apply same rule. Student 1 will give a 3rd number
to Student 2, and after Student 2 applies the rule, Student 1 will try to guess what the rule
is. Caution students about using division as a rule because if Student 1’s number can’t be
evenly divided, it will be difficult to give the output back. Switch places being the one to
apply the rule.
Input Output Robot lesson template PDF is included for use if favored.
When time is up, have students pick an example they used and draw an input output table
that shows the expression represented by the rule. Reflect together on the experience and
how easy or difficult it was to determine the rule. Share with the group.
Assess individual understanding using the last page of the table intro lesson resource.
What’s the teacher doing?
What are the students doing?
Modeling the activity students will complete,
with clear directions and cautions.
Working cooperatively with partner to complete
the activity.
Monitoring while students complete activity and
reteaching when necessary.
Writing the example and clearly explaining the
process of determining the rule.
Giving students assessment and checking for
understanding.
Completing the assessment.
Phase One/Two Engage/Explore
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Day Four Activity: Tell students that today the class will be discussing a different way
that we work with input and output in our homes and everyday lives.
Read Alexander Who Used to be Rich Last Sunday by Judith Viorst
http://bookbuilder.cast.org/view.php?op=view%20&book=51704&page=1
During the reading, discuss ideas of income saving, expenses (spending). How was
Alexander spending money? How was he trying to make money?
What are your financial goals for the future? How do you earn money now? What are
some things you might be saving for? What are some things you buy now? What about
college-how do you think that will be paid for? What kind of job do you hope to have?
What kind of income do you expect to earn? What do you want to have as far as material
possessions-house, car, vacations etc?
Make an Anchor Chart for Budget. Divide it into two parts-Income and Expenses.
Discuss that Income is money earned. It is mostly Salary from a job (mowing lawns,
babysitting, cleaning house or allowance for kids). Under expenses divide it into Fixed
and Variable Expenses. Explain that Fixed Expenses are ones that don’t change month to
month such as house payment, rent, insurance, car payment, utilities, groceries, tithe.
Variable expenses are things that change or are varied, such as doctor appointments, gifts,
entertainment, activities (kids mostly have variable expense now). To make sure you
have enough money, you can subtract your expenses from your income.
Pass out the Sample Monthly Budget for Kids. Go through the one that is already filled
out together. Have them fill it out one individually. Share with the class when complete.
Reflection Journal: Why do you think it’s important that you keep track of what you earn
and spend, and save money? Write about a way you can start earning money now, and
what you might spend that money on or save.
What’s the teacher doing?
What are the students doing?
Reading and discussing Alexander book and
relating it to financial literacy.
Listen and participate during book reading.
Leading discussion on income and expenses,
fixed vs variable expenses.
Produce ideas for income and expenses anchor
chart.
Complete sample budget and share with class.
Review the sample budget for kids and
monitor while kids fill out their own sample
budget.
Write in reflection journal.
Assess whether students are understanding
budgeting, income and expenses during share
time.
Phase Three/Four Explain/Elaborate
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Day Five Activity: Display the Blank Budget Sheet printable. Tell students they are going
to use the sample budget they completed from yesterday to fill in the budget showing
income and expenses, fixed and variable. Use the example from yesterday to model first
how students will transfer the information to the Blank Budget Sheet. Then allow students
time to complete their own.
Show the quick power point on fixed and variable expenses. Create a T chart for Fixed
and Variable Expenses. Go through several examples and put in the correct column. If
there are any misconceptions about the differences, reteach why they are different.
Display this problem scenario:
Mrs. Carter just bought a car. She has several expenses that come with owning a car:
