Middle School Curriculum Map - Garfield Public Schools October 2014/7t… · · 2015-02-05Middle...
Transcript of Middle School Curriculum Map - Garfield Public Schools October 2014/7t… · · 2015-02-05Middle...
Garfield Middle School Aligned to the 2013 Common Core Curriculum Content Standards
ENGAGING STUDENTS • FOSTERING ACHIEVEMENT • CULTIVATING 21ST
CENTURY GLOBAL SKILLS
Middle School Curriculum Map
7th
Grade Math Apps Marking Period 1
Topic Chapters Number of Blocks Dates
Algebraic Reasoning Chapter 1 4 9/9 – 9/18
PRE-TEST 1 9/25
Integers and Rational
Numbers Chapter 2 9 9/19– 10/17
Applying Rational
Numbers Chapter 3 9 10/18– 11/15
MP 1
ASSESSMENT
Chapters 1, 2 and
half of 3 1 11/6
Marking Period 2 Topic Chapters Number of Blocks Dates
Proportional
Relationships Chapter 4 8 11/18– 12/11
Graphs Chapter 5 4 12/12-12/20
Percents Chapter 6 5 1/2 -1/15
MP 2
ASSESSMENT
Chapters- half of
3,4,5,6 1 1/24
Marking Period 3 Topic Chapters Number of Blocks Dates
Collecting, Displaying
and Analyzing Data Chapter 7 4 1/26– 1/31
Geometric Figures Chapter8 6 2/3 – 2/28
Measurement and
Geometry Chapter 9 6 3/3-3/18
NJ ASK REVIEW 4 3/19 – 3/27
MP 3
ASSESSMENT Chapters 7-9 3/28
Marking Period 4 Topic Chapters Number of Blocks Dates
NJ ASK REVIEW 6 3/31 – 4/25
Probability Chapter 10 10 5/5 – 5/30
Multi-step Equations
and Inequalities Chapter 11 5 6/2- 6/13
MP 4
ASSESSMENT Chapters 10-11 1 6/16
Topic Chapters Number of Blocks Dates
NJ ASK REVIEW 6 3/31 – 4/25
Graphing Lines Chapter 8 7 5/5 – 5/23
Data, Predications and
Linear Functions Chapter 9 6 5/27- 6/11
MP 4
ASSESSMENT Chapters 8 and 9 1 6/12
Garfield Middle School Aligned to the 2013 Common Core Curriculum Content Standards
ENGAGING STUDENTS • FOSTERING ACHIEVEMENT • CULTIVATING 21ST
CENTURY GLOBAL SKILLS
Unit Overview
Content Area: Math Applications
Unit Title: Algebraic Reasoning, Integers and Rational Numbers
Target Course/Grade Level 7th
Duration: 27 Blocks
Description
In this section students will apply prior knowledge of algebraic properties and number sense as they learn to compare and order integers, and to add, subtract, multiply, and divide them. Further, students will extend the order of operations to include exponents. Lastly, they learn why fractions and decimals are rational numbers.
Concepts & Understandings
Concepts
Order of operations.
Properties of numbers.
Variables and algebraic expressions.
Translating words into math
Simplifying algebraic expressions.
Integers.
Adding integers.
Subtracting integers.
Multiplying and dividing integers.
Solving equations containing integers.
Equivalent fractions and decimals.
Comparing and ordering rational numbers.
Understandings
Student understandings from the concepts include:
Simplify numerical expressions involving order of operations and exponents.
Using variables and symbols to translate words into math.
Simplifying algebraic expressions using properties of addition and multiplication.
Comparing and ordering integers and rational numbers.
Converting between fractions and decimals mentally, on paper, and with a calculator.
Using models to add, subtract, multiply and divide integers.
Learning Targets
CPI Codes
MA.CC - EE.7.01 MA.CC - EE.7.02 MA.CC - EE.7.0
,MA.CC -EE.7.04
MA.CC - G.7.03 MA.CC - NS.7.01 MA.CC - NS.7.02 MA.CC-NS. 7.03 MA.CC - RP.7.02
Math Practices-see addendum
21st Century Themes and Skills
See addendum
Garfield Middle School Aligned to the 2013 Common Core Curriculum Content Standards
ENGAGING STUDENTS • FOSTERING ACHIEVEMENT • CULTIVATING 21ST
CENTURY GLOBAL SKILLS
Guiding Questions What is the order of operations?
What are the properties of rational numbers?
How do you simplify numerical expressions? How do you evaluate algebraic expressions? How do you translate words into numbers, variable and operations?
