MONTVILLE TOWNSHIP PUBLIC SCHOOLS
OFFICE OF CURRICULUM & INSTRUCTION
MATH
Grades 6-8
ABSTRACT
In Grades 6-8, the Life Skills Math program focuses on functional skills for Special Education Students: The Life Skills Math
curriculum is designed to foster growth of independent living skills for middle school students. Emphasis is placed upon selfawareness, health and self-care, social interaction, problem solving, household and money management, career awareness,
and daily living skills. Content is modified to address specific student needs based upon goals set forth in the Individual
Education Plan. Opportunities to acquire independent living skills, positive self-esteem and greater self-sufficiency are taught
at an appropriate pace based upon ability in order for students to experience success. In this content area all units will be
addressed throughout the year considering that these skills overlap and need to be revisited in order to reinforce the skill and
ensure retention. Learning life skills are best done "by doing"; "We learn by doing."
BOE approved 10/20/2015
MONTVILLE TOWNSHIP PUBLIC SCHOOLS
Unit of Study:
Description of Unit E:
NJ CCCS and/or
CCSS:
Life Skills Math (relationships, computation, and estimation)
Unit A
Skills are not expected to be mastered in a set time frame and are introduced, reinforced, and revisited throughout the school
year. Math is integrated into all the content areas.
Life skills are essential to job functioning and daily living. The Life Skills Operational Skills Unit is designed to foster
growth of daily independent living skills. This Unit will cover the basic operational skills necessary to perform higher level
independent and vocational skills. The unit will begin with basic math skills and operations (estimation, adding, subtraction,
multiplication, division in various formats through multiple modalities)
The content is modified to address specific student needs at their own pace based upon goals set forth in the IEP.
CCSS K.OAA.1, K.OAA.2, K.OAA.5, 1.OAA.1, 1.OAA.2, 1.OAB.3, 1.OAB.4, 1.OAC.6, 2.OAA.1, 2.OAB.2, 3.OAA.1,
3.OAA.2, 3.OAA.3, 3.OAC.7, 3.AD.8
(include technology and 21st
century standards)
Enduring
Understandings:
1. Estimation is a way to get a proper answer
2. Computation involves taking apart and combining numbers using a variety of approaches
3. Proficiency with basic facts aids estimation and computation of larger and smaller numbers
Essential (Guiding)
Questions:
• How will acquisition of operational skills be essential to job functioning and daily living skills
• What kinds of experiences help develop operational skills?
• How important are estimations in real life situations?
• What is the relationship between solving problems and computation?
• Form concrete sets to add and subtract, multiply and divide
• Recognize +, -, X, ÷
• Add, subtract, multiply, and divide basic facts
• Add subtract multiple digit numbers without renaming
• Use calculator to solve addition, subtraction, multiplication, and division problems
• Add and subtract multiple digit numbers with renaming
• Solve one step word problems using addition and subtraction skills
• Solve multi step word problems using addition and subtraction skills
• Student feedback in response to the teacher questioning
• Class discussion/oral participation
• Simulations and role play
• Worksheet completion
• Practical application
Hands on (manipulatives)
Multi-media presentations
Interactive White Board
Skills:
Assessments:
Resources:
BOE approved 10/20/2015
MONTVILLE TOWNSHIP PUBLIC SCHOOLS
Interdisciplinary
Connections: (e.g.
writing, literacy, math, science,
history, 21st century life and
careers, technology)
BOE approved 10/20/2015
Educational Excursions
Games (bingo, jeopardy, card games, board games.)
Hands on activities (cooking, shopping, estimating, manipulatives etc.)
Math Applications:
• Mee Genius
• Math Bingo
• Jungle Time
• Flash to Pass
• Math Operation
Websites:
• www.ixl.com/math
• www.math-drills.com
• www.mathstory.com
Books:
• Annos Mysterious Multiplying Jar, by: Masaichrio and Mitsumasa Anno
• How Much is a Million, by: David M. Schwartz
• Even Steven and Odd Todd, by: Kathryn Cristoldi
• The Baseball Counting Book
Reading: read number stories, word problems, recipes,
Writing: number stories, numbers, word problems
Science: cooking, shopping,
Technology: computer games, calculators
MONTVILLE TOWNSHIP PUBLIC SCHOOLS
Lesson 1:
Description of Skills
for this lesson based
on students levels
NJ CCCS and/or
CCSS:
Representing Addition and Subtraction
Students will represent addition and subtraction with objects and actions.