Monthly car payment, monthly car insurance, oil change, gas, tires, tune up, car washes,
yearly inspection and registration. Working collaboratively in a group, students will place
each expense in a T chart under either Fixed or Variable Expenses.
Car Expenses
Fixed Variable
Once the group has sorted the expenses, have them pick one from each column. They
must write a statement for each one explaining why the put it in the column they did.
Reflection Journal: What are some fixed and variable expenses that you think your parents
might have? Make a t chart in your journal and list them.
What’s the teacher doing?
What are the students doing?
Assisting students in filling out the budget
sheet, placing expenses in the right column.
Describing the difference between fixed and
variable expenses.
Creating and leading the t chart discussion on
fixed and variable expenses.
Sorting expenses into the correct column and
working collaboratively to describe reasons why.
Describing the problem scenario and
monitoring the group discussions.
Phase One/Two Engage/Explore
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Day Six Activity: Read Alex and the Amazing Lemonade Stand by Liz Scott
http://www.youtube.com/watch?v=RcTrDY7Lx4s
How much do you think Alex charged for each cup of her lemonade? This is her income.
If she sold 5 cups, how much did she make? 10 cups? Make an input output table to show
what she might make if she sold 100, 500 or 1,000 cups. What things do you think Alex
needed to buy to run her lemonade stand? What do these things cost? These were her
expenses. Make an input output table to show what her expenses would be for 100, 500 or
1,000 cups.
When you run a business, you receive income from people who pay for your goods or
services. You also have expenses, much like the fixed and variable expenses we’ve been
discussing. When your income is greater than your expenses, this is called a PROFIT.
Add profit to the Anchor Chart.
Model what Alex’s business plan would look like by listing and estimating her expenses
and figuring out what she should charge per cup to cover her expenses and make a profit.
Alex’s Lemonade Stand
Expenses
Cups (fixed)
Lemonade (fixed)
Sugar (fixed)
Pitchers or Containers (variable-one time)
Sign (variable-one time)
Markers to make sign (variable-one time)
Table for Stand (variable-one time)
Chair for Stand (variable-one time)
Alex should charge ____ per cup in order to make a profit.
As a class, brainstorm ideas for a class business. What could good could you make or
service could you provide? What would be your expenses? How much would you charge
to make a profit? Create a business plan and list fixed and variable expenses. Project what
your income might be in 1 week, 2 weeks, 1 month, etc.
Reflection Journal: How did Alex’s lemonade stand help people? What could you do like
Alex to help someone less fortunate than yourself?
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What’s the teacher doing?
What are the students doing?
Reading and facilitating the discussion on
Alex and the Amazing Lemonade Stand.
Participating in the book discussion.
Explaining the vocabulary for profit including
income and expenses.
Leading and monitoring the brainstorming on
a class business and creation of a business
plan.
Displaying understanding of the vocabulary for
profit , income and expenses.
Brainstorming ideas for classroom business and
helping with the business plan.
Phase Three/Four Explain/Elaborate
Day Seven Activity: Show students the chart from yesterday with the lemonade expenses
and profit information. Discuss the formula for finding profit. Profit = Income-Expenses.
Add to anchor chart.
Do the first Profit, Income and Expenses Card together as a class.
Income = $1,500
Expenses = $325
Profit = ?
Write an equation to find profit.
Profit = 1,500-325
Profit = $1,175
Give each table one Profit, Income and Expenses index card with a profit problem on it.
Everyone at the table works the problem, then compare answers to get ready to share the
correct solution.
Next , pick the first problem from the 2nd set of cards.
Profit = $743
Income = $1,078
Expenses = ?
Write an equation to find the expenses.
Expenses = $1,078-$743
Expenses = $335
Model how if you know two parts of the equation, you can find the other parts. Related it
to addition and subtraction facts to show that Expenses = Income – Profit and Income =
Profit + Expenses.