Explain how to combine like terms? What is the difference between whole numbers and integers?
Explain absolute value? What are the rules for adding integers? Explain how to subtract integers?
What are the rules for multiplying and dividing integers? Explain which operation are the inverse of each other?
Why is it necessary to perform the same operation on both sides of the equation?
How do you write fraction as a decimal?
Explain how to use place value to convert a decimal into a fraction?
What needs to be the same before you can add or subtract fractions? How do you compare fractions with different denominators?
Unit Results
Students will ... The student will use the order of operations to simplify numerical expressions.
The student will identify properties of rational numbers and use them to simplify numerical expressions.
The students will evaluate algebraic expressions.
The students will translate words into numbers, variables, and operations.
The students will simplify algebraic expressions.
The student will compare and order integers and determine absolute value.
The student will add and subtract integers.
The student will multiply and divide integers.
The student will solve one step equations with integers. The student will write fractions as decimals, and vice versa, and determine whether a decimal is terminating or
repeating.
The student will compare and order fractions and decimals.
Suggested Activities The following activities can be incorporated into the daily lessons:
Do Now
Exploration worksheet
Challenge worksheet
Problem Solving worksheet
Journal Writing
Exit Ticket
Quiz
Garfield Middle School Aligned to the 2013 Common Core Curriculum Content Standards
ENGAGING STUDENTS • FOSTERING ACHIEVEMENT • CULTIVATING 21ST
CENTURY GLOBAL SKILLS
Test
Projects
Unit Overview
Content Area: Math Applications
Unit Title Applying Rational Numbers
Target Course/Grade Level 7th
Duration: 19 Blocks
Description Students will build on fraction concepts to estimate and compute with fractions and mixed numbers. Students will evaluate, write, and solve equations that involve fraction, mixed numbers and decimals.
Concepts & Understandings
Concepts
Adding and subtracting decimals.
Multiplying decimals.
Dividing decimals.
Solving equations containing decimals.
Adding subtracting fractions.
Multiplying fractions and mixed numbers.
Dividing fractions and mixed numbers.
Solving equations containing fractions.
Understandings
Student understandings from the concepts include:
Use addition, subtraction, multiplication, and division to solve problems involving fractions and decimals.
Solve equations with rational numbers.
Learning Targets
CPI Codes
MA.CC - EE.7.04 MA.CC - NS.7.03 MA.CC - NS.7.02 MA.CC - NS.7.01
Math Practices-see addendum
21st Century Themes and Skills
See addendum Guiding Questions
Describe the steps necessary to add and subtract decimals?
How can you check an answer when adding or subtracting decimals?
Compare multiplication of decimals with multiplication of integers.
How do you determine the decimal placement in a product when multiplying decimals?
What are the rules when dividing an integer by a decimal?
Explain how to solve each type of decimal equation; addition, subtraction, multiplication, and division.
How do you obtain a common denominator?
Describe the process for subtracting/adding fractions with different denominators.
Describe how to multiply and divide mixed number and a fraction.
How do you determine the steps of a product?
Compare the steps used in multiplying mixed numbers with those used in dividing mixed numbers?
What is the process of solving an equation that involves mixed numbers?
Garfield Middle School Aligned to the 2013 Common Core Curriculum Content Standards
ENGAGING STUDENTS • FOSTERING ACHIEVEMENT • CULTIVATING 21ST
CENTURY GLOBAL SKILLS
Unit Results Students will ...
Add and subtract decimals.
Multiply decimals.
Divide decimals and integers by decimals.
Solve one step equations that contain decimals.
Add and subtract fractions.
Multiply fractions and mixed numbers.
Divide fractions and mixed numbers.
Solve one step equations that contain fraction.
Be assessed on students’ mastery of concepts and skills.
Suggested Activities
The following activities can be incorporated into the daily lessons:
Do Now
Exploration worksheet
Challenge worksheet
Problem Solving worksheet
Exit Ticket
Journal Writing
Quiz
Test
Projects
Garfield Middle School Aligned to the 2013 Common Core Curriculum Content Standards
ENGAGING STUDENTS • FOSTERING ACHIEVEMENT • CULTIVATING 21ST
CENTURY GLOBAL SKILLS
Unit Overview
Content Area: Math Applications
Unit Title: Proportions and Ratios
Target Course/Grade Level 7th
Duration: 15 Blocks
Description Students will learn to find equivalent ratios and to see if ratios can form a proportion. They use unit rates to solve proportions involving variable, and they use proportions to solve problems involving scale. Further, they solve proportions to find missing lengths in missing figures.
