Grade 7Mathematics Curriculum Map

2011-2012

Unit / Skills / Standards / Lesson Materials
Unit 1
Variables & Patterns / Discover, describe and generalize patterns
Represent relationships with tables, graphs and verbal or symbolic rules
Analyze tables ,graphs and rules
Understand that variables are those quantities that change such as time and temperature
Represent patterns of change
Create tables, graphs and symbolic rules that describe patterns of change / 6.A.2 Use substitution to evaluate algebraic expressions
(may include exponents of one, two and three)
6.A.3 Translate two-step verbal sentences into algebraic equations
6.G.10 Identify and plot points in all four quadrants
7.A.1 Translate two-step verbal expressions into algebraic expressions
7.A.2 Add and subtract monomials with exponents of one
7.A.3 Identify a polynomial as an algebraic expression containing one or more terms
7.A.4 Solve multi-step equations by combining like terms, using the distributive property or moving variables to one side of the equation
7.A.5 Solve one-step inequalities (positive coefficients only)
7.A.6 Evaluate formulas for given input values (surface area, rate, and density problems)
7.A.7 Draw the graphic representation of a pattern from an equation or from a table of data
7.A.8 Create algebraic patterns using charts/tables, graphs, equations, and expressions
7.A.9 Build a pattern to develop a rule to determine the sum of the interior angles of polygons
7.A.10 Write an equation to represent a function from a table of values
7.G.1 Calculate the radius or diameter, given the circumference or area of a circle
8.A.3 Describe a situation involving relationships that matches a given graph
8.A.4 Create a graph given a description or an expression for a situation involving a linear or nonlinear relationship
8.A.15 Understand that numerical information can be represented in multiple ways: arithmetically, algebraically and graphically
8.A.19 Interpret multiple representations using equation, table of values and graph
8.G.15 Graph a line using a table of values
7RP2. Recognize and represent proportional relationships between quantities.
b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
c. Represent proportional relationships by equations.
d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
7EE1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
2. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.
4. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. / Note that the CMP Teachers Guide has suggested questions for each Investigation. Teachers are recommended to read the Teachers Guide before embarking on the unit.
Application, Connections & Extensions (ACE) apply when using CMP 2
CMP unit: Variables & patterns
Investigation 1: 1.1, 1.2
Investigation 2 : 2.1, 2.2, 2.3
Investigation 3: 3.1, 3.2, 3.3
Investigation 4: 4.1, 4.2, 4.3
(optional use of graphing calculators)
Impact Book 2:
Chapters 1, 3 & 6
Skills Intervention
Skills: 23, 24, 41, 71, 74
Assessment Resources for CMP 2
Teacher handouts
Activityp81 – Unit Review Project
Extension Worksheets
6A2:
Where’s my Substitute
An Exasperating Expression
6A3:
Singapore math
Sentences into equations
6G10:
Plotting Points
Once upon a time, please
What happened to the reporter….
7A2:
Add and subtract monomials
Singapore Math
How did Betsy Ross know…..
7A4:
Distributive with negative
Distributive with negative (advanced)
7A6:
Solving equations for variables
7A7:
Equations with graphs & tables
7A8:
Handshake problem
Telephone game
Unit / Skills / Standards / Lesson Materials
Unit 2
Accentuate the Negative / Developing strategies for:
Addition of integers
Subtraction of integers
Multiplication of integers
Division of integers
Absolute values
The concept of ‘opposites’
Ordering from least to greatest
Represent integers on a number line
Graph in four quadrants
Graphing inequalities
Solving inequalities / 6.A.4 Solve and explain two-step equations involving whole numbers using inverse operations
6.G.10 Identify and plot points in all four quadrants
7. N.1 Distinguish between the various subsets of real numbers (counting/natural numbers, whole numbers, integers, rational numbers, and irrational numbers.)
7. N.2 Recognize the difference between rational and irrational numbers (e.g., explore different approximations of π.)
7.N.3 Place rational and irrational numbers (approximations) on a number line and justify the placement of the numbers
7.N.4 Develop the laws of exponents for multiplication and division
7.N.5 Write numbers in scientific notation
7.N.6 Translate numbers from scientific notation into standard form
7.N.7 Compare numbers written in scientific notation
7.N.8 Find the common factors and greatest common factor of two or more numbers
7.N.9 Determine multiples and least common multiple of two or more numbers
7.N.10 Determine the prime factorization of a given number and write in exponential form
7. N.11 Simplify expressions using order of operations. Note: Expressions may include absolute value and/or integral exponents greater than 0
7.N.12 Add, subtract, multiply and divide integers
7. N.13 Add and subtract two integers (with and without the use of a number line.)
7. N.14 Develop a conceptual understanding of negative and zero exponents with a base of ten and relate to fractions and decimals (e.g., 10-² = .01 = 1/100.)