Give each table one Profit, Income and Expenses index card with an income or expenses
problem on it. Everyone at the table will work the problem, then compare answers to get
ready to share the correct solution.
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In the Math Journal, add the equations to find Profit, Income and Expenses using three
colored sticky notes.
Next, have students complete the Fourth Grade Grocer worksheet independently.
Reflection Journal: Why do you think keeping track of income and expenses are important
for budgeting and businesses?
What’s the teacher doing?
What are the students doing?
Modeling the equations for finding Profit,
Income and Expenses.
Working equations to find unknown information
on index cards with cooperative group.
Monitoring and reteaching while students are
solving equations in cooperative groups.
Recording information in journal regarding profit
equations.
Leading math journal entry.
Completing Fourth Grader Grocer worksheet
using information from lesson and math journal.
Monitoring and assessing Fourth Grade
Grocer.
Phase Three/Four Explain/Elaborate
Day Eight Activity: Present the following problem: Sarah is selling decorated Christmas
cookies. It costs her $3.60 per dozen to make and decorate the cookies. If she charges
$1.00 a cookie, how much profit will she make on 10 dozen?
Model
What do we know?
10 dozen cookies = 120 cookies (12x10=120)
Each cookie cost her $0.30 to make ($3.60/12=$0.30)
How do we figure profit? Income-Expenses=Profit
She will make $0.70 on each cookie ($1.00-$0.30=$0.70)
Her income on 120 cookies will be $84.00 (120x$0.70=$84.00)
In cooperative groups, have students work on one or more of these problems. Monitor and
correct misconceptions as they work. Have students share solutions with the class.
1) Joe mows lawns for $25 each. His expenses for each lawn are $3.00 in gas. He
also pays his dad $5.00 a lawn to use the lawn mower. How much profit will Joe
make after mowing 10 lawns?
2) Susie makes necklaces to sell at a store. Last month she made $200 profit. Her
expenses for each necklace were $6.00, and she sold 20 necklaces. How much did
she charge for each necklace?
3) Mark hangs holiday decorations to make money. He charges $10 per hour. He
pays his dad $0.75 cents per house to use the ladder, and he pays his friend Steve
4.00 and hour to help him. What is Mark’s profit per hour?
4) Makayla makes cupcakes and sells them at her brother’s baseball games. She sells
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the cupcakes for $1.00 each. If Makayla makes $19.00 profit on 24 cupcakes, what
were her expenses for the 24 cupcakes?
5) Peter is selling tshirts. He pays $4.10 in expenses for each shirt. He makes a profit
of $99.00 on 10 shirts. What did he charge for each shirt?
Once groups are done working, have them share their solutions.
Students will then complete Personal Financial Literacy Task Cards.
Reflection Journal: Create a profit, income or expense word problem that a friend can
solve.
What’s the teacher doing?
What are the students doing?
Modeling the procedure for solving profit,
income and expense problems given certain
information.
Working cooperatively to complete group profit
problems.
Reteaching and monitoring as students work
in groups on problems.
Completing Personal Financial Task Card
activity.
Assessing Task Card activity.
Phase Five Evaluate
Day Nine Activity: Give Performance Assessment
Analyze the problem situation(s) described below. Organize and record your work for each of the
following tasks. Using precise mathematical language, justify and explain each solution process.
1) John loves being a cat owner but is learning that there are many expenses involved in cat
ownership, as can be seen from the list that he made.
a) Sort the expenses from the list into fixed expenses and variable expenses.
b) Display your sort in a graphic organizer.
c) Choose one expense from each category and explain why you sorted them the way that you did.
2) Every month John buys a bag of food for his cat for $25.00. Each week he also buys 6 cans of
cat food for $1.50 each.
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a) Represent and determine the amount of money John spends for his cat’s dry and canned food for
January and February with a strip diagram and an equation where drepresents the amount of money
he spends on cat food.
o
o
January: 5 weeks
February: 4 weeks
3) John and his sister start a business decorating tote bags to sell. The profits they make will help