Concepts & Understandings
Concepts
Rates
Identifying and writing proportions
Solving Proportions
Similar figures and proportions
Using similar figures
Scale drawings and scale models
Understandings
Student understandings from the concepts include:
Use division to find unit rates and ratios in proportional relationships
Estimate and find solutions to application problems involving proportional relationships.
Use critical attributes to define similarity.
Use ratios and proportions in scale drawings and scale models.
Learning Targets
CPI Codes
MA.CC - RP.7.01 MA.CC - RP.7.02 MA.CC - G.7.01
Math Practices-see addendum
21st Century Themes and Skills
See addendum Guiding Questions
Explain how you can tell whether a rate represents a unit rate?
What does it mean for ratios to be proportional?
Explain how the term cross product can help you remember how to solve a proportion. What are the characteristics of corresponding angles and corresponding sides in similar figures? How do you know if two shapes are proportional? How do you find a missing side length for one or two similar figures? How do find the actual height of an object whose scale drawing is smaller than the object?
Unit Results
Students will ... Find and compare unit rates, such as average speed and unit price.
Find equivalent ratios and identify proportions.
Garfield Middle School Aligned to the 2013 Common Core Curriculum Content Standards
ENGAGING STUDENTS • FOSTERING ACHIEVEMENT • CULTIVATING 21ST
CENTURY GLOBAL SKILLS
Solve proportions by using cross products.
Use ratios to determine if two figures are similar.
Use similar figures to find unknown measures.
Understand ratios and proportions in scale drawings and use ratios and proportions with scale.
Be assessed on students’ mastery of concepts and skills. Suggested Activities
The following activities can be incorporated into the daily lessons:
Do Now
Exploration worksheet
Challenge worksheet
Problem Solving worksheet
Exit Ticket
Journal Writing
Quiz
Test
Projects
Garfield Middle School Aligned to the 2013 Common Core Curriculum Content Standards
ENGAGING STUDENTS • FOSTERING ACHIEVEMENT • CULTIVATING 21ST
CENTURY GLOBAL SKILLS
Unit Overview
Content Area: Math Applications
Unit Title: Graphs
Target Course/Grade Level: 7th Grade
Duration: 7 Blocks
Description :
In this section students will study graphing in the coordinate plane. They explore linear relationships and the concept of slope as they graph point and lines in all four quadrants. Furthermore, they also investigate no-linear relationships, translations, reflections, rotations, and symmetry.
Concepts & Understandings
Concepts
The Coordinate Plane
Interpreting graphs
Slope and rates of change
Direct Variation
Understandings
Student understandings from the concepts include
Plotting and identifying ordered pairs of integers on a coordinate plane.
Graphing to demonstrate relationships between data sets.
Using rates of change to solve problems.
Writing and graphing linear equations to solve problems.
Learning Targets
CPI Codes
MA.CC - RP.7.02
MA.CC - RP.7.01 Math Practices-see addendum
21st Century Themes and Skills
See addendum Guiding Questions
Explain the meaning of a horizontal segment on a graph that compares distance to time?
Describe a real world situation that could be represented by a graph that has connected lines or curves?
Compare constant and variable rates of change? Describe a line with a negative slope?
Explain how to use the table of data to check whether the relationship between two variables is a direct variation.
Describe how to recognize a direct variation from an equation, from a table, and from a graph? Unit Results
Students will ... Plot and identify ordered pairs on a coordinate plane.
Relate graphs to situations.
Garfield Middle School Aligned to the 2013 Common Core Curriculum Content Standards
ENGAGING STUDENTS • FOSTERING ACHIEVEMENT • CULTIVATING 21ST
CENTURY GLOBAL SKILLS
Determine the slope of a line and recognize constant and variable rates of change?
Identify, write, and graph an equation of direct variation.
Be assessed on students’ mastery of concepts and skills.
Suggested Activities
The following activities can be incorporated into the daily lessons:
Do Now
Exploration worksheet
Challenge worksheet
Problem Solving worksheet
Exit Ticket
Journal Writing
Quiz
Test
Projects
Garfield Middle School Aligned to the 2013 Common Core Curriculum Content Standards
ENGAGING STUDENTS • FOSTERING ACHIEVEMENT • CULTIVATING 21ST
CENTURY GLOBAL SKILLS
Unit Overview
Content Area: Math Applications
Unit Title: Percents
Target Course/Grade Level: 7th
Duration: 11 Blocks
Description :
Students will work with percents, including percents less than 1 and greater than 100. They begin by comparing percent to fractions and decimals. Then, using real-world applications they solve problems involving percents, including finding a percent of a number and finding a percent of change.
