Roselle School District
Grade 7 Pre-Algebra Honors Curriculum
Unit 3—Fractions, Decimals and Percents
Summative Assessment TaskEssential Question(s) / Enduring Understanding(s)
How can a procedure lead you to an accurate solution?
How do mathematical properties make calculations easier?
How do operations affect rational numbers?
How can we use rational numbers to solve real world application problems? / 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
NS 1a. Describe situations in which opposite quantities combine to make 0.;
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.
EE 1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
W.7.2. Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content.
8.F.B.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally
NJCCCS 2.5.8.A.1 – Demonstrate mechanically correct form and control when using and combining movement skills in applied settings.
Learning Expectations
TLWBAT… / Activities/Resources / Student Strategies / Formative Assessments / Technology Infusion/
Resources
Compare and order numbers of all named types.
Define rational number as any integer, any fraction, and any decimal that terminates or repeats
Convert rational number to a decimal by converting to a multiple of 10 whenever possible
Transform rational numbers to decimals using long division
Recognize that a decimal will either terminate or repeat (use the bar over the repeating section of the decimal to denote repeating decimal)
Use equivalent representations of numbers such as fractions, decimals, and percents to facilitate estimation / Teacher reviews rational numbers with video clips
Converting Fractions to Decimals and percents
Teacher uses the end of video quiz as a formative assessment for the entire class.
Teacher-created interactive power point used with student responders.
Teacher reviews conversion of rational number to decimal utilizing long division by modeling; models converting rational numbers to decimals by converting to a multiple of 10 whenever possible; converting rational numbers to decimals by converting to a multiple of 10 whenever possible; Student practice as needed using interactive games on teacher class page
Online activity Use Interactive Textbook 5-1 comparing and ordering numbers of all types (optional)
Additional practice, if necessary pgs. 228-229in Algebra Readiness textbook
Student practice as needed (pgs. 231-235)in Algebra Readiness textbook
Students participate in “free throw” activity where they collect data by team and compare their free throw percentages to NBA player free throw percentages by converting fractions, decimals, and percent at first by hand, and then using a calculator
Teacher models conversion of fractions to decimals and percent using calculator / Small group instruction
Individualized instruction
Peer tutoring
Computer activities for remediation
Choice activities
Chunking information
Rephrasing of questions
Working with partner
Video tutorials from textbook
Use of calculators to do conversions / Exit ticket: Comparing & Ordering Rational Numbers
Edgar, Mufasa, and Ben shoveled the walkway of their houses. Edgar shoveled of his walkway, Mufasa shoveled 27%, and Ben shoveled 0.34. Who is the furthest along?
a. Edgar
b. Mufasa
c. Ben
For a science project, Ms. Dube asked each of her students to measure how much gas they used driving to school each week. The students measured the amount of gas in fractions of a tank. Mike used of a tank, Jamie used of a tank, Josh used of a tank, Adam used of a tank, and Kate used of a tank.
Rank the amount of gas used by each student, from least to greatest
Solving Equations with Decimals
You sell your stereo for $383.50 which is 18% more than you paid for it. What was the price you paid for the stereo?
Solving Equations by Adding & Subtracting Fractions
In order to buy wall paper, Telesee needed to find the perimeter (total distance around the outside) of her bedroom. She measured each of the following lengths of her walls
East wall: 10 3/8 ft
North Wall: 12 7/16 ft
West Wall: 10 3/8 ft
South Wall: 8 5/16 ft
What is the perimeter of Telesee’s room?