CCSS K.OAA.1, K.OAA.2, K.OAA.5
(include technology and 21st
century standards)
Pre-Assessment &
Post-Assessment
Learning Activities:
BOE approved 10/20/2015
The day before the lesson, write 7 + 6 and 13 - 6 on the blackboard. Give each student a post-it note, and see if they know how to
solve the problems. If a large number of students successfully answer these problems, you can begin this lesson midway through the
procedures described below.
Once you know where each student is at during the pre-assessment, make a chart for each student and measure progress to
determine if they master the skills using student worksheets reflecting specific skill level (be sure to list accommodations
used…calculator, independently, with prompting, using manipulatives, etc.)
Materials:
• Pencils
• Paper
• Manipulatives
• Smart Board
• Work mat
Procedure:
1. Write 9 + 9 on the blackboard. Ask students if they know what this means. Using manipulatives ask them to show one group of
nine and another group of nine. Show students that this means nine and nine together equals 18 (manipulatives.) (Bring your
groups together to reinforce the concept.)
2. Draw two flowers on the board. Write down a plus sign, then three more flowers. Say this aloud, “Two flowers together with
three flowers make what?” They should be able to count and make five flowers. Then, write down 2+3=5 to show how to
record equations like this. Use real items where possible
3. Give students their bags of manipulatives and a piece of paper. Together, do the following problems and say them like this.
Have the students represent the problem using manipulatives and then write the equation.
(connecting cubes of different colors work well)
• 4 pieces together with 1 piece is 5 (write 4 + 1 = 5)
• 6 pieces together with 2 pieces is 8 (write 6 + 2 = 8)
• 3 pieces together with 6 pieces is 9 (write 3 + 6 = 9)
4. Continue with problems such as these until the students are feeling comfortable with addition.
5. On the smart board show 5 images. Ask students, “How many do I have?” Then cross out two of them. “Now how many do I
have?” Discuss that if you start with five pieces, then take away two, your will have three left over. Repeat this several times to
MONTVILLE TOWNSHIP PUBLIC SCHOOLS
Differentiated
Instructional Support:
Vocabulary
BOE approved 10/20/2015
reinforce skill.
6. Have the students use manipulatives to show three, then have them take away two, and tell how many are leftover. Have
students record there subtraction problem on paper.
7. Together, do the following problems and say them like this (adjust as you see fit)
• 6 pieces, taking away 2 pieces, is 4 left over (write 6 - 2 = 4)
• 8 pieces, taking away 1 piece, is 7 left over (write 7 - 1 = 4)
• 3 pieces, taking away 2 pieces, is 1 left over (write 3 - 2 = 1)
8. After students have had some practice with this, it’s time to have them create their own simple problems. Divide them into
groups of 2, and tell them that they can make their own 2 addition and 2 subtraction problems for the class. They can use their
fingers (5 + 5 = 10), their books, their pencils, their crayons, or even each other!
9. As students show their problems to the class, have the seated students record their problems on a piece of paper. Students can
role play different scenarios as well using addition and subtraction problems
Differentiation: Students may be assisted through adjustments to assignments deemed necessary as per Individual Education Plan.
Some students may do some activities at the beginning level and others at the developing level….etc. Worksheets and presentation
materials maybe modified to their level (some may need to start with leaning to read time on a digital clock, others analog, some
may tell time already and need to work on time-management etc…) Teachers may utilize tiered activities and/or learning stations.
Teachers will present a single concept through a variety of learning modes and may access students in this manner.
Beginning (B): With assistance/ prompting, students will be able to show addition and subtraction through manipulatives/ pictures
using math mats to show their work.
Developing (D): Students will independently represent the problem by writing an addition or subtraction sentence.
Advancing (A): Independently students will create addition or subtraction problems.
Addition, subtraction, together, apart, take away, left over, total
MONTVILLE TOWNSHIP PUBLIC SCHOOLS
Lesson 2:
Description of Skills
for this lesson based
on students levels
NJ CCCS and/or
CCSS:
Fact Families
•
•
Students will identify addition and subtraction fact families to 10.