Concepts & Understandings
Concepts
Fractions, decimals, and percents
Estimating with percents
Using properties with rational numbers
Percent of change
Applications of percents
Simple interest
Understanding
Student understandings from the concepts include:
Modeling and estimating percents
Writing equivalent fractions, decimals and percents, including percents less than 1 and greater than 100
Solving percent problems involving discounts, sales tax, tips, profit, and percent of change, commission, and simple interest.
Comparing fractions, decimals, and percents.
Learning Targets
CPI Codes
MA.CC,EE.7.02 MA.CC,EE.7.03 MA.CC - NS.7.01
MA.CC - NS.7.02 MA.CC - RP.7.03
Math Practices-see addendum
21st Century Themes and Skills
See addendum Guiding Questions
Explain two methods for writing a decimal as a percents and for writing a fraction as a percent? Describe two ways to estimate with percents and tell when each is more appropriate to use?
Explain how the multiplication property of equality is used to write an equivalent equation without fractions or decimals?
Explain what is meant by 100 percent decrease? Explain how to find a price of an item if you know the total cost after 5 percent sales tax? How is finding commission similar to finding sales tax?
Garfield Middle School Aligned to the 2013 Common Core Curriculum Content Standards
ENGAGING STUDENTS • FOSTERING ACHIEVEMENT • CULTIVATING 21ST
CENTURY GLOBAL SKILLS
Explain the meaning of each variable in the interest formula? Name the variables in the simple interest formula that represent dollar amounts.
Unit Results
Students will ... Write decimals and fraction as fractions and percents.
Estimate percents.
Use properties of rational numbers to write equivalent expressions and equations.
Solve problems involving percent of change.
Find commission, sales tax, and percent of earnings.
Compute simple interest.
Be assessed on students’ mastery of concepts and skills.
Suggested Activities
The following activities can be incorporated into the daily lessons:
Do Now
Exploration worksheet
Challenge worksheet
Problem Solving worksheet
Exit Ticket
Journal Writing
Quiz
Test
Projects
.
Garfield Middle School Aligned to the 2013 Common Core Curriculum Content Standards
ENGAGING STUDENTS • FOSTERING ACHIEVEMENT • CULTIVATING 21ST
CENTURY GLOBAL SKILLS
Unit Overview
Content Area: Math Applications
Unit Title: Collecting, Displaying, and Analyzing Data.
Target Course/Grade Level: 7th
Duration: 9 Blocks
Description :
In this section students will build on their knowledge of graphing and statistics as they investigate different ways of obtaining and displaying data. They work with frequency tables and data displays like spreadsheets, histograms, stem-and-leaf plots, and scatter plots. Furthermore, they learn about sampling, surveys, and how to use data to make predictions.
Concepts & Understandings
Concepts
Mean median, mode, and range.
Box-and-whisker plots.
Populations and samples.
Understandings
Student understandings from the concepts include:
Using an appropriate representation for displaying relationships among data.
Choosing among mean, median, mode, or range to describe a set of data.
Making inferences and convincing arguments based on analysis of data.
Learning Targets
CPI Codes
MA.CC.SP.7.01 MA.CC. SP 7.02, MA.CC. SP 7.03, MA.CC. SP 7.04
Math Practices-see addendum
21st Century Themes and Skills
See addendum Guiding Questions
Explain how the outlier affects the mean, median, and mode of a data set?
Describe what you can tell about a data set from a box-and-whisker plot? Explain why it might be difficult to obtain a truly random sample of a very large population?
Unit Results
Students will ...
Garfield Middle School Aligned to the 2013 Common Core Curriculum Content Standards
ENGAGING STUDENTS • FOSTERING ACHIEVEMENT • CULTIVATING 21ST
CENTURY GLOBAL SKILLS
Find the mean, median, mode, and range of a data set.
Display and analyze data in box-and –whisker plots.
Compare and analyze sampling methods.
Be assessed on students’ mastery of concepts and skills.
Suggested Activities
The following activities can be incorporated into the daily lessons:
Do Now
Exploration worksheet
Challenge worksheet
Problem Solving worksheet
Exit Ticket
Journal Writing
Quiz
Test
Projects
Garfield Middle School Aligned to the 2013 Common Core Curriculum Content Standards
ENGAGING STUDENTS • FOSTERING ACHIEVEMENT • CULTIVATING 21ST
CENTURY GLOBAL SKILLS
Unit Overview
Content Area: Math Applications
Unit Title: Geometric Figures
Target Course/Grade Level: 7th grade
Duration: 13 Blocks
Description :
In this section students will learn about the properties of lines and angles then, they classify angles according to their degree measures. They work with triangles, quadrilaterals, and other polygons, including congruent figures.
