CAT Prep Essentials

Grade 8 | Duration: 60 minutes | 25 Students

Overview

This lesson is designed to prepare Grade 8 students for the California Achievement Test (CAT) by focusing on critical Common Core State Standards aligned math topics. The session incorporates interactive practice, strategic test-taking skills, and CAT-style questions covering:

Linear Equations and Inequalities
Functions and Graphing
Geometry (Angles, Volume, Surface Area)
Rational Numbers and Operations
Statistics and Probability

Common Core Standards Addressed

Standard Code	Description
8.EE.B.5-6	Graph proportional relationships, solve linear equations and inequalities.
8.F.A.1-2	Understand and analyze functions and interpret graphs.
8.G.A.1-3	Understand congruence and similarity, calculate volume and surface area of 3D figures.
8.NS.A.1-2	Perform operations with rational numbers fluently.
8.SP.A.1-3	Investigate patterns of association in bivariate data, calculate probabilities.

Learning Objectives

By the end of this 60-minute class, students will:

Solve and graph linear equations and inequalities with confidence (8.EE.B.5-6).
Interpret functions from tables and graphs and relate to real-world problems (8.F.A.1-2).
Calculate volume and surface area of composite 3D shapes, and solve angle problems (8.G.A.1-3).
Perform accurate operations with rational numbers in diverse formats (8.NS.A.1-2).
Analyze simple probability scenarios and summarize data through statistics (8.SP.A.1-3).
Employ effective CAT test-taking strategies to maximize performance.

Materials Needed

Whiteboard and markers
Student notebooks or worksheets (CAT-style questions handout)
Graph paper
Calculator (optional, as allowed by CAT guidelines)
Timer or clock
Colored pens for annotations

Lesson Procedure

1. Warm-Up and Strategy Introduction (7 minutes)

Activity: Begin with a brief open discussion: "What strategies do you already know for test-taking?"
Introduce 3 key test-taking tips for CAT:
1. Eliminate obviously wrong answers first.
2. Manage your time—don’t get stuck on one question.
3. Double-check units and answer formats.
Write these on the board for visual reinforcement.

2. Linear Equations & Inequalities (12 minutes)

Focus CCSS: 8.EE.B.5-6
Mini-Lesson: Quick refresher on solving and graphing linear equations and inequalities.
Example 1: Solve and graph: 3x - 7 ≤ 8
Example 2: Given a table representing a function y = 2x + 1, plot points and graph.
CAT-Style Practice:
- Question: If 4x + 5 = 21, what is x?
- Inequality: Graph x/2 - 3 > 1 on a number line.
Class Activity: Students solve and graph on their paper, then pair-share answers.

3. Functions & Graphing (8 minutes)

Focus CCSS: 8.F.A.1-2
Mini-Lesson: Function concept review, including how to determine if a relation is a function; interpret slope and intercept.
Example: Identify if a set of ordered pairs represents a function; graph y = -x + 4.
CAT-Style Practice:
- If y = 3x - 2, what is y when x = 5? What is the slope of the line?
Class Activity: Students work in small groups to determine function or not, and sketch graphs.

4. Geometry: Angles, Volume, Surface Area (10 minutes)

Focus CCSS: 8.G.A.1-3
Mini-Lesson:
- Calculate volume of composite solids (cylinders and rectangular prisms).
- Surface area formula review with examples.
- Angle relationships: supplementary, complementary, and vertical angles.
CAT-Style Practice:
- Find the volume of a cylinder with radius 3 cm and height 7 cm (π≈3.14).
- Calculate the surface area of a rectangular prism 4 cm by 5 cm by 6 cm.
- If two angles are supplementary and one is 65°, what is the other angle?
Class Activity: Students compute answers, write reasoning beneath each.

5. Rational Numbers and Operations (8 minutes)

Focus CCSS: 8.NS.A.1-2
Mini-Lesson: Multiplying, dividing, adding, and subtracting rational numbers (fractions, decimals, and negatives).
Example: -2.5 + 4.1 = ?; multiply: (3/4) × (2/5)
CAT-Style Practice:
- Solve: 5/6 ÷ 2/3
- Evaluate: -7 + (3 × -2)
Class Activity: Individual worksheet completion with immediate teacher feedback.

6. Statistics and Probability (7 minutes)

Focus CCSS: 8.SP.A.1-3
Mini-Lesson: Understanding simple probability problems and describing data distributions.
Example: Find the probability of rolling a sum of 7 with two dice.
CAT-Style Practice:
- If 30% of the class are left-handed, what is the probability a randomly selected student is right-handed?
- Interpret a box plot showing test scores.
Class Activity: Pair students to discuss and answer, then share results aloud.

7. Wrap-Up, Review, and Reflection (8 minutes)

Quick review quiz: 5 rapid-fire CAT-style questions pulling from each topic.
Ask students to write one ‘strategy’ and one ‘math tip’ they learned today on an exit ticket.
Encourage questions about content or test anxiety strategies.
Assign optional extra practice questions for homework.

Assessment & Feedback

Formative checks through individual and group activities.
Exit ticket reflections to gauge student confidence and understanding.
Collect worksheets for quick grading and identify areas needing reteach before the CAT.
Informally observe peer discussions and group work for engagement and comprehension.

Extensions & Differentiation

For advanced learners: Challenge them with multi-step CAT questions involving combined concepts (e.g., graphing linear inequalities from volume-related contexts).
For struggling learners: Provide graph templates and step-by-step problem scaffolding. Use manipulatives for geometry concepts (3D models).
Provide extra test-taking tips on time management and stress reduction for anxious students.

Notes to Teachers

Rotate between direct instruction and peer-supported learning to maintain engagement.
Model test-taking mindset by thinking aloud while solving sample CAT problems.
Remind students that accuracy and strategy matter equally for good test results.
This lesson strengthens both content and confidence—the perfect combination for CAT success!

End of Plan

Teaching Instructions