Students need to have a basic understanding of addition and subtraction
1.OAB.3, 1.OAA.1
(include technology and 21st
century standards)
Pre-Assessment &
Post-Assessment
Learning Activities:
• Pretest
• Checklists
• Post-tests
Materials:
• Computer with Internet Access
• Smartboard
• Unifix Cubes
• Marker
• Fact Family Work Mat
• Tree Trunk Template
• Apples Template
• Baskets Template
• Construction Paper
• Scissors
• Glue.
•
Introduce the lesson by telling students they are going to learn addition and subtraction fact families. Then use the SmartBoard
or chalkboard to show how addition facts and subtraction facts are related. Demonstrate how 3 numbers can make up two
addition and two subtraction number sentences.
Example:
• 4+2=6
• 2+4= 6
• 6-2= 4
• 6-4 =2
• After, modeling (using visuals and real items) the number sentences on the board then draw lines and have students come up to
the board and match and connect the three numbers in all four problems.
Example:
• ___ + 2 = 6
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MONTVILLE TOWNSHIP PUBLIC SCHOOLS
• ___ + 4 = 6
• 6 - ___ = 4
• ___ - 4 = 2
Procedure:
1. Give each student seven cubes and a fact family work mat.
2. Write 3+4=7 on the smart board. Ask students to place three linked cubes in the first circle and four linked cubes in the second
circle on their mats.
3. Ask, “What does 3+4 equal?”
4. Invite students to share their answers. Then write =7 on the board to complete the equation.
5. Explain that you are now going to switch the first two numbers in the equation. Under the first equation, write 4+3. Ask the
students to build the new equations on their matts by placing 4 cubes in the first circle and 3 cubes in the second circle. Invite
students to share their answers and write =7 on the board.
6. Discuss the fact that both equations have the same answer.
7. Write the 7-4 on the board. Ask students to put seven linked cubes in the first circle. Then ask them to removes four cubes.
How many are left? Add =3 to the equation board.
Independent Practice:
Give each student a tree trunk template and a 12" x 18" sheet of light blue construction paper. Instruct students to cut out the trunk
and glue it to the light blue paper.
1. Invite each student to choose a basket with a fact family printed on it. Have students glue their baskets to the bottoms of the tree
trunks.
2. Give each student a set of four apples. Prompt them to write the four equations in their fact family on the apples. Then have
students glue the apples to their trees.
3. Display the trees on a bulletin board titled “Fall Fact Family Trees!”
Guided Practice:
Introduce fact families with dominos. Dominos have 2 parts, and if we combine those 2 parts we would have the total. Draw a
domino on your white board, and erase the middle line to show the combination. Have students give you addition facts.
For lower students
• Show the domino horizontally so the sentence is 5+3=8. Then actually flip the domino so they can see that 3+5=8, thing has
changed.
• Guided practice together and then have then practice writing facts or give them facts to draw on their domino
Independent Practice
• Explain that three numbers they got from the domino are a family. The biggest number is the “boss”
• Explain that the boss has the ability to get rid of a family member.
• So the 5/3 domino, the boss can decide to get rid of the 5 this leaves the 3.
• Write the subtraction problem. 8-5=3. Then explain that the boss can change his mind and decide that he wants to get rid of the
3. Cover the 3. Then write 8-3=5. Do a couple of guided practices and then give them dominoes and have them go write fact
families for those dominos.
• Give them a worksheet that has space for them to write the family members and then the 2 addition and subtraction problems.
BOE approved 10/20/2015
MONTVILLE TOWNSHIP PUBLIC SCHOOLS
Example:
Family Members: ____, _____, _____
_______+______=_____
_______+_______=_____
_______-_______=______
_______-________=______
Students may be assisted through adjustments to assignments.
Differentiated
Instructional Support:
BOE approved 10/20/2015
• Teacher created tiered activities or work stations that focus in on skills
More Independent practice
• Have your students create fact family triangles game.
• They cover one number and do not let their partner see the number they have covered.
• Then they have to say the fact to their partner.
• Their shares their answer. They check their answer by uncovering the number . If they need harder they can cover the number
that is not the sum or difference but instead a missing number in the problem (ex: 5 + ___ = 8...the 3 would be covered).
For students that need a little more support
Once they have completed their dominos they can play memory fame. Where they are matching turn around facts.. Example a
match would be 3+5=8 and 5+3=8.
Differentiation: Students may be assisted through adjustments to assignments deemed necessary as per Individual Education Plan.