them with their pet expenses. They buy tote bags for $3 each, a package of fabric paints for $14.95,
and a set of paint brushes that cost $9.83. They plan to sell each decorated bag for $12. After
completing 38 bags, they ran out of their first set of paints.
a) Calculate the profit that John and his sister will make if they sell all 38 tote bags.
b) To sell more bags, John and his sister decide to sell sets of three bags for $25. Determine the
amount of profit they would make if the sold 11 sets of bags.
What’s the teacher doing?
What are the students doing?
Monitor student performance on PA.
Complete performance assessment.
Use data from assessment for information
on reteaching and enrichment.
Phase One/Two Engage/Explore
Day 10 Activity: Read aloud You Can Toucan Math by David Adler or other problem
solving book, such as a Greg Tang book. Discuss how you know how to solve problems
and what information you have. What words are helpful in solving problems? What are
some strategies that you can use to solve problems? How do you know that you have the
right answer?
Make an anchor chart with problem solving strategies. Include Guess and Check, Draw a
Picture, Strip Diagrams, Write a Number Sentence, Work Backwards, and other strategies
used in class. Tell students you are going to use these same strategies to solve multi step
problems.
Discuss with your children how one danger when solving this type of problem is stopping
too soon – after answering only the first part of the problem.
Steven is reading a book that has 260 pages. He read 35 pages on Monday night, and
40 pages on Tuesday night. How many pages does he have left to read?
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Steven is reading a book that has 260 pages. He read 35 pages on Monday night,
and 40 pages on Tuesday night. How many pages does he have left to read?
260 pages tells you the total pages to be read.
35 pages is the amount read on Monday.
40 pages is the amount read on Tuesday.
How many pages does he have left to read? is the question you are being asked.
Most students recognize that they need to add together 35 + 40 to get the pages read
so far. The danger is you might think you can stop there.
Adding 35 + 40 will tell you that Steven has read 75 pages so far, but if you go back to
check the question you are being asked, you will see that your answer does not match
what you are being asked. You will have to take another step to get there.
Steven has read 75 pages so far, but you are being asked what he has left to read, not
what he has already read. To get your final answer, you must subtract what he has
read from the total pages to be read: 260 – 75. Steven has 185 pages left to read.
260 – 75 = 185
It’s important to clearly show that you understand what your answer means. Instead
of just writing 185, write:
Steven has 185 pages left to read.
Whenever you finish a math problem of any kind, always go back to the original
problem. Think: “What is the question I am being asked?” Make sure that your final
answer is a reasonable answer for the question you are being asked.
I was asked, “How many pages does he have left to read?” My answer is: Steven has
185 pages left to read.
My answer is reasonable because it tells how many pages Steven still needs to read. I
added together 35 and 40 to find out the total pages he had already read, and
subtracted from the total pages in the book. The number he has left should be less
than the total in the book, since he’s already read some. 185 is smaller than 260. My
answer makes sense.
You can tell that there are lots of things to remember with a multi-step word problem, even
when the problem itself is relatively easy. But that’s what makes these problems
challenging: you get to use both sides of your brain – your logical math skills, and your
verbal language skills (working with words). That’s why they are often more fun to do
than problems that are just numbers without the details and context that word problems
give you. The better you understand how to solve them, the more fun they are to solve.
Multi-Step Word Problem: Example #2
You might find that this problem is more difficult that the one above.
A man bought a dozen boxes, each with 24 highlighter pens inside, for $8 each box.
He repacked five of these boxes into packages of six highlighters each, and sold them
for $3 per package. He sold the rest of the highlighters separately at the rate of three
pens for $2. How much profit did he make?

