In Math 7, we use a combination of resources including Open Up Resources and Connected Math Project 3 (CMP3). Below are some family resources for each of these curriculum products.  

In addition, the Department of Education's family guide to Massachusetts' expectations and standards for what every seventh grader should know is linked here.

http://www.doe.mass.edu/frameworks/pguide/g7.pdf 

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Shapes and Designs: Angle Relationships

Concepts and Explanations          Worked Homework Examples         Math Background

Goals:

Properties of Polygons: 

• Explore the ways that polygons are sorted into families according to the number and length of their sides and the size of their angles

• Explore the patterns among interior and exterior angles of a polygon

• Explore the patterns among side lengths in a polygon

• Investigate the symmetries of a shape-rotation or reflection

• Determine which polygons fit together to cover a flat surface and why

• Reason about and solve problems involving various polygons

Relationships Among Angles: 

• Investigate techniques for estimating and measuring angles

• Use tools to sketch angles

• Reason about the properties of angles formed by parallel lines and transversals

• Use information about supplementary, complementary, vertical, and adjacent angles in a shape to solve for an unknown angle in a multi-step problem

Constructing Polygons: 

• Draw or sketch polygons with given conditions by using various tools and techniques such as freehand, use of a ruler and protractor, and use of technology

• Determine what conditions will produce a unique polygon, more than one polygon, or no polygon, particularly triangles and quadrilaterals

• Recognize the special properties of polygons such as angle sum, side-length relationships and symmetry, that make them useful in building, design, and nature

• Solve problems that involve properties of shapes  

As your child works on the Problems in this Unit, ask questions about situations that involve shapes such as:

• What do these polygons have in common? How do they differ from each other?

• When should I use estimation, freehand drawing, or special tools to measure and construct angles and polygons?

• How do the side lengths and angles of polygons determine their shapes?

• Why do certain polygons appear so often in buildings, artistic designs, and natural objects?

• How can I give directions for constructing polygons that meet conditions of any given problem?

Accentuate the Negative - Rational Numbers

Concepts and Explanations          Worked Homework Examples         Math Background

Goals:

In Accentuate the Negative, your student(s) will extend their knowledge of negative numbers. They will use negative numbers to solve problems. They will learn how to:

• Use appropriate notation to indicate positive and negative numbers and zero

• Compare and order rational numbers and locate them on a number line

• Understand the relationship between a number and its opposite (additive inverse)

• Relate direction and distance to the number line

• Develop and use different models (number line, chip model) for representing addition, subtraction, multiplication, and division

• Develop algorithms for adding, subtracting, multiplying, and dividing positive and negative numbers

• Interpret and write mathematical sentences to show relationships and solve problems

• Write and use related fact families for addition/subtraction and multiplication/division to solve simple equations

• Use parentheses and the Order of Operations in computations

• Use the commutative properties of addition and multiplication

• Apply the Distributive Property to simplify expressions and solve problems

• Use models and rational numbers to represent and solve problems

When your child encounters a new problem, it is a good idea to ask questions such as:

• How do negative and positive numbers and zero help describe the situation?

• What will addition, subtraction, multiplication, or division of rational numbers tell about the problem?

• What model(s) for positive and negative numbers and zero help show relationships in the problem situation? 

Stretching and Shrinking: Scale Drawings/Proportional Relationships

Concepts and Explanations          Worked Homework Examples        Math Background

Goals:

Similar Figures: 

• Identify similar figures by comparing corresponding sides and angles

• Use scale factors and ratios to describe relationships among the side lengths, perimeters, and areas of similar figures

• Generalize properties of similar figures

• Recognize the role multiplication plays in similarity relationships

• Recognize the relationship between scale factor and ratio in similar figures

• Use informal methods, scale factors, and geometric tools to construct similar figures (scale drawings)

• Compare similar figures with nonsimilar figures

• Distinguish algebraic rules that produce similar figures from those that produce nonsimilar figures

• Use algebraic rules to produce similar figures

• Recognize when a rule shrinks or enlarges a figure

• Explore the effect on the image of a figure if a number is added to the x- or y-coordinates of the figure’s vertices

Reasoning With Similar Figures Develop strategies for using similar figures to solve problems.

• Use the properties of similarity to find distances and heights that cannot be measured directly

• Predict the ways that stretching or shrinking a figure will affect side lengths, angle measures, perimeters, and areas

• Use scale factors or ratios to find missing side lengths in a pair of similar figures

• Use similarity to solve real-world problems

When your child encounters a new problem, it is a good idea to ask questions such as:

• What determines whether two shapes are similar?

• What is the same and what is different about two similar figures?

• When figures are similar, how are the side lengths, areas, and scale factors related?

• How can I use similar figures to find missing measurements?

Comparing and Scaling: Ratios, Rates, Percents, and Proportions 

Concepts and Explanations          Worked Homework Examples        Math Background

 Goals:

Ratios, Rates, and Percents: 

• Use ratios, rates, fractions, and percents to write statements comparing two quantities in a given situation 

• Distinguish between and use both part-to-part and part-to-whole ratios in comparisons 

• Use percents to express ratios and proportions 

• Recognize that a rate is a special ratio that compares two measurements with different units 

• Analyze comparison statements made about quantitative data for correctness and quality 

• Make judgments about which kind of comparison statements are most informative or best reflect a particular point of view in a specific situation

Proportionality: 

• Recognize that constant growth in a table, graph, or equation is related to proportional situations 

• Write an equation to represent the pattern in a table or graph of proportionally related variables 

• Relate the unit rate and constant of proportionality to an equation, graph, or table describing a proportional situation

Reasoning Proportionally: 

• Recognize situations in which proportional reasoning is appropriate to solve the problem

• Scale a ratio, rate, percent, or fraction to make a comparison or find an equivalent representation

• Use various strategies to solve for an unknown in a proportion, including scaling, rate tables, percent bars, unit rates, and equivalent ratios

• Set up and solve proportions that arise from real-world applications, such as finding discounts and markups and converting measurement units 

As you work on the Problems in this Unit, ask yourself these questions about situations that involve comparisons.