Some students may do some activities at the beginning level and others at the developing level, etc. Worksheets and presentation
materials maybe modified to their level (some may need to start with leaning to read time on a digital clock, others analog, some
may tell time already and need to work on time-management etc.) Teachers may utilize tiered activities and/or learning stations.
Teachers will present a single concept through a variety of learning modes and may access students in this manner
Beginning (B): Solve fact families given the addition and subtraction sentences
Example:
• 4+6=____
• 6+4=____
• 10-4=____
• 10-6=_____
Developing (D): Given the first addition and subtraction fact families. Create the second fact family.
Example:
• 4+6=____
• __+___=_____
• 10-4=____
• __-___=_____
Advancing (A): Given the fact family numbers create a fact family.
MONTVILLE TOWNSHIP PUBLIC SCHOOLS
Vocabulary
BOE approved 10/20/2015
Example:
• 4,6,10 Make a fact family
Fact families, equal
MONTVILLE TOWNSHIP PUBLIC SCHOOLS
Lesson 3
Description of Skills
for this lesson based
on students levels
NJ CCCS and/or
CCSS:
Multiplication
In this lesson students will represent combining equal groups with related addition and multiplication equations. Students learn how
to play the multiplication game Circle and Stars, focusing on drawing and combining equal groups of stars.
CCS 3.OA.A.1, 3.OA.A.3
(include technology and 21st
century standards)
Pre-Assessment &
Post-Assessment
Learning Activities:
BOE approved 10/20/2015
Use pretests, surveys, and checklists, to determine what the student already knows and keep a record.
Materials:
• Smartboard
• White boards (one for each student)
• Markers (one for each student)
• Dice (one for each student)
• Paper (enough for class plus extra)
• Worksheet/Assessment (one for each child)
Procedure:
1. Discuss as a group “what is multiplication?” and record the students’ responses on chart paper.
2. Have volunteer roll a die. (Example child rolls a five)
3. Teacher on the board draw a circle.
4. Have the student draw that many stars in that circle. (Example five stars)
5. Have a second volunteer roll a die. (example child rolls a 3)Draw that many stars in each circle. (Example 3 stars in 5 circles)
6. Write and addition sentence. (Example 3+3+3+3+3=15)
7. Say to children, “doesn’t that take a long time to add three five times? There is an easier way to write this.”
Write a multiplication sentence. (example 3x5=15)
8. Discuss how it gives you the same answer.
9. Repeat as needed as a group.
Group work:
Pass out dice, paper, and markers to each pair and give them directions:
• Each child gets one die.
• First person roll your die and draw that many circles
• Second person roll your dire and draw that many stars inside your partner’s circles
• As a pair write an addition sentence and multiplication sentence
Independent Work:
Worksheets with circles and stars already made up and have students write an addition and multiplication sentence. Did children
write the correct addition and multiplication sentences?
MONTVILLE TOWNSHIP PUBLIC SCHOOLS
Differentiation: Students may be assisted through adjustments to assignments deemed necessary as per Individual Education Plan.
Differentiated
Some
students may do some activities at the beginning level and others at the developing level, etc. Worksheets and presentation
Instructional Support:
Vocabulary
BOE approved 10/20/2015
materials maybe modified to their level (some may need to start with leaning to read time on a digital clock, others analog, some
may tell time already and need to work on time-management etc.) Teachers may utilize tiered activities and/or learning stations.
Teachers will present a single concept through a variety of learning modes and may access students in this manner
Beginning (B): With assistance and prompting the students will use manipulatives to show repeated addition as multiplication.
Using the manipulatives the students name how many groups X how many in each group in order to set up a multiplication
sentence.
Developing (D): Students will independently identify the correct multiplication sentence for each repeated addition sentence.
Given a multiplication sentence the student will set up manipulatives to show multiplication (3X5).
Advancing (A): Identify when to use multiplication vs. addition and solve using a calculator. The students will begin applying their
knowledge of multiplication to cooking, job skills, etc. though teacher- created hands- on activities.
