Unit 5: Moving Straight Ahead: Linear Relationships

The next unit in your child’s mathematics class this year is Moving Straight Ahead: Linear Relationships. In this unit, students are developing skills in areas that are traditionally known as algebra. This unit introduces them to situations that can be modeled with linear functions and graphed with straight lines.

UNIT GOALS

The primary goal of this unit is to develop understanding of linear relationships or linear functions. Students learn to recognize linear functions by the constant rate of change between two variables in a verbal context, table, graph, and equation.

Students identify, represent, and interpret linear relationships. They solve linear equations and write equations for lines. These last two ideas will be revisited with more complexities in later units—in particular, the Thinking with Mathematical Models and Say It with Symbols units.

Investigation 1: Running Rates

• Notebook (Sem 2, Week 3 and part of Week 4)
• ACE Questions

Investigation 2: Exploring Linear Functions with Graphs and Tables

• Notebook (Sem 2, Week 4)
• ACE Questions

Investigation 3: Solving Equations

• Notebook (Sem 2, Week 5)
• ACE Questions

Investigation 3 continued: Solving Equations

• Notebook (Sem 2, Week 6)
• ACE Questions

Unit 3: Comparing and Scaling: Ratio, Proportion and Percent

The next unit in your child’s mathematics class this year is Comparing and Scaling: Ratio, Proportion, and Percent. Students look at problems involving many situations and learn to make comparisons using ratios, fractions, percents, and rates.

UNIT GOALS

One goal of this unit is to develop students’ abilities to make useful comparisons of quantitative information using ratios, fractions, decimals, rates, unit rates, and percents. A second goal is to have students learn to use quantitative comparison information to make larger or smaller scale models.

Students should also learn different ways to reason in proportional situations and to recognize when such reasoning is appropriate.List of Class Readings/Resources (organized by date)

Investigation 1: Making Comparisons

• Notebook
• ACE Questions
• Text 1.1 (Monday 1/10)
• Text 1.2 (Tuesday 1/11)
• Text 1.3 (Friday 1/15)

Investigation 2: Comparing Ratios, Percents and Fractions

• Notebook (Sem 2, Week 1)
• ACE Questions

Investigation 3: Comparing and Scaling Rates

• Notebook (Sem 2, Week 2)
• ACE Questions

Unit 2: Stretching and Shrinking: Similarity

The next unit in your child’s mathematics class this year is Stretching and Shrinking: Similarity. Its focus is geometry, and it develops understanding of and skill in the use of concepts of similarity.

UNIT GOALS

In this unit, your child will use properties of similar figures to explore reductions and enlargements such as those made on copy machines. Similarity will also be used to estimate the height of real objects (such as buildings and flagpoles) and the distance across large areas (such as ponds).

The problems are designed to help students begin to reason proportionally by scaling in geometry situations. By the end of this unit, your child will know how to create similar figures, how to determine whether two figures are similar, and how to predict the relationship between lengths and areas for two similar figures. The next unit, Comparing and Scaling, continues to develop proportional ideas in numerical, rather than geometric, contexts.

List of Class Readings/Resources (organized by date)

Investigation 1: Enlarging and Reducing Shapes

• Notebook
• ACE Questions
• Text 1.1 (Tuesday - 11/02)
• Text 1.2 (Wednesday - 11/03)
• Text 1.3 (Thursday - 11/04)

Investigation 2: Similar Figures

• Notebook
• ACE Questions
• Text 2.1 (Monday - 11/08)
• Text. 2.2 (Tuesday - 11/09)
• Text 2.3 (Wednesday - 11/10)

Investigation 3: Similar Polygons

• Notebook
• ACE Questions
• Text 3.1 (Monday - 11/15 and Tuesday 11/16)
• Text. 2.2 (Wednesday - 11/17)
• Text 2.3 (Thursday - 11/18)

Investigation 4: Similarity and Ratios

• Notebook
• ACE Questions
• Text 4.1 (Monday - 11/29 and Tuesday 11/30)
• Text. 4.2 (Wednesday - 12/01)
• Text 4.3 (Thursday - 12/02)

Investigation 5: Using Similar Triangles and Rectangle

• Notebook
• ACE Questions
• Text 4.1 (Monday - 12/06 and Tuesday 12/07)
• Text. 4.2 (Wednesday - 12/08)
• Text 4.3 (Thursday - 12/09)

End of Unit Project: Shrinking or Enlarging Pictures

Unit 1: Variables and Patterns: Introducing Algebra

The first unit in your child’s mathematics class this year is Variables and Patterns: Introducing Algebra.

UNIT GOALS

This unit’s focus is on ways to describe situations that change. In the first part of the unit, students explore three ways of representing a changing situation: with a description in words, with a data table, and with a graph. These representations are compared to one another to elicit the strengths of each presentation.

Students learn to write symbolic expressions as a shorter, quicker way to give a summary of the relationship between two variables.

List of Class Readings/Resources (organized by date)

Investigation 1: Variables, