Roselle
Math Curriculum
Unit Title: 2 Grade: 7
Essential Question(s) / Enduring Understanding(s)How can a procedure lead you to an accurate solution?
How do mathematical properties make calculations easier? / Rational numbers can be expressed in multiple ways.
Mathematical properties reveal multiple appropriate methods to compute.
Every numerical operation has an inverse.
Common Core Standards, 2010
NS1b. Interpret sums of rational numbers by describing real-world contexts;
NS1c. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
NS 1d. Apply properties of operations as strategies to add and subtract rational numbers.
NS 2a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.
NS 2c. Apply properties of operations as strategies to multiply and divide rational numbers.
NS 2d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
NS 3. Solve real-world and mathematical problems involving the four operations with rational numbers.11 Computations with rational numbers extend the rules for manipulating fractions to complex fractions.
Learning Expectations
TLWBAT… / Activities/Resources / Student Strategies / Formative Assessments / Technology Infusion/Resources
Define rational number as any integer, any fraction, and any decimal that terminates or repeats / Use laptops to have students explore the definition of rational numbers.Then have them create asmall poster that contains the formal definition, a definition in their own words, a picture or illustration, and examples of rational numbers.
Have students complete the Rational Numbers Lesson on Study Island scoring at least 70% correct out of 10 questions. / Small group instruction and guided math. Students will do math centers while the teacher takes a small group and attacks their issues.
Individualized instruction is for students that need intensive instruction on all issues.
Peer tutoring a stronger student can help the weaker student to understand the material on their level.
Use of manipulatives will help the student who is a visual learner. They will need to see the math in relation to the manipulative.
Computer activities for remediation for students who have trouble with using pencil and paper to understand math concepts.
Choice activitiesgives students a choice of activities through menu choices which becomes a project.
Chunking information is for students who need information presented in pieces like word problems, tests and instruction.
Rephrasing of questions, directions and instructions helps to clarify what is needed from the student.
Working with partner Helps the student to understand the material on their level. / Exit ticket
Do now
Test
Directed paraphrasing
One-sentence summary
Transfer and apply
Homework / Laptops
Interactive White Boards
Convert rational numbers to decimals using long division
The decimal will either terminate or repeat (use the bar over the repeating section of the decimal to denote repeating decimal)
Convert rational number to a decimal by converting to a multiple of 10 whenever possible / Review the process of long division with students. Have students use grid paper to keep numbers lined up by place value. Have students choose fractions out of a hat and complete the long division to convert to a decimal or to convert the fraction to a multiple of ten to change it to a decimal.
Online Activities:
Article:
Practice:
Practice:
Students fill in a chart showing the conversion from fraction to decimal to percent.
Students practice converting fractions by playing a dice game in which the student rolls two dice, makes a fraction with the numbers rolled, then converts the fraction to a decimal using long division. / Small group instruction and guided math. Students will do math centers while the teacher takes a small group and attacks their issues.
Individualized instruction is for students that need intensive instruction on all issues.
Peer tutoring a stronger student can help the weaker student to understand the material on their level.
Use of manipulatives will help the student who is a visual learner. They will need to see the math in relation to the manipulative.
Computer activities for remediation for students who have trouble with using pencil and paper to understand math concepts.
Choice activities gives students a choice of activities through menu choices which becomes a project.
Chunking information is for students who need information presented in pieces like word problems, tests and instruction.
Rephrasing of questions, directions and instructions helps to clarify what is needed from the student.
Working with partner Helps the student to understand the material on their level. / Exit ticket
Journal entry
Do now
Quiz
Oral questioning
Minute paper
Transfer and apply
Cubing Activities
Homework
Stations work / Laptops
Interactive White Board
Qwizdom
Compare and order numbers of all named types. / Give each of five student volunteers a number card containing a positive or negative fraction, decimal, or integer. Have them stand in the front of the classroom and let the class work out what order the students should stand in to arrange the numbers from least to greatest. Repeat this activity multiple times with different volunteers if necessary. During the activity, question students about how they are determining the order of the numbers. Next have volunteers come up to the interactive white board and order numbers on a number line. Have students complete the Comparing Rational Numbers Menu. Students choose three of the following activities (one from each section):
Appetizers:
-Complete the Review for Mastery 2-11 Worksheet.
-Play Flower Power Online.