A dozen boxes tells you he had 12 boxes.

Each with 24 tells you the number of highlighters in each box.

$8 each box tells you the amount he paid for all the highlighters.
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
Repacked five boxes into packages of six highlighters each separates 5 sets of
24 away from the original 12 sets of 24.

$3 per package is the selling price of the separated sets.

The rest is the 7 sets of 24 still left after separating away the 5 sets.

Three pens for $2 is the selling price of those 7 sets.
How much profit did he make? is ultimately the question you are being asked. Profit
is the amount earned from all sales, minus the amount spent to buy the highlighters.

There are 12 boxes, and each cost the man $8 to buy. 12 x $8 is $96, so the man
spent $96 to buy all the highlighters.

He separated 5 boxes of 24 away from the original 12 boxes, and made new
packages with six highlighters in each package. 5 x 24 = 120, so he repacked 120
highlighters in all.

120 ÷ 6 = 20, so he had 20 new packages. He sold each for $3. 20 x $3= $60, so
he has earned $60 so far.

He still had 7 of his original boxes of 24. 7 x 24 = 168, so he had 168
highlighters still to sell.

He sold them in sets of 3 for $2 each set. 168 ÷ 3 = 56 sets, and 56 x$2 = $112.
He earned $112 from selling the 7 boxes.

Then we must add together the two amounts he earned. $60 plus $112 is$172,
so he earned $172 from all his sales.
The danger is stopping here, because it took so long to get to this point, that it feels
like the end. Don’t forget that the question asks you how much profit he earned.
Profit is the amount earned minus the amount spent to buy the highlighters.