Solving Equations by Multiplying & Dividing Decimals
Solving Equations by Multiplying & Dividing Fractions
Journal entry
Do now
Compare. Use <, >, and = to complete each statement
(a) 2/7___ 2/8
(b) 2/9___0.24
(c) -1 2/3___ -1 5/6
Quiz: Formative Assessment Comparing & Ordering Rational Numbers
Converting fractions and decimals to percentages while completing an online textbook quiz
Solving Equations with Decimals
Solving Equations with Fractions
webcode: bja-0503 and bja-0504
Test
Oral questioning
Directed paraphrasing
Homework /
webcode: bja-0503 and bja-0504
Use real-world contexts to interpret sums of rational numbers
Recognize that the definition of subtraction is adding the oppositeand relating that to the term additive inverse
Demonstrate prior knowledge of rational numbers by calculating the difference of two decimals
Demonstrate prior knowledge of rational numbers by applying concepts related to subtracting fractions
Apply properties of operations when adding and subtracting rational numbers
Understand the history of Bowling and the fundamentals of the game while being able to compute their own bowling score manually and graph results / Model subtraction as the additive inverse, adding the opposite with manipulatives
Practicesolving equations involving subtracting fractions and decimals (pgs. 237 – 239)in Algebra Readiness textbook
Provide real-world problems utilizing addition and subtraction of rational numbers and application of properties of operations to solve problems with ease
Working in pairs, have students create real-world problems involvingequations with addition and subtraction of fractions and decimals. Have students solve their partners practice problems and have a dialogue with their partner in terms of the rationale involved in setting up the equation and solving the problem.
Students will work independently in “Math Stations” while reviewing concepts related to Fractions, Decimals and Percents
Students will be given a real-world experience as to how fractions, decimals and percents can be applied to real life situations. Students will understand and apply the rules and regulations of the game of bowling. Each student is responsible to write down their scores manually and compare their manual calculation to the electronic score board by applying the concepts related to fractions, decimals and percents and graphing. / Small group instruction
Individualized instruction
Peer tutoring
Computer activities for remediation
Choice activities
Chunking information
Rephrasing of questions
Working with partner
Video tutorials from textbook / Exit ticket
Journal entry
Do now
Quiz
Test
Oral questioning
Homework
Apply concepts related to multiplying rational numbers while utilizing the same rules as multiplying whole numbers
Apply concepts related to multiplying fractions – change from mixed number to improper fraction prior to multiplying
Interpret products of rational numbers by using real-world situations
Interpret quotients of rational numbers by using real-world situations
Apply properties of operations as strategies to multiply and divide rational numbers.
Apply rules of order of operations to simplify expressions / Review multiplication and division of fractions utilizing video clip:
Teacher uses the end of video quiz as a formative assessment for the entire class.
Model multiplication of fractions:
- Straight multiplication
- Simplifying prior to multiplying
- Multiplying mixed numbers converting to improper fraction first
- Using multiplicative inverse to divide fractions
Use real-world problems using multiplication and division of fractions
- Use the site to create “Math Stations” worksheets utilizing fractions
Have students solve their partners practice problems and have a dialogue with their partner in terms of the rationale involved in setting up the equation and solving the problem.
Students will work independently playing Bingo while working on concepts related to finding percentages of numbers.
Students will work in groups of 3-4 on a Fractions Decimal Percents Practice Puzzle where they will align a group of 24 triangles in such a way that their adjacent sides are equivalent and when complete, all the triangles together will form a hexagon. / Small group instruction
Individualized instruction
Peer tutoring
Computer activities for remediation
Choice activities
Chunking information
Rephrasing of questions
Working with partner
Video tutorials from textbook / Exit ticket
Journal entry
Do now
Quiz
Test
Oral questioning
Homework
Unit Map
Unit # andTimeline / Topic(s) / Skill(s)
Unit 1
Sept. 2012 – October 22, 2012
( 7 weeks) / Fraction /
- Fraction Operation
Integers /
- Integer Operation
Unit 2
October 24, 2012– January 04, 2012
(6 weeks)
*Hurricane Sandy, Thanksgiving break + Winter Break / Equations /
- Distributive Property
- Creating, and solving equations from real-world problems.
Inequalities /
- Isolating the Variable
- Creating, Solving and graphing inequalities from real world problems
Unit 3
January 7, 2013 –January 24, 2013
(3 weeks) / Rational Numbers /
- Fraction Operation
- Converting Fraction to Decimal to Percent