Concepts & Understandings
Concepts
Building blocks of geometry
Classifying angles
Line and angle relationships Angles in polygons Congruent figures
Understandings
Student understandings from the concepts include:
Classifying pairs of angles as complementary or supplementary.
Identifying parallel and perpendicular lines. Using congruence to solve problems.
Learning Targets
CPI Codes
G.7.05 G.7.02 Math Practices –see addendum
21st Century Themes and Skills
See addendum Guiding Questions
How many ways can a line segment be named?
What are three different ways to classify an angle?
How do you find a complementary angle when one angle is given?
Explain why perpendicular lines can also be called intersecting lines?
Explain how to find the measure of an angle in a triangle when the measure of the two other angles are known?
Why are congruent figures always similar figures?
What does it mean when two polygons are congruent?
Unit Results
Students will ...
Identify and describe geometric figures Identify angles and angle pairs Identify parallel, perpendicular, and skew lines, and angles formed by a transversal.
Find the measures of angles in a polygon.
Garfield Middle School Aligned to the 2013 Common Core Curriculum Content Standards
ENGAGING STUDENTS • FOSTERING ACHIEVEMENT • CULTIVATING 21ST
CENTURY GLOBAL SKILLS
Identify congruent figures and use congruence to solve problem. Be assessed on students’ mastery of concepts and skills.
Suggested Activities The following activities can be incorporated into the daily lessons:
Do Now
Exploration worksheet
Challenge worksheet
Problem Solving worksheet
Exit Ticket
Journal Writing
Quiz
Test
Projects
Garfield Middle School Aligned to the 2013 Common Core Curriculum Content Standards
ENGAGING STUDENTS • FOSTERING ACHIEVEMENT • CULTIVATING 21ST
CENTURY GLOBAL SKILLS
Unit Overview
Content Area: Math Applications
Unit Title : Measurement and geometry
Target Course/Grade Level:
Duration: 13 Blocks
Description :
In this section students will build on their knowledge of the geometric concepts to estimate and calculate areas of different types of polygons. Furthermore, they also calculate the circumference and area of circles, as well as the surface area and volume of prisms and cylinders.
Concepts & Understandings
Concepts
Perimeter and circumference.
Area of circles.
Area of irregular figures.
Three-dimensional figures.
Volume of prism and cylinders.
Surface area of prisms and cylinders.
Understandings
Student understandings from the concepts include:
Finding the circumference and area of circles.
Finding the area of irregular figures. Finding the volume and surface area of three-
dimensional figures.
Learning Targets
CPI Codes
MA.CC,G.7.03,
MA.CC,G.7.04 MA.CC,G.7.06
Math Practices-see addendum
21st Century Themes and Skills
See addendum Guiding Questions
Describe two ways to find a perimeter of a volleyball court?
How are the circumference of a circle and a perimeter of a polygon alike?
Compare finding the area of a circle when given a radius with finding an area when given a diameter? Describe two different ways to find the area of irregular figures?
Compare and contrast cylinders and prisms.
What is a cubic unit?
Compare and contrast the formulas for volume of a prism and volume of a cylinder. Explain how to use a net to find the surface area of a rectangular prism and a cylinder?
Unit Results Students will ...
Find the perimeter of a polygon and the circumference of a circle.
Find the area of circles.
Find the area of irregular figures.
Identify various three-dimensional figures.
Garfield Middle School Aligned to the 2013 Common Core Curriculum Content Standards
ENGAGING STUDENTS • FOSTERING ACHIEVEMENT • CULTIVATING 21ST
CENTURY GLOBAL SKILLS
Find the volume of prisms and cylinders.
Find the surface area of prisms and cylinders.
Be assessed on students’ mastery of concepts and skills. Suggested Activities
The following activities can be incorporated into the daily lessons:
Do Now
Exploration worksheet
Challenge worksheet
Problem Solving worksheet
Exit Ticket
Journal Writing
Quiz
Test
Projects
Garfield Middle School Aligned to the 2013 Common Core Curriculum Content Standards
ENGAGING STUDENTS • FOSTERING ACHIEVEMENT • CULTIVATING 21ST
CENTURY GLOBAL SKILLS
Unit Overview
Content Area: Math Applications
Unit Title: Probability
Target Course/Grade Level: 7th
Duration: 19 Blocks
Description :
In this section students will work with both theoretical and experimental probability. They find the probability of both simple and compound events. Furthermore, they conclude the chapter by learning about permutations and combinations.