He spent $96 and earned $172, so $172 - $96 tells you his profit, $76.
It’s important to clearly show that you understand what your answer means.
Instead of just writing $76, write:
The man made $76 profit.
Remember, whenever you finish a math problem, always go back to the original
problem. Think: “What is the question I am being asked?” Make sure that your final
answer is a reasonable answer for the question you are being asked.
I was asked, “How much profit did he make?” My answer is: The man made $76
profit.
My answer is reasonable because it tells the man’s profit. I figured out the total he
had spent, $96, and subtracted it from the total earned, $172. Profit should be smaller
than money earned, since the cost of the highlighters has to be taken out. $76 is
smaller than $172. My answer makes sense.
The first problem we did was relatively simple, while the second was much more
complicated. All multi-step problems require you to slow down and think clearly.
Remember: you won’t know if your answer is reasonable if you don’t understand what you
are being asked to solve. Take time to highlight and make notes before you solve the
problem, and always go back to the original problem when you finish to make sure you
really answered the question you were being asked.
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Use the Multistep Word Problems WS for partner and individual practice.
Reflection Journal: What is a good way to make sure that you have completed all steps
when solving multistep problems? What are some strategies you can use?
What’s the teacher doing?
What are the students doing?
Leading discussion on problem solving
strategies.
Participating in discussion on multistep problems.
Modeling multi step problems procedures and
strategies.
Assisting students during partner and
independent practice.
Working through problems with teacher during
guided practice.
Working problems with partner and
independently using multistep procedures.
Phase Three/Four Explain/Elaborate
Day 11 Activity: Show the video below on multistep problems solving.
http://www.showme.com/sh/?h=jC6LTns
Copy problem in math journal and discuss how you would solve the problem. What does
the x represent? What operations are you going to use? What will your answer tell you?
Model for students how solving for an unknown quantity can be represented by a letter,
such as 3 + d = 5, or 5 – c = 1. Have students give other examples you can use.
Use the Solving Problems Using Strip Diagrams resource cards 1-4 to model more
problems using S as the unknown quantity. Remaining cards may be used in small groups
or partners for students to practice.
Reflection Journal: Explain how a letter represents an unknown quanity in an equation by
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giving an example equation and solving for the unknown quantity.
What’s the teacher doing?
What are the students doing?
Modeling problems solving procedures and
demonstrating unknown quantities using
letters.
Using teacher examples to understand problem
solving using unknown quantities.
Monitoring students as they practice with task
cards and reteaching misconceptions.
Practice solving for unknown quantities by using
task cards.
Phase Three/Four Explain/Elaborate
Day 12 Activity: Show Brain Pop Video on Equations with Variables
http://www.brainpop.com/math/algebra/equationswithvariables/
Alternate video:
https://www.youtube.com/watch?v=LwrWD1wC9TE
Model for students with task cards 1-4 like yesterday. Tell students they are going to play
a scoot game using task cards like those used yesterday, but these will use different
operations. Have students fold a piece of paper into eight boxes. Use the front and back.
Task cards from the Multiplication Divison Strip Diagram Resource should be taped
around the room. Students will move about the room answering any 16 problems, using
the front and back on their answer sheet. Make sure students put the number of the task
card for each problem they work, so that they can be checked at the end.
One finished, students will get into groups and check answers of alike problems. If there is
a difference, students can go back to the card on the wall and discuss why their answer is
correct, or change their answer.
Give students correct answer and review more difficult cards.
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What’s the teacher doing?
What are the students doing?
Modeling procedures for students.
Working independently to solve task card
problems.
Monitoring while students rotate around
task cards.
Working collaboratively to check answers and
rework where necessary.
Facilitating discussion on wrong and right
answers.
Phase Three/Four Explain/Elaborate
Day 13 Activity: Show video on solving problems with unknowns.
https://learnzillion.com/lessons/1525-solve-two-step-problems-using-letters-to-representunknowns
Students will use index cards and work with one or two other students to create their own
strip diagram memory game. Students must create 10 strip diagram and/or multi step
problems. They may use the activities over the last two days to help them, but may not
copy any of the task cards. On one card they must write the problem, on another card, they
must write the solution. The questions must use all four operations, addition subtraction,
multiplication and division.
Example Problem: Carlie sold 32 raffle tickets for the school fundraiser. That’s 4 times as
many as many as Caroline sold. How many more raffle tickets did Carlie sell than
Caroline?
Example Solution:
32 tickets
Carlie
Tickets:
Caroline
Tickets:
?
Solution:
4 blocks = 32 tickets
1 block =8 tickets
3 blocks = 8x3=? So the answer is 24. Carlie sold
24 more tickets than Caroline.
When finished, groups should trade cards and play the game to make sure that the game
works correctly. Games can be laminated and used for future classes.
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What’s the teacher doing?
What are the students doing?
Facilitating the creation of the memory games.
Working cooperatively to correctly create a
memory game with multistep word problems.
Assisting students when they are stuck or
having questions about problems.
Phase Five Evaluate
Day 14 Activity: Give Performance Assessment
Analyze the problem situation(s) described below. Organize and record your work for each of the
following tasks. Using precise mathematical language, justify and explain each solution process.
1) Callie is making cupcakes for the school bake sale. She packs them into boxes and finds that two
boxes will hold 12 cupcakes, three boxes will hold 18 cupcakes, eight boxes will hold 48 cupcakes,
and five boxes will hold 30 cupcakes.
a) Represent the situation using an input-output table and a numerical expression that could be used
to find the number of cupcakes that will fill b boxes.
b) Describe the relationship between the input-output table and the expression you wrote.
c) Use the rule represented by the expression from the problem situation to find b, the number of
boxes needed to package 72 cupcakes.
d) Use the rule represented by the expression from the problem situation to generate the first 10
terms in a sequence that represents the relationship between the input and output values from your
input-output table.
2) Callie decorates her cupcakes using miniature chocolate chips. She notices that for every 6
cupcakes she decorates she uses 60 miniature chocolate chips. Her mom bought several packages
of miniature chocolate chips for her project. So Callie decides that every time she finishes
decorating 6 cupcakes, she will treat herself to a dozen miniature chocolate chips.
a) Use strip diagrams and equations to represent the total number of miniature chocolate chips
Callie will have used (including the ones she has eaten) after she has decorated 78 cupcakes.
b) One serving of miniature chocolate chips is 10 chips. If one package of miniature chocolate
chips contains 48 servings, determine if Callie is now using her first, second, or third bag of
miniature chocolate chips for the 78 cupcakes.
c) Determine how many more cupcakes Callie can decorate with the miniature chocolate chips
remaining in the bag she is using after decorating 78 cupcakes.
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What’s the teacher doing?
What are the students doing?
Monitor student performance on PA.
Complete performance assessment.
Use data from assessment for information
on reteaching and enrichment.
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