Multiplication, equal, times
MONTVILLE TOWNSHIP PUBLIC SCHOOLS
Lesson 4:
Description of Skills
for this lesson based
on students levels
NJ CCCS and/or
CCSS:
Multiplication Patterns
This lesson enables students to begin the process of mastering multiplication facts. Students will learn property theories as
strategies for recalling those facts. Students will develop computational fluency by exploring patterns in multiplication for products
involving one- digit factors. Students will understand and use the zero property multiplication and the property of one as a factor in
multiplication
CCS 3.OA.A.1, 3.OA.A.3
(include technology and 21st
century standards)
Pre-Assessment &
Post-Assessment
Learning Activities:
BOE approved 10/20/2015
Use pre-tests, surveys, and checklists, to determine what the student already knows and keep record.
Materials:
• Crayons
• Markers
• Hundred chart
• Doubles worksheet
• Independent practice worksheet
• Multiplication table
Procedure:
1. Display hundreds chart on overhead transparency. Hand out copies of hundred chart.
2. Have students count by 2s, shading multiples of 2 yellow on their hundred chart. Ask them to examine the numbers carefully.
Ask:
• What patterns do they notice? (The multiples of 2 are even and always end in 0, 2, 4, 6 or 8.)
3. Have students count by 5s, circling the multiples of 5 with a blue marker on their number charts. Ask:
• What patterns do they notice? (The multiples of 5 end in 5 or 0).
4. Model your thinking:
• When I look at the multiples of both 2 and 5, I see that they all end in zero. It’s like counting by 10s. I notice that 2 x 5 is
10.
5. Have the students count by 9s on the number chart. Write out the multiplication sentences and answers on the chalkboard (9 x 1
= 9, 9 x 2 = 18, and so on) and ask students to find a pattern and discuss what they find.
• (The sum of the product’s digits is 9. The tens digit is 1 less than the other factor. Show them how to use their finger to
figure out product of 9 up to ten.
6. Have students look at their charts and find:
• the multiples that 2 and 9 have in common (18, 36, 54, 72, 90, and so on).
• the multiples that 2 and 5 have in common (10, 20, 30, 40, 50, and so on).
• the multiples that 5 and 9 have in common (45, 90).
MONTVILLE TOWNSHIP PUBLIC SCHOOLS
Differentiated
Instructional Support:
7. Ask students what would happen if they shaded in all the multiples of 1 on their charts. (They should soon realize that they’d be
shading in everything.) Articulate the property of one:
• The product of a number and 1 is that same number.
• Every number is a multiple of 1 and itself.
8. To illustrate, ask several easy questions to the class at large. What is 8 x 1? What is 9 x 1? Get increasingly harder: What is 52 x
1? What is 1 million x 1?)
9. Ask students to think about multiplying with zero in terms of repeated addition. What is 0 + 0? What is 3 x 0? What is 52 x
0? What is 1 million x 0? Help students to determine the zero property for multiplication:
• the product of a number and 0 is 0.
10. Hand out one or more of the Independent Practice Worksheet for students to practice finding the product.
Students may be assisted through adjustments to assignments.
Teacher created tiered activities or work stations that focus in on skills
Beginning (B): Memorize facts 1,2, 5, 10
Developing (D): Memorize facts 3,4,7, 8, 9
Advancing (A): All facts are memorized by using previously taught strategies and can be applied.
Differentiation: Students may be assisted through adjustments to assignments deemed necessary as per Individual Education Plan.
Some students may do some activities at the beginning level and others at the developing level, etc. Worksheets and presentation
materials maybe modified to their level (some may need to start with leaning to read time on a digital clock, others analog, some
may tell time already and need to work on time-management etc.) Teachers may utilize tiered activities and/or learning stations.
Teachers will present a single concept through a variety of learning modes and may access students in this manner.
Teaching Visual Learners
• Show students a group of five buttons and ask them how many buttons they would have in only one group of buttons. Then
ask them how many candies there would be in two groups of five.
• Color coding is beneficial to many visual learners. Use different colors to represent each number when demonstrating the
multiplication patterns presented above. For example, color the number 1 red, the number 10 blue, 2 green, 4 purple, 5
yellow and 9 orange. Follow through by using these colors on flash cards to reinforce the same concepts
Teaching Auditory Learners
• Use partners or small groups for these students. They'll learn by repeating multiplication facts aloud as they learn them. It
may also help to read instructions out loud and whisper the steps they're following as they complete problems. Auditory
learners benefit from writing a sequence of steps in sentence form and reading them aloud as a means of learning them.
• Reading can be considered an auditory exercise because the same portions of the brain that process language are involved.