Concepts & Understandings
Concepts
Probability
Experimental probability
Sample spaces
Theoretical probability
Making predictions.
Probability of independent and dependent events.
Combinations Permutations Probability of compound events
Understandings
Finding experimental and theoretical probabilities, including those of dependent and independent events.
Using lists and tree diagrams to find combinations and all possible outcomes of an experiment.
Using the fundamental counting principle and factorials to find permutations.
Learning Targets
CPI Codes
MA.CC,SP.7.05
MA.CC,SP.7.06 MA.CC,SP.7.07 MA.CC,SP.7.08
Math Practices –see addendum
21st Century Themes and Skills
See addendum Guiding Questions
Describe an event that has a probability of zero percent and an event that has a probability of 100 percent. Explain how experimental probability can be used to make predictions? Compare using a tree diagram and using the fundamental counting principle to find a sample space? Give an example of an experiment in which all of the outcomes are not equally likely?
Explain a difference between a prediction based on experimental probability and one based on theoretical probability?
Compare probabilities of independent and dependent events. Describe how combinations could help you find the probability of an event?
Garfield Middle School Aligned to the 2013 Common Core Curriculum Content Standards
ENGAGING STUDENTS • FOSTERING ACHIEVEMENT • CULTIVATING 21ST
CENTURY GLOBAL SKILLS
What are the possible ways to find the number of permutations of a group of objects? Explain how organized list, tree diagram, and tables help find the sample space in an experiment?
Unit Results Students will ...
Use informal measures of probability Find experimental probability Use counting methods to determine all possible outcomes Find the theoretical probability of an event Use probability to predict events
Find the probability of an independent and dependent events
Find the numbers of possible combinations Find the number of possible permutations Find probability of compound events Be assessed on students’ mastery of concepts and skills.
Suggested Activities The following activities can be incorporated into the daily lessons:
Do Now
Exploration worksheet
Challenge worksheet
Problem Solving worksheet
Exit Ticket
Journal Writing
Quiz
Test
Projects
Garfield Middle School Aligned to the 2013 Common Core Curriculum Content Standards
ENGAGING STUDENTS • FOSTERING ACHIEVEMENT • CULTIVATING 21ST
CENTURY GLOBAL SKILLS
Unit Overview
Content Area: Math Application
Unit Title: Multi-Step equations and Inequalities
Target Course/Grade Level: 7th
Duration: 11 Blocks
Description :
In this section students evaluate and write algebraic expressions and write and solve both one-step and two-step equations. Lastly, they draw upon their understandings of expressions and equations to graph, write, and solve inequalities.
.
Concepts & Understandings
Concepts
Solving two-step equations.
Solving multi-step equations.
Solving equations with variables on both sides.
Inequalities
Solving inequalities by adding or subtracting.
Solving inequalities by multiplying or dividing.
Solving multi-step inequalities
Understandings
Student understandings from the concepts include:
Solving two-step and multi-step equations and equations with variables on both sides.
Reading, writing, and graphing inequalities on a number line.
Solving one-step and two-step inequalities Solving equations for a variable
Learning Targets
M.A.CC. EE 7.01,
M.A.CC. EE 7.04 Math Practices –see addendum
21st Century Themes and Skills
See addendum. Guiding Questions
Explain how you decide which inverse operations to use first when solving two-step equation?
Select a multi-step equation and challenge students to list the required steps.
Select an equation with variables on both sides and challenge students to decide which variable term to add or subtract.
Explain how to graph each type of compound inequalities.
Compare solving addition and subtraction equations with solving addition and subtraction inequalities.
Compare solving multiplication and division equations with solving multiplication and division inequalities.
Explain how to solve a simple two step inequality.