7.N.15 Recognize and state the value of the square root of a perfect square (up to 225)
7.N.16 Determine the square root of non-perfect squares using a calculator
7.N.17 Classify irrational numbers as non-repeating/non-terminating decimals
7.N.18 Identify the two consecutive whole numbers between which the square root of a non-perfect square whole number less than 225 lies (with and without the use of a number line)
7.N.19 Justify the reasonableness of answers using estimation
7NS1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
a. Describe situations in which opposite quantities combine to make 0.
For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.
b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
c. 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.
d. Apply properties of operations as strategies to add and subtract rational numbers
7NS2. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
a. 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.
b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q =
p/(–q). Interpret quotients of rational numbers by describing real world contexts.
c. Apply properties of operations as strategies to multiply and divide rational numbers.
d. 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.
7NS3. Solve real-world and mathematical problems involving the four operations with rational numbers.
7EE3. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. / Note that the CMP Teachers Guide has suggested questions for each Investigation. Teachers are recommended to read the Teachers Guide before embarking on the unit.
Application, Connections & Extensions (ACE) apply when using CMP 2
CMP unit: Accentuate the Negative
Investigation 1: 1.1, 1.2, 1.3
Investigation 2 : 2.1, 2.2
Investigation 3: 3.1, 3.2, 3.3
Investigation 4: 4.1, 4.2, 4.3
Investigation 5: 5.1, 5.2
Impact Book 2: Chapter 41., 4.2, 4.3
Teacher handouts
Skills Intervention
Skills: 5, 6, 7, 33
Pizzazz E55 -68
Punchlines Bridge to Algebra 25-29, 33, 35
Extension Worksheets
6A4:
Books ever written
Practice worksheet
7N1-3; N15-18:
Why did the Orgo……..
7N4:
Why did the scientist create…
What is the wrong way……
What did people say…..
7N5:
Where should you take…..
7N11:
Mixed practice with integers
Integer expressions
Parenthesis
7N12:
Up and down the line
Take it away
Multiplying integers
It’s fun, sum-times
Unit / Skills / Standards / Lesson Materials
Unit 3
Exponents, Scientific Notation & Polynomials / Convert standard form into scientific notation
Convert scientific notation into standard form
Order numbers in scientific notation and standard form from least to greatest
Identify polynomials / 7.N.4 Develop the laws of exponents for multiplication and division
7.N.5 Write numbers in scientific notation
7.N.6 Translate numbers from scientific notation into standard form
7.N.7 Compare numbers written in scientific notation
7.A.2 Add and subtract monomials with exponents of one
7.A.3 Identify a polynomial as an algebraic expression containing one or more terms / Note that the CMP Teachers Guide has suggested questions for each Investigation. Teachers are recommended to read the Teachers Guide before embarking on the unit.
Application, Connections & Extensions (ACE) apply when using CMP 2
CMP unit: Data Around Us
Investigations 3 & 4
Teacher handouts
Skills Intervention
Skills: 21, 22
Unit / Skills / Standards / Lesson Materials
Unit 4
Filling & Wrapping / Conceptualize area as a measure of wrapping an object
Conceptualize volume as a measure of filling
Explore the relationship of the surface area of rectangular prisms and cylinders to the total area of a flat pattern needed to wrap the solid
Understand the relationship between a cubic centimeter and a millimeter
Calculate the area, surface area and volume of 3-D figures
Develop strategies for finding the dimensions, surface area & volume of cylinders
Be aware that changing the dimensions of an object changes its volume and changing the volume of an object will alter its dimensions
Investigate methods of finding the volume of irregular objects / 7.N.19 Justify the reasonableness of answers using estimation
7.A.6 Evaluate formulas for given input values (surface area, rate, and density problems)
7.G.1 Calculate the radius or diameter, given the circumference or area of a circle
7.G.2 Calculate the volume of prisms and cylinders, using a given formula and a calculator
7.G.3 Identify the two-dimensional shapes that make up the faces and bases of three-dimensional shapes (prisms, cylinders, cones and pyramids)
7.G.4 Determine the surface area of prisms and cylinders, using a calculator and a variety of methods
7.M.2 Convert capacities and volumes within a given system
7.M.11 Estimate surface area
7G3. Describe the two-dimensional figures that result from slicing three dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
7G4. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
7G6. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. / Note that the CMP Teachers Guide has suggested questions for each Investigation. Teachers are recommended to read the Teachers Guide before embarking on the unit.