Multiplying Menace
The Revenge of Rumpelstiltskin by Pam Calvert
The Best of Times
Math Strategies That Multiply by Greg Tang
BOE approved 10/20/2015
MONTVILLE TOWNSHIP PUBLIC SCHOOLS
Vocabulary
BOE approved 10/20/2015
• Website for more book resources: http://www.the-best-childrens-books.org/teaching-multiplication.html
Teaching Kinesthetic Learners
Teach students to take notes. Allow children to perform demonstrations. Have students use manipulatives, computer learning and
games. Sometimes kinesthetic learners process information best when they can walk back and forth as they learn facts.
Math games: Utilize the i-pad for multiplication apps:
• Math Tutor 2 Lite
• MathTappers: Multiples - a math game to help children learn basic facts for multiplication and division
• Ace Multiply Matrix HD
• Math made real easy - Multiplication Division
• Portable Math Multiplication Free
• Kiddie animated multiplication and division
• Multiplication Genius Lite
• Chalkboard Multiplication
• Multiplication Tables
http://www.multiplication.com/games/all-games
http://www.fun4thebrain.com/mult.html
http://www.learninggamesforkids.com/math_multiplication_games.html
Multiple, factor, product, double
MONTVILLE TOWNSHIP PUBLIC SCHOOLS
Lesson 5:
Description of Skills
for this lesson based
on students levels
NJ CCCS and/or
CCSS:
Division (As repeated subtraction)
•
•
Basic understanding of subtraction.
Division by Repeated Subtraction is a "different" way to divide that reduces introduction of division errors by
incomplete/incorrect knowledge of basic multiplication facts
3.OA.C.7, 3.OA.B.6
(include technology and 21st
century standards)
Pre-Assessment &
Post-Assessment
Learning Activities:
Differentiated
Instructional Support:
BOE approved 10/20/2015
Use pretests, surveys, and checklists, to determine what the student already knows and keep a record.
Materials:
• Manipulative
• Smartboard
Procedure:
• Discuss with students what division means to them.
• Divide students’ into pairs and give them 6 (M&M’s, skittles, etc) and ask them to share the manipulative between the two of
the equally.
• Discuss with the students that they just divide 6 into 2 equal groups and got three.
• Using smart board technology reinforce the skill with videos (brainpop)
Guided Practice: Play Division Bang Game
1. Decide who will go first.
2. The first person draws a stick from the container.
3. If the stick has a questions or problem, answer it, if you got it right keep it, but if you are wrong put it back.
4. If the stick says, “Bang” you must put all of your sticks back, except for your bang sticks. You lose your turn this time.
5. Pass the container to the person on your right and continue playing the same way.
6. Once all of the sticks are gone or time is call the game is over.
7. The person with the most sticks wins.
Independent Practice:
• Use supplemental worksheets that address skills in this lesson
• Use technology such as website games, or i-pad apps.
Differentiation: Students may be assisted through adjustments to assignments deemed necessary as per Individual Education Plan.
Some students may do some activities at the beginning level and others at the developing level, etc. Worksheets and presentation
materials maybe modified to their level (some may need to start with leaning to read time on a digital clock, others analog, some
may tell time already and need to work on time-management etc.) Teachers may utilize tiered activities and/or learning stations.
Teachers will present a single concept through a variety of learning modes and may access students in this manner
Beginning (B): With assistance/prompting the student will be able to perform basic division using manipulatives/pictures.
MONTVILLE TOWNSHIP PUBLIC SCHOOLS
Vocabulary
BOE approved 10/20/2015
Developing (D): Students will begin to recognize that division is the reverse operation of multiplication. Independently that will
identify when to perform basic division operations by setting up equation and solving with a calculator.
Advancing (A): Students will solve long division problems. Students will identify when a division problem has a remainder.
Divide and Counter: Divide students into small groups and give each group a set of counters. You may want to divide the small
groups into twos, threes, fours, or fives. Then have each group divide the counters equally among them. Be sure each group comes
up with a division sentence, solves the problem, and checks over their work for accuracy. Then groups can swap counters and repeat
the activity. Make sure that every group gets a set that can be divided equally among the members.
Equal, groups, share, dividend, divisor, quotient, operation, quotient sign
MONTVILLE TOWNSHIP PUBLIC SCHOOLS
Lesson 6:
Description of Skills for
this lesson based on
students levels
NJ CCCS and/or
CCSS:
Using Key Words
•
•
•
Identifying key words help students solve mathematical word problems.