-Watch the Comparing Rational Numbers video on Teacher Tube and write three things you learned.
Entrees:
-Play Jeopardy online with a classmate. Record each question and answer on a separate sheet of paper.
- Complete Pg. 128 # 25-38 on lined paper.
-Create three story problems that can be solved by comparing rational numbers.
Desserts:
- Create a set of 20 Concentration Cards with fractions and their corresponding decimal Equivalents.
- Create a Fractions are Fun and Decimals are Delicious! Children’s book showing how to convert between fractions and decimals.
- Create a 10-Flap Foldable with decimals on the top flaps and four equivalent fractions under each flap.
- Create a Spin-Wheel that contains 8 pairs of equivalent fractions and decimals.
Online Activities:
Teacher Tube Video:
Flower Power Game:
Jeopardy:
Practice: / Small group instruction and guided math. Students will do math centers while the teacher takes a small group and attacks their issues.
Individualized instruction is for students that need intensive instruction on all issues.
Peer tutoring a stronger student can help the weaker student to understand the material on their level.
Use of manipulatives will help the student who is a visual learner. They will need to see the math in relation to the manipulative.
Computer activities for remediation for students who have trouble with using pencil and paper to understand math concepts.
Choice activities gives students a choice of activities through menu choices which becomes a project.
Chunking information is for students who need information presented in pieces like word problems, tests and instruction.
Rephrasing of questions, directions and instructions helps to clarify what is needed from the student.
Working with partner Helps the student to understand the material on their level. / Online Quiz: Comparing Rational Numbers
Online Quiz Ordering Rational Numbers:
Paper Quiz created by teachers. / Laptops
Manipulatives
Interactive Whiteboard
Qwizdom
Use real-world contexts to interpret sums of rational numbers / Power Point Presentation reviewing how to add fractions, decimals, and integers. Use number chips, fraction bars, and/or grid paper if necessary to help students.
Skill Practice (if necessary):
Adding Fractions:
Adding Decimals:
Adding Integers:
Begin by looking at sample word problems that involve the addition of rational numbers. Have students work in small groups to create 3 word problems that involve the addition of fractions, decimals, or integers. Write the 3 problems on chart paper, leaving room to solve between problems. Have the groups switch papers with another group and solve the first problem, then switch papers again and solve the second problem, switch a 3rd time and solve the third problem. Return the chart paper to the original group and have them check the solutions to each problem.
Students independently complete problems on white boards or on clear communicators and share them with the class. / Small group instruction and guided math. Students will do math centers while the teacher takes a small group and attacks their issues.
Individualized instruction is for students that need intensive instruction on all issues.
Peer tutoring a stronger student can help the weaker student to understand the material on their level.
Use of manipulatives will help the student who is a visual learner. They will need to see the math in relation to the manipulative.
Computer activities for remediation for students who have trouble with using pencil and paper to understand math concepts.
Choice activities gives students a choice of activities through menu choices which becomes a project.
Chunking information is for students who need information presented in pieces like word problems, tests and instruction.
Rephrasing of questions, directions and instructions helps to clarify what is needed from the student.
Working with partner Helps the student to understand the material on their level. / Exit ticket
Do now
Quiz
Test
Oral questioning
Minute paper
Transfer and apply
Cubing Activities
Homework
Stations work / Fraction bars
Clear Communicators/white boards
Grid Paper
Qwizdom
Laptops
The definition of subtraction is adding the opposite (additive inverse)
Subtract decimals
Subtract fractions / PowerPoint Presentation reviewing how to subtract decimals, fractions, and integers. Remind students that when we learned to subtract integers we created rules to add the opposite or keep, change, change. Use colored chips if necessary to demonstrate why adding the opposite is the same as subtracting. Also use fraction bars or grid paper to help students visually represent subtraction problems.
Fraction Subtraction: Have students complete practice problems using fraction bars or grid paper to represent the problem visually. In partners, have students pick cards from a deck of standard playing cards to create two fractions. Students then work together to solve the subtraction problem. To challenge students, have any fractions with red numerators be negative and black numerators be positive.
Online Activities/Tools:
Fraction Bars:
Fifi’s Fraction Game:
Practice:
Students independently complete problems on white boards or on clear communicators and share them with the class. / Small group instruction and guided math. Students will do math centers while the teacher takes a small group and attacks their issues.
