Math Overview - Grade 7

Unit 1: Scaled Copies

Instructional Snapshot

• Use several different “printers” to copy a figure and use descriptions of how these printers are broken to develop characteristics of figures that are and are not scaled copies
• Explore scaling a mosaic they designed using different scale factors and notice how the number of small tiles is affected by the scale factor
• Use real-world distances of states to calculate scaled distances and create their own scale drawings
• Work with the idea of scale in the context of scaled copy of a basketball court, determining how to make the court fit in a particular space  
• Choose an appropriate scale for a scale drawing and create a drawing using that scale as they redesign a room

Unit 2: Introducing Proportional Relationships

Instructional Snapshot

• Determine, interpret, and use constants of proportionality to make sense of proportional relationships about sugary drinks
• Examine graphs of proportional relationships in the context of gas mileage and explore strategies for determining the constant of proportionality from points on these lines
• Make connections between the features of a proportional relationship's graph, equation and table of values using graphic organizers
• Use their understanding of proportional relationships to explore whether baths or showers use more water

Instructional Snapshot

• Measure various round objects to explore the relationship between diameter and circumference
• Calculate the perimeter of complex shapes composed of fractions of circles
• Reason and make sense of the relationship between the radius of a circle, the square of the radius, and the area of the circle
• Solve challenges like calculating the area of a square and a circle based on the perimeter

Unit 4: Proportional Relationships and Percentages

Instructional Snapshot

• Use constants of proportionality to decide which of three recipes is the least sweet and to scale up a recipe to serve more people
• Represent problems involving percent increase or decrease using equations, tape diagrams and double number lines
• Calculate the original amount, the new amount, or the percent change in the context of sales tax and tip
• Solve problems about increases in minimum wage and the cost of college over time
• Generate questions related to either prison populations or the wage gap in the U.S. and work in pairs to use representations to answer their questions using the information given
• Convert fractions to decimals using the standard algorithm for division

Unit 5: Operations with Positive and Negative Numbers

Instructional Snapshot

• Manipulate visual models (floats and anchors, bumpers on number lines) to add and subtract integers
• Reason about the signs and values of expressions by solving number puzzles 
• Explore the product of two numbers using floats and anchors to represent positive and negative numbers
• Use the context of position, rate and time as a model to understand division of signed numbers
• Analyze our environment and make sense of changing temperatures around the world and sea ice melt

Unit 6: Expressions, Equations, and Inequalities

Instructional Snapshot

• Manipulate shapes on balanced hangers to solve equations
• Compare and contrast visual representations and equations, in factored and expanded form
• Collaborate on Equation Roundtable while solving equations to receive feedback from peers and revise their thinking
• Practice writing, graphing and solving inequalities in the context of required height at an amusement park
• Use what they know to write and solve inequalities related to situations about budgeting and spending money

Unit 7: Angles, Triangles and Prisms

Instructional Snapshot

• Use rulers and protractors to draw triangles given three measurements and consider information needed to make identical copies 
• Use virtual manipulatives to notice that not all combinations of three side lengths create a triangle and reason about the characteristics of side lengths that do create triangles
• Investigate possible cross sections of different solids using the cross-section interactive tool to explore a cube and a triangular pyramid; reason about possible cross sections of a triangular prism
• Consider how to maximize a piece of paper to create a popcorn container that holds the most popcorn  

Unit 8: Probability and Sampling

Instructional Snapshot

• Conduct experiments and use phrases such as “likely” and “equally likely as not” to describe different events
• Use repeated experiments and proportionality to predict the contents of a mystery bag, recognizing that the number of repeated experiments affects the accuracy of your prediction
• Challenge their assumptions about probability tools such as coins and number cubes; decide whether or not an object is fair by comparing probabilities from a model to the results of a repeated experiment
• Use lists, tables, and tree diagrams to represent the sample space of events with multiple pennies or spinners, use these tools to determine the probabilities of multistep events and consider whether or not different games are fair
• Review headlines produced from different samples of data and explain whether or not a given sampling method is likely to produce data that is representative of the population
• Analyze real data about asthma rates; generate random samples and use them to compare the asthma rates of different places in New York