Unit Results
Students will ... Solve two- step equations
Solve multistep equations
Solve equations that have variables on both sides
Read and write inequalities and graph them on a number line
Solve one-step inequalities by adding or subtracting
Solve one-step inequalities by multiplying and dividing
Garfield Middle School Aligned to the 2013 Common Core Curriculum Content Standards
ENGAGING STUDENTS • FOSTERING ACHIEVEMENT • CULTIVATING 21ST
CENTURY GLOBAL SKILLS
Solve simple two- step inequalities
Be assessed on students’ mastery of concepts and skills. Suggested Activities
The following activities can be incorporated into the daily lessons:
Do Now
Exploration worksheet
Challenge worksheet
Exit Ticket
Problem Solving worksheet
Journal Writing
Quiz
Test
Projects
Garfield Middle School Aligned to the 2013 Common Core Curriculum Content Standards
ENGAGING STUDENTS • FOSTERING ACHIEVEMENT • CULTIVATING 21ST
CENTURY GLOBAL SKILLS
MATH PRACTICES
1. CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them.
Mathematically proficient students start by explaining to themselves the meaning of a problem
and looking for entry points to its solution. They analyze givens, constraints, relationships,
and goals. They make conjectures about the form and meaning of the solution and plan a
solution pathway rather than simply jumping into a solution attempt. They consider analogous
problems, and try special cases and simpler forms of the original problem in order to gain
insight into its solution. They monitor and evaluate their progress and change course if
necessary. Older students might, depending on the context of the problem, transform
algebraic expressions or change the viewing window on their graphing calculator to get the
information they need. Mathematically proficient students can explain correspondences
between equations, verbal descriptions, tables, and graphs or draw diagrams of important
features and relationships, graph data, and search for regularity or trends. Younger students
might rely on using concrete objects or pictures to help conceptualize and solve a problem.
Mathematically proficient students check their answers to problems using a different method,
and they continually ask themselves, “Does this make sense?” They can understand the
approaches of others to solving complex problems and identify correspondences between
different approaches.
2. CCSS.Math.Practice.MP2 Reason abstractly and quantitatively.
Mathematically proficient students make sense of quantities and their relationships in problem
situations. They bring two complementary abilities to bear on problems involving quantitative
relationships: the ability to de-contextualize—to abstract a given situation and represent it
symbolically and manipulate the representing symbols as if they have a life of their own,
without necessarily attending to their referents—and the ability to contextualize, to pause as
needed during the manipulation process in order to probe into the referents for the symbols
involved. Quantitative reasoning entails habits of creating a coherent representation of the
problem at hand; considering the units involved; attending to the meaning of quantities, not
just how to compute them; and knowing and flexibly using different properties of operations
and objects.
Garfield Middle School Aligned to the 2013 Common Core Curriculum Content Standards
ENGAGING STUDENTS • FOSTERING ACHIEVEMENT • CULTIVATING 21ST
CENTURY GLOBAL SKILLS
3. CCSS.Math.Practice.MP3 Construct viable arguments and critique the reasoning of
others.
Mathematically proficient students understand and use stated assumptions, definitions, and
previously established results in constructing arguments. They make conjectures and build a
logical progression of statements to explore the truth of their conjectures. They are able to
analyze situations by breaking them into cases, and can recognize and use counterexamples.
They justify their conclusions, communicate them to others, and respond to the arguments of
others. They reason inductively about data, making plausible arguments that take into
account the context from which the data arose. Mathematically proficient students are also
able to compare the effectiveness of two plausible arguments, distinguish correct logic or
reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is.
Elementary students can construct arguments using concrete referents such as objects,
drawings, diagrams, and actions. Such arguments can make sense and be correct, even
though they are not generalized or made formal until later grades. Later, students learn to
determine domains to which an argument applies. Students at all grades can listen or read
the arguments of others, decide whether they make sense, and ask useful questions to clarify
or improve the arguments.
4. CCSS.Math.Practice.MP4 Model with mathematics.
Mathematically proficient students can apply the mathematics they know to solve problems
arising in everyday life, society, and the workplace. In early grades, this might be as simple as
writing an addition equation to describe a situation. In middle grades, a student might apply
proportional reasoning to plan a school event or analyze a problem in the community. By high
school, a student might use geometry to solve a design problem or use a function to describe
how one quantity of interest depends on another. Mathematically proficient students who can
apply what they know are comfortable making assumptions and approximations to simplify a
complicated situation, realizing that these may need revision later. They are able to identify
important quantities in a practical situation and map their relationships using such tools as
diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those
relationships mathematically to draw conclusions. They routinely interpret their mathematical
results in the context of the situation and reflect on whether the results make sense, possibly
improving the model if it has not served its purpose.