Basic understanding of four operations (-,+,x,/)
In this lesson, students will take turns acting as “math coaches” who will assist other students in solving real world word
problems by identifying key words that usually indicate specific mathematical operations.
3.OA.D.8
(include technology and 21st
century standards)
Pre-Assessment &
Post-Assessment
Learning Activities:
BOE approved 10/20/2015
Use pretests, surveys, and checklists, to determine what the student already knows and keep a record.
Students will:
• brainstorm key words that usually indicate specific mathematical operations
• create flash cards to review the relationships between key words and operations
• coach one another in collectively solving mathematical word problems
• synthesize their knowledge of word problems by writing some of their own
Materials:
• Paper
• Smartboard
• Index cards (four per student)
• Solving word problems translation worksheet
Warm-up:
Solving an authentic word problem:
• Open the class by having the students solve an authentic word problem in pairs: "There are _________ (fill in the number)
students in this classroom. I need to distribute four index cards per student. How many index cards do I need?"
• Circulate around the room as students work, ensuring that students are multiplying the number of students in the classroom by
four in order to determine how many index cards are needed.
• Have a student volunteer come to the front board to write the mathematical equation that he or she used to determine the answer
to the problem. Then, above that equation, write the original word problem and ask students which specific word in the problem
let them know that they needed to multiply the two numbers in order to determine the number of index cards needed for the
class
Instruction:
Brainstorming key words that indicate mathematical equations:
• Explain to the class that whether they notice it or not, they are constantly interpreting key words in word problems in order to
determine which mathematical operations to use in solving the problems.
• Draw a four-quadrant table on the board and write a different mathematical operation title in each quadrant: addition,
subtraction, multiplication, and division. Write the word "per" under the title "multiplication" and have students brainstorm
MONTVILLE TOWNSHIP PUBLIC SCHOOLS
additional key words that belong under each of the four mathematical operation categories.
• If students get stuck in this brainstorming process, you could suggest different key words (within the context of simple
word problems) and have students direct you where to write the words in the table. At the end of this brainstorming session,
make sure you have at least the following words and phrases listed in your table:
Mathematical Operations and Key Words
Subtraction
Addition
add(ed) to
decreased by
all together
difference
both
fewer than
combined
how many more
in all
left
increase by
less
more than
less than
perimeter
minus
plus
remaining
sum
take away
total
Multiplication
Division
a
divided
area
half
multiplied by
how many each
of
out of
per
percent
product of
quarter
rate
quotient of
times
percent
triple
twice
Creating key word flash cards:
• Have a student count out the number of index cards that the class determined in the warm up problem and distribute four cards
to each student.
• Direct students to create four flash cards — one for each of the four mathematical operations. On the blank side of each card,
they should boldly write an operation and its symbol (i.e., +, -, x, where is the division symbol?), and on the reverse, lined sign
they should list the key words associated with that operation. (Students should base these flash cards on the table you created on
the front board.)
Playing the role of "math coach":
• Organize the class into small groups of no more than three to four students in each group, and explain that they will be using
BOE approved 10/20/2015
MONTVILLE TOWNSHIP PUBLIC SCHOOLS
Differentiated
Instructional Support:
Vocabulary
BOE approved 10/20/2015
their new flash cards as visual aids in math coaching!
• Distribute a "Solving Real World Word Problems through Key Words" sheet to a student in each group and explain that the
student with the sheet will act as the reader and recorder during the first round. The reader and recorder's job is to read a word
problem aloud and to allow his fellow "math coaches" to advise him on which mathematical operation to follow in solving the
problem.
• Advise the math coaches in the class to listen to the word problem closely, to advise the reader and recorder to underline any
key words in the problem that they detect, and to follow the flash card mathematical operation that they decide to "flash."
• Direct groups to complete the sheet, alternating the role of reader and recorder so that each student has at least one or two turns
in that role.
Differentiation: Students may be assisted through adjustments to assignments deemed necessary as per Individual Education Plan.
Some students may do some activities at the beginning level and others at the developing level, etc. Worksheets and presentation
materials maybe modified to their level (some may need to start with leaning to read time on a digital clock, others analog, some
may tell time already and need to work on time-management etc.) Teachers may utilize tiered activities and/or learning stations.
Teachers will present a single concept through a variety of learning modes and may access students in this manner.