Individualized instruction is for students that need intensive instruction on all issues.
Peer tutoring a stronger student can help the weaker student to understand the material on their level.
Use of manipulatives will help the student who is a visual learner. They will need to see the math in relation to the manipulative.
Computer activities for remediation for students who have trouble with using pencil and paper to understand math concepts.
Choice activities gives students a choice of activities through menu choices which becomes a project.
Chunking information is for students who need information presented in pieces like word problems, tests and instruction.
Rephrasing of questions, directions and instructions helps to clarify what is needed from the student.
Working with partner Helps the student to understand the material on their level. / Exit ticket
Journal entry
Do now
Quiz
Test
Oral questioning
Minute paper
Muddiest point
Directed paraphrasing
One-sentence summary
Transfer and apply
Cubing Activities
Homework
Stations work / Fraction bars
Clear Communicators/white boards
Grid Paper
Qwizdom
Laptops
The distance between two rational numbers on the number line is the absolute value of their difference / Students will draw two playing cards (black=positive and red=negative) from a deck to create subtraction problems. They will represent the problems on a number line and see that the absolute value of the difference between the two numbers is also the distance between the two numbers on the number line. / Small group instruction and guided math. Students will do math centers while the teacher takes a small group and attacks their issues.
Individualized instruction is for students that need intensive instruction on all issues.
Peer tutoring a stronger student can help the weaker student to understand the material on their level.
Use of manipulatives will help the student who is a visual learner. They will need to see the math in relation to the manipulative.
Computer activities for remediation for students who have trouble with using pencil and paper to understand math concepts.
Choice activities gives students a choice of activities through menu choices which becomes a project.
Chunking information is for students who need information presented in pieces like word problems, tests and instruction.
Rephrasing of questions, directions and instructions helps to clarify what is needed from the student.
Working with partner Helps the student to understand the material on their level. / Exit ticket
Journal entry
Do now
Quiz
Test
Oral questioning
Minute paper
Muddiest point
Directed paraphrasing
One-sentence summary
Transfer and apply
Cubing Activities
Homework
Stations work
Use equivalent representations of numbers such as fractions, decimals, and percents to facilitate estimation / Review how to convert between decimals, fractions, and percentages. Have students work in pairs to create index cards with the fraction on one side and the equivalent decimal or percentage on the back. Have partners switch cards with another group. The partners should quiz each other using the new cards they received.
Online Activities/Games:
Convert Fractions to Decimals:
Fraction/Decimal Concentration:
Matching Game:
Use fraction bars and rounding rules to have students round numbers to the nearest whole number to facilitate estimation. Give students 2-3 recipes and have them estimate the amount of each ingredient they will need to make all of the recipes. Also, give students a price list and have them estimate the cost of given items so they will know how much money to bring to the grocery store. / Small group instruction and guided math. Students will do math centers while the teacher takes a small group and attacks their issues.
Individualized instruction is for students that need intensive instruction on all issues.
Peer tutoring a stronger student can help the weaker student to understand the material on their level.
Use of manipulatives will help the student who is a visual learner. They will need to see the math in relation to the manipulative.
Computer activities for remediation for students who have trouble with using pencil and paper to understand math concepts.
Choice activities gives students a choice of activities through menu choices which becomes a project.
Chunking information is for students who need information presented in pieces like word problems, tests and instruction.
Rephrasing of questions, directions and instructions helps to clarify what is needed from the student.
Working with partner Helps the student to understand the material on their level. / Exit ticket
Journal entry
Do now
Quiz
Test
Oral questioning
Minute paper
Muddiest point
Directed paraphrasing
One-sentence summary
Transfer and apply
Cubing Activities
Homework
Stations work / Qwizdom
Laptops
Multiplying rational numbers follows the same rules as multiplying whole numbers
Multiplying fractions – change from mixed number to improper fraction prior to multiplying / Have students complete a do now activity that requires them to convert between mixed numbers and improper fractions. Review the process for converting between mixed numbers and improper fractions. Use pictures or fraction bars if necessary. Students may also practice this skill at mathplayground.com. Next have students visit and read the example problems. Next have students work in pairs to create pencasts teaching how to convert between mixed numbers and improper fractions and how to multiply rational numbers. Students can choose to create a power point instead of a pencast. / Small group instruction and guided math. Students will do math centers while the teacher takes a small group and attacks their issues.