• What quantities are being compared?

• Why does the situation involve a proportional relationship (or not)?

• How might ratios, rates, or a proportion be used to solve the problem?

Moving Straight Ahead: Expressions, Equations and Inequalities

Concepts and Explanations          Worked Homework Examples        Math Background

Goals:

Linear Relationships: 

• Identify and describe the patterns of change between the independent and dependent variables for linear relationships represented by tables, graphs, equations, or contextual settings

• Construct tables, graphs, and symbolic equations that represent linear relationships

• Identify the rate of change between two variables and the x- and y-intercepts from graphs, tables, and equations that represent linear relationships

• Translate information about linear relationships given in a context, a table, a graph, or an equation to one of the other forms

• Write equations that represent linear relationships given specific pieces of information, and describe what information the variables and numbers represent

• Make a connection between slope as a ratio of vertical distance to horizontal distance between two points on a line and the rate of change between two variables that have a linear relationship

• Recognize that y = mx represents a proportional relationship

• Solve problems and make decisions about linear relationships using information given in tables, graphs, and equations

Equivalence: 

• Recognize that the equation y = mx + b represents a linear relationship and means that mx + b is an expression equivalent to y

• Recognize that linear equations in one unknown, k = mx + b or y = m(t) + b, where k, t, m, and b are constant numbers, are special cases of the equation y = mx + b

• Recognize that finding the missing value of one of the variables in a linear relationship,y = mx + b, is the same as finding a missing coordinate of a point (x, y) that lies on the graph of the relationship

• Solve linear equations in one variable using symbolic methods, tables, and graphs

• Recognize that a linear inequality in one unknown is associated with a linear equation

• Solve linear inequalities using graphs or algebraic reasoning

• Solve linear inequalities using graphs or algebraic reasoning

• Write and interpret equivalent expressions

When your child encounters a new problem, it is a good idea to ask questions such as:

• What are the variables in the problem?

• Do the variables in the problem have a linear relationship to each other?

• What patterns in the problem suggest that the relationship is linear?

• How can the linear relationship in a situation be represented with a verbal description, a table, a graph, or an equation?

• How do changes in one variable affect changes in a related variable?

• How are these changes captured in a table, a graph, or an equation?

• How can tables, graphs, and equations of linear relationships be used to answer questions?

Filling and Wrapping:  Volume and Surface Area

Concepts and Explanations         Worked Homework Examples        Math Background

Goals:

In Filling and Wrapping, your child will explore surface area and volume of three-dimensional objects, and will learn how to:

• Develop the ability to visualize and draw three-dimensional shapes

• Develop strategies for finding volumes of three-dimensional objects, including prisms, cylinders, pyramids, cones, and spheres

• Design and use nets to develop formulas for finding surface areas of prisms and cylinders

• Develop formulas and strategies for finding the area and circumference of a circle

• Explore patterns relating the volumes of prisms, cylinders, cones, spheres, and pyramids

• Understand that three-dimensional figures may have the same volume but different surface areas

• Investigate the effects of scaling dimensions of figures on the volume and surface area

• Recognize and solve problems involving volume and surface area

When your child encounters a new problem, it is a good idea to ask questions such as:

• What are the shapes and properties of the figures in the problem?

• Which measures of a figure are involved—length, surface area, or volume?

• What measurement strategies or formulas might help in using given information to find unknown measurements?

What Do You Expect?:  Probability 

Concepts and Explanations         Worked Homework Examples        Math Background

Goals:

Experimental and Theoretical Probabilities: 

• Recognize that probabilities are useful for predicting what will happen over the long run

• For an event described in everyday language, identify the outcomes in the sample space, which compose the event

• Interpret experimental and theoretical probabilities and the relationship between them and recognize that experimental probabilities are better estimates of theoretical probabilities when they are based on larger numbers

• Distinguish between equally likely and non-equally likely outcomes by collecting data and analyzing experimental probabilities

• Realize that the probability of simple events is the fraction of outcomes in the sample space for which the event occurs

• Recognize that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring

• 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

• Determine the fairness of a game

Reasoning with Probability: 

• Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events 

• Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process

• Represent sample spaces for simple and compound events and find probabilities using organized lists, tables, tree diagrams, area models, and simulation

• Realize 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

• Design and use a simulation to generate frequencies for simple and compound events

• Analyze situations that involve two stages (or two actions)

• Use area models to analyze the theoretical probabilities for two-stage outcomes

• Analyze situations that involve binomial outcomes

• Use probability to calculate the long-term average of a game of chance

• Determine the expected value of a probability situation

• Use probability and expected value to make a decision

As you work on Problems in this Unit, ask your child questions about situations that involve analyzing probabilities:

• What are the possible outcomes for the event(s) in this situation?

• Are these outcomes equally likely?

• Is this a fair or unfair situation?

• Can I compute the theoretical probabilities or do I conduct an experiment?

• How can I determine the probability of one event followed by a second event: two-stage probabilities?

• How can I use expected value to help me make decisions?

Samples and Populations: Statistics

Concepts and Explanations         Worked Homework Examples        Math Background

Goals:

In Samples and Populations, your student(s) will learn about different ways to collect and analyze data in order to make comparisons and draw conclusions. They will learn how to:

• What is the population?

• What is the sample?

• Is the sample a representative sample?

• How can I describe the data I collected?

• How can I use my results to draw conclusions about the population?

• How can I use samples to compare two or more populations?