Students may be assisted through adjustments to assignments.
Teacher created tiered activities or work stations that focus in on skills
Beginning (B): With assistance/ prompting students will use cue card identify basic key words in a word problem to solve for
addition or subtraction.
Developing (D): Students will independently identify what operation they need to use in order to solve the problem.
Advancing (A): Students will solve multi step math problems by identifying what operations they will need to use in order to solve
the problem. Students will understand and apply their knowledge to solve functional problems.
See words above in chart
MONTVILLE TOWNSHIP PUBLIC SCHOOLS
Lesson 7:
Description of Skills
for this lesson based
on students levels
NJ CCCS and/or
CCSS:
Rounding
Students will explore the use of rounding to the nearest 100th place, by rounding to the nearest dollar amount when using the
grocery store items and given a set amount of money.
3.NBT.A.1
(include technology and 21st
century standards)
Pre-Assessment &
Post-Assessment
Use pretests, surveys, and checklists, to determine what the student already knows and keep a record.
Learning Activities:
Materials:
• Several grocery store items that are labeled with a dollar amount
• Fake money
Procedure:
• Discuss with students what rounding is, and when they would use it. Get the students thinking about rounding by having them
give examples of when they think they could use it in their day to day life.
• Hold up several different price tags and have students explain how they would round to a particular price and why.
• Discuss when they would round up to the nearest dollar, and when they would round down to the nearest dollar amount using
example price tags.
A table of grocery store items will be displayed. Each item will be priced. The students will be divided into small groups; each
group will be given a specific dollar amount with which they will purchase the items. Each group of student will work together
using rounding to ensure that they have enough money to cover the cost of their selected items.
Independence:
Students will be assessed informally as they explain to the rest of the class what rounding methods they used in order to stay within
the set dollar amount.
After each group explains their rounding method, discuss the differences in the techniques that each group used.
Whole Class Instruction and Practice:
Explain to students that when you round, you essentially find a number that has fewer non-zero digits. Start by discussing how to
round to the nearest ten. Draw a large number line on the board with the numbers 10, 20, and 30 circled and larger than the rest.
Then write a number on the board, such as 18. Ask students which two "big" numbers 18 is between, and they should answer 10 and
20. Then have them identify which of the two "big" numbers 18 is closer to. It would be useful to have a number line available to
help the students decide. (They should answer "20.") Discuss with them the fact that they have just rounded up.
Group/Individual Practice:
Give each student ten small objects as manipulatives, such as beans. Point to the number 18 again, and tell them "Let's see how
many numbers we would have to add in order to get to twenty." Then count out two beans and say out loud "Nineteen...twenty - I
needed two beans. Now let's see how many numbers we would have to subtract in order to get to ten. (Count aloud) seventeen,
sixteen, fifteen, fourteen, thirteen, twelve, eleven, and ten. I needed eight beans to get to ten." Inform students that they should
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MONTVILLE TOWNSHIP PUBLIC SCHOOLS
Differentiated
Instructional Support:
round to the number that needed the fewest beans - in this case, twenty. Let them use the number line together with the beans to
help them round several more numbers individually or in small groups. This review activity is particularly helpful for kinesthetic
learners and other learners who benefit greatly from manipulatives.
Differentiation: Students may be assisted through adjustments to assignments deemed necessary as per Individual Education Plan.
Some students may do some activities at the beginning level and others at the developing level, etc. Worksheets and presentation
materials maybe modified to their level (some may need to start with leaning to read time on a digital clock, others analog, some
may tell time already and need to work on time-management etc.) Teachers may utilize tiered activities and/or learning stations.
Teachers will present a single concept through a variety of learning modes and may access students in this manner
Students may be assisted through adjustments to assignments.
Teacher created tiered activities or work stations that focus in on skills
Beginning (B): With assistance and prompting students will identify when they need to round to the next whole dollar. Students
will recognize if the amount has change and then round it to the next dollar.
Developing (D): ): In pairs, students will be given a specific dollar amount with which they will purchase items. Each group of
students will work together using the next dollar strategy to ensure that they have enough money to cover the cost of their selected
items.
Advancing (A): Students will understand and apply their knowledge of next dollar strategy to shopping/ budgeting. Independently
the students will use their next dollar strategy to ensure they have enough money to make a purchase given a specific amount of
money
BOE approved 10/20/2015