Garfield Middle School Aligned to the 2013 Common Core Curriculum Content Standards
ENGAGING STUDENTS • FOSTERING ACHIEVEMENT • CULTIVATING 21ST
CENTURY GLOBAL SKILLS
5. CCSS.Math.Practice.MP5 Use appropriate tools strategically.
Mathematically proficient students consider the available tools when solving a mathematical
problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a
calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic
geometry software. Proficient students are sufficiently familiar with tools appropriate for their
grade or course to make sound decisions about when each of these tools might be helpful,
recognizing both the insight to be gained and their limitations. For example, mathematically
proficient high school students analyze graphs of functions and solutions generated using a
graphing calculator. They detect possible errors by strategically using estimation and other
mathematical knowledge. When making mathematical models, they know that technology can
enable them to visualize the results of varying assumptions, explore consequences, and
compare predictions with data. Mathematically proficient students at various grade levels are
able to identify relevant external mathematical resources, such as digital content located on a
website, and use them to pose or solve problems. They are able to use technological tools to
explore and deepen their understanding of concepts.
6. CCSS.Math.Practice.MP6 Attend to precision.
Mathematically proficient students try to communicate precisely to others. They try to use
clear definitions in discussion with others and in their own reasoning. They state the meaning
of the symbols they choose, including using the equal sign consistently and appropriately.
They are careful about specifying units of measure, and labeling axes to clarify the
correspondence with quantities in a problem. They calculate accurately and efficiently,
express numerical answers with a degree of precision appropriate for the problem context. In
the elementary grades, students give carefully formulated explanations to each other. By the
time they reach high school they have learned to examine claims and make explicit use of
definitions.
Garfield Middle School Aligned to the 2013 Common Core Curriculum Content Standards
ENGAGING STUDENTS • FOSTERING ACHIEVEMENT • CULTIVATING 21ST
CENTURY GLOBAL SKILLS
7. CCSS.Math.Practice.MP7 Look for and make use of structure.
Mathematically proficient students look closely to discern a pattern or structure. Young
students, for example, might notice that three and seven more is the same amount as seven
and three more, or they may sort a collection of shapes according to how many sides the
shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in
preparation for learning about the distributive property. In the expression x2 + 9x + 14, older
students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an
existing line in a geometric figure and can use the strategy of drawing an auxiliary line for
solving problems. They also can step back for an overview and shift perspective. They can
see complicated things, such as some algebraic expressions, as single objects or as being
composed of several objects. For example, they can see 5 – 3(x – y)2 as 5 minus a positive
number times a square and use that to realize that its value cannot be more than 5 for any
real numbers x and y.
8. CCSS.Math.Practice.MP8 Look for and express regularity in repeated reasoning.
Mathematically proficient students notice if calculations are repeated, and look both for
general methods and for shortcuts. Upper elementary students might notice when dividing 25
by 11 that they are repeating the same calculations over and over again, and conclude they
have a repeating decimal. By paying attention to the calculation of slope as they repeatedly
check whether points are on the line through (1, 2) with slope 3, middle school students might
abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when
expanding (x – 1)(x + 1), (x – 1)(x2 + x + 1), and (x – 1)(x3 + x2 + x + 1) might lead them to the
general formula for the sum of a geometric series. As they work to solve a problem,
mathematically proficient students maintain oversight of the process, while attending to the
details. They continually evaluate the reasonableness of their intermediate results.
Garfield Middle School Aligned to the 2013 Common Core Curriculum Content Standards
ENGAGING STUDENTS • FOSTERING ACHIEVEMENT • CULTIVATING 21ST
CENTURY GLOBAL SKILLS
Connecting the Standards for Mathematical Practice to the Standards for Mathematical Content
The Standards for Mathematical Practice describe ways in which developing student
practitioners of the discipline of mathematics increasingly ought to engage with the subject
matter as they grow in mathematical maturity and expertise throughout the elementary,
middle and high school years. Designers of curricula, assessments, and professional
development should all attend to the need to connect the mathematical practices to
mathematical content in mathematics instruction.
The Standards for Mathematical Content are a balanced combination of procedure and
understanding. Expectations that begin with the word “understand” are often especially good
opportunities to connect the practices to the content. Students who lack understanding of a
topic may rely on procedures too heavily. Without a flexible base from which to work, they
may be less likely to consider analogous problems, represent problems coherently, justify
conclusions, apply the mathematics to practical situations, use technology mindfully to work
with the mathematics, explain the mathematics accurately to other students, step back for an
overview, or deviate from a known procedure to find a shortcut. In short, a lack of
understanding effectively prevents a student from engaging in the mathematical practices.
In this respect, those content standards which set an expectation of understanding are
potential “points of intersection” between the Standards for Mathematical Content and the
Standards for Mathematical Practice. These points of intersection are intended to be weighted
toward central and generative concepts in the school mathematics curriculum that most merit
the time, resources, innovative energies, and focus necessary to qualitatively improve the
curriculum, instruction, assessment, professional development, and student achievement in
mathematics.