Application, Connections & Extensions (ACE) apply when using CMP 2
CMP unit: Filling & Wrapping
Investigation 1: 1.1, 1.2, 1.3, 1.4
Investigation 2: 2.1 (it is recommended that teachers start with smaller # of cubes first) , 2.2
Investigation 3: 3.1, 3.2
Investigation 4: 4.1, 4.2, 4.3
Investigation 6: 6.1, 6.2, 6.3
Investigation 7: 7.1
Note: Use the additional Practice Questions recommended in the Teachers Guide
Unit Project p73
Impact Book 2:
Chapter 2
Chapter 7.3, 7.4
Skills Intervention
Skills: 52 – 65
Pizzazz D64, 66
Extension Worksheets
Volume challenge
Exercise sheet
What might you send…..
Question bank
Unit / Skills / Standards / Lesson Materials
Unit 5
Pythagorean Theorem / Identify the legs and hypotenuse of a right triangle and justify this answer using definitions
Substitute into the Pythagorean Theorem and solve the equation to find the missing side of a right triangle.
Know that the Pythagorean Theorem works only on right triangles and that it works on every right triangle.
Substitute into the Pythagorean Theorem to determine if a triangle is a right triangle.
Answer word problems using the Pythagorean Theorem by drawing a diagram. / 7.G.5 Identify the right angle, hypotenuse and legs of a right triangle
7.G.6 Explore the relationship between the lengths of the three sides of a right triangle to develop the Pythagorean Theorem
7.G.8 Use the Pythagorean Theorem to determine the unknown length of a side of a right triangle
7.G.9 Determine whether a given triangle is a right triangle by applying the Pythagorean Theorem and using a calculator / Note that the CMP Teachers Guide has suggested questions for each Investigation. Teachers are recommended to read the Teachers Guide before embarking on the unit.
Application, Connections & Extensions (ACE) apply when using CMP 2
CMP unit:Looking for Pythagoras
Pizzazz D71 - 73
Unit / Skills / Standards / Lesson Materials
Unit 6
Statistics & Probability / Develop an understanding of probability
Determine experimental and theoretical probability
Represent and determine probability as a fraction of a set of equally likely outcomes
Make predictions based on experimental probabilities
Construct sample spaces
Predict the results of a series of trials once the probability for one trial is known.
Present data in a circle graph and interpret circle graphs. / 6.S.1 Develop the concept of sampling when collecting data from a population and decide the best method to collect data for a particular question
6.S.2 Record data in a frequency table
6.S..3 Construct Venn diagrams to sort data
6.S.4 Determine and justify the most appropriate graph to display a given set of data(pictograph, bar graph, line graph, histogram, or circle graph)
6.S.8 Justify predictions made from data
6.S.9 List possible outcomes for compound events
6.S.10 Determine the probability of dependent events
6.S.11 Determine the number of possible outcomes for a compound event by using the fundamental counting principle and use this to determine the probabilities of events when the outcomes have equal probability
7.N.19 Justify the reasonableness of answers using estimation
7. M.8 Justify the reasonableness of answers using estimation.
7.S.1 Draw central angles in a given circle using a protractor (circle graphs)
7.S.2 Display data in a circle graph
7.S.3Convert raw data into double bar graphs and double line graphs
7.S.4 Calculate the range for a given set of data
7.S.5 Select the appropriate measure of central tendency
7.S.6 Read and interpret data represented graphically (pictograph, bar graph, histogram, line graph, double line/bar graphs, or circle graph.)
7.S.7 Identify and explain misleading statistics and graphs
7.S.8 Interpret data to provide the basis for predictions and to establish experimental probabilities
7.S.9 Determine the validity of sampling methods to predict outcomes
7.S.10 Predict the outcome of experiment
7.S.11 Design and conduct an experiment to test predictions
7.S.12 Compare actual results to predicted results
7SP1. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.
7SP2. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.
7SP5. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
7SP6. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.
For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.
7SP7. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.
For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.
b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.
For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?
7SP8. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.