Grade 7 Mathematics Units 7-9 Summary

Illustrative Mathematics® Grade 7 Study Notes

Unit 7: Angles, Triangles, and Prisms

Angle Relationships

Lesson 1: Relationships of Angles

  • Special Angles: Understanding various angles including acute, obtuse, and straight angles.

  • Visualizing Angles:
      1. Comparison of Angles: Explore which angle is bigger; use diagrams for visualization.
      2. Obtuse Angles Identification: Identify obtuse angles in given diagrams.

  • Pattern Block Angles:
      1. Tracing Angles: Trace pattern blocks to identify angles, noting the number of unique angles per block.
      2. Hexagon Analysis: Determine the degree measure of angles in a hexagon by tracing and fitting multiple hexagons together.

  • Measurement of Angles:
      1. Concept of Straight Angles: An angle that forms a straight line; measure is 180 degrees.
      2. Tyler and Priya's Angle Measurement: Two students disagree on the angle measure, discussing reasoning behind their measurements.

Summary of Lesson 1

  • Adjacent Angles: Angles that share a side and a vertex and do not overlap.

  • Definitions:
      - Right Angle: Measures 90 degrees, can be visualized as a quarter turn.
      - Straight Angle: Two angles that form a line produce a straight angle measuring 180 degrees.

  • Practice Problems:
      - Practice drawing right angles and straight angles; quantify angles in triangles, squares, and octagons.

Lesson 2: Adjacent Angles

  • Estimating Angle Measures: Utilize protractors to measure angles.
      - Practice identifying complementary and supplementary angles that add to 90 and 180 degrees respectively.

  • Folding Paper Exercise: Predict angle measures through practical activities involving folding paper.

Summary of Lesson 2

  • Complementary Angles: Angles that add up to 90 degrees.

  • Supplementary Angles: Angles that add up to 180 degrees.

Nonadjacent Angles

Lesson 3: Nonadjacent Angles

  • Angle Relationships: Investigate angle measures through intersections using methods such as protractors.

  • Pairs Identification: Identify complimentary and supplementary pairs of angles among intersecting lines.

Solving for Angles

Lesson 4: Solving for Unknown Angles

  • Finding Unknown Angle Measures: Use equations to derive unknown angles in complex figures.

  • Angle Equations: Establish equations for adjacent and vertical angles relating to overall geometry problems.

Using Equations to Solve for Unknown Angles

Lesson 5: Using Equations to Solve for Unknown Angles

  • Equations Set Up: Key skills include deriving and manipulating equations to discover unknown angles in various geometric compositions.

Unit 8: Probability and Sampling

Introduction to Probability

Lesson 1: Mystery Bags

  • Likelihood Predictions: Understand how previous outcomes affect future predictions in random experiments (e.g., picking colored blocks).

Lesson 2: Chance Experiments

  • Define outcomes of chance events and probabilities associated with them.

  • Identify impossible, unlikely, equally likely, likely, and certain events.

Lesson 3: What Are Probabilities?

  • Defining Probability: Probability reflects how likely an event is to occur, represented as a fraction from 0 to 1.

  • Utilize sample spaces for calculating outcomes.

Lesson 4: Estimating Probabilities Through Repeated Experiments

  • Running Experiments: Observing likelihood through trial runs, appropriately estimating probabilities based on experimental data.

Lesson 5: More Estimating Probabilities

  • Dealing with variable outcomes and recognizing that probabilities can be expected based on empirical evidence collected through experimentation.

Unit 9: Putting It All Together

Restaurant Management and Operations

Lesson 1: Planning Recipes

  • Nutritional Information Calculations: For each ingredient, record the amount, calories per serving, and applicable conversions for serving sizes.

  • Serving Size Determination: Calculate amounts and calories based on meal servings.

Lesson 2: Costs of Running a Restaurant

  • Cost Estimation: Delve into the ongoing costs versus single-time costs for restaurant items, comparing measurable prices and predicting budget forecasts based on expected customer turnover.