MAFS.7.EE: Expressions and Equations

MAFS.7.EE.1: Use properties of operations to generate equivalent expressions.

MAFS.7.EE.1.1: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Adding Real Numbers
Finding Factors with Area Models
Sums and Differences with Decimals

MAFS.7.EE.2: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

MAFS.7.EE.2.3: 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.

Percents, Fractions, and Decimals
Real Number Line - Activity A
Real Number Line - Activity B

MAFS.7.EE.2.4: 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.

MAFS.7.EE.2.4.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.

Modeling and Solving Two-Step Equations
Order of Operations
Road Trip (Problem Solving)
Solving Two-Step Equations

MAFS.7.EE.2.4.b: Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.

Compound Inequalities
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

MAFS.7.G: Geometry

MAFS.7.G.1: Draw, construct, and describe geometrical figures and describe the relationships between them.

MAFS.7.G.1.1: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Adding Real Numbers
Area of Triangles

MAFS.7.G.1.2: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Classifying Triangles
Segment and Angle Bisectors

MAFS.7.G.2: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

MAFS.7.G.2.4: 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.

Circles: Circumference and Area

MAFS.7.G.2.5: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Modeling and Solving Two-Step Equations
Solving Two-Step Equations

MAFS.7.G.2.6: 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.

Area of Parallelograms
Area of Triangles
Prisms and Cylinders - Activity A
Segment and Angle Bisectors
Surface and Lateral Area of Prisms and Cylinders

MAFS.7.RP: Ratios and Proportional Relationships

MAFS.7.RP.1: Analyze proportional relationships and use them to solve real-world and mathematical problems.

MAFS.7.RP.1.1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

Area of Triangles
Part-to-part and Part-to-whole Ratios
Polling: Neighborhood
Road Trip (Problem Solving)

MAFS.7.RP.1.2: Recognize and represent proportional relationships between quantities.

MAFS.7.RP.1.2.a: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

Fraction Garden (Comparing Fractions)
Points, Lines, and Equations
Polling: Neighborhood
Toy Factory (Set Models of Fractions)

MAFS.7.RP.1.2.b: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Elevator Operator (Line Graphs)
Road Trip (Problem Solving)

MAFS.7.RP.1.2.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.

Elevator Operator (Line Graphs)
Road Trip (Problem Solving)

MAFS.7.RP.1.3: Use proportional relationships to solve multistep ratio and percent problems.

Part-to-part and Part-to-whole Ratios
Percents and Proportions
Polling: Neighborhood

MAFS.7.SP: Statistics and Probability

MAFS.7.SP.1: Use random sampling to draw inferences about a population.

MAFS.7.SP.1.1: 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.

Polling: City
Polling: Neighborhood
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

MAFS.7.SP.1.2: 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.

Polling: City
Polling: Neighborhood
Probability Simulations

MAFS.7.SP.2: Draw informal comparative inferences about two populations.

MAFS.7.SP.2.3: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability.

Describing Data Using Statistics
Mean, Median and Mode
Movie Reviewer (Mean and Median)
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

MAFS.7.SP.2.4: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.

Mean, Median and Mode
Movie Reviewer (Mean and Median)
Polling: Neighborhood
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

MAFS.7.SP.3: Investigate chance processes and develop, use, and evaluate probability models.

MAFS.7.SP.3.5: 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.

Spin the Big Wheel! (Probability)

MAFS.7.SP.3.7: 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.

MAFS.7.SP.3.7.a: Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.

Spin the Big Wheel! (Probability)

MAFS.7.SP.3.7.b: Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

Spin the Big Wheel! (Probability)

MAFS.7.SP.3.8: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

MAFS.7.SP.3.8.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.

Compound Independent Events
Compound Independent and Dependent Events

MAFS.7.SP.3.8.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., Â?rolling double sixesÂ?), identify the outcomes in the sample space which compose the event.

Compound Independent Events
Compound Independent and Dependent Events
Histograms
Permutations and Combinations
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

MAFS.7.SP.3.8.c: Design and use a simulation to generate frequencies for compound events.

Compound Independent Events
Compound Independent and Dependent Events

MAFS.7.NS: The Number System

MAFS.7.NS.1: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

MAFS.7.NS.1.1: 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.

MAFS.7.NS.1.1.a: Describe situations in which opposite quantities combine to make 0.

Comparing and Ordering Integers

MAFS.7.NS.1.1.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.

Adding Real Numbers
Adding and Subtracting Integers
Adding and Subtracting Integers with Chips
Sums and Differences with Decimals

MAFS.7.NS.1.1.c: Understand subtraction of rational numbers as adding the additive inverse, p Â? q = p + (Â?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.

Real Number Line - Activity A
Real Number Line - Activity B
Sums and Differences with Decimals

MAFS.7.NS.1.1.d: Apply properties of operations as strategies to add and subtract rational numbers.

Sums and Differences with Decimals

MAFS.7.NS.1.2: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

MAFS.7.NS.1.2.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 (Â?1)(Â?1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

Chocomatic (Multiplication, Arrays, and Area)
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals

MAFS.7.NS.1.2.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 Â?(p/q) = (Â?p)/q = p/(Â?q). Interpret quotients of rational numbers by describing real-world contexts.

Dividing Fractions
Dividing Mixed Numbers

MAFS.7.NS.1.2.c: Apply properties of operations as strategies to multiply and divide rational numbers.

Dividing Fractions
Dividing Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals

MAFS.7.NS.1.2.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.

Percents, Fractions, and Decimals

MAFS.7.NS.1.3: Solve real-world and mathematical problems involving the four operations with rational numbers.

Adding Real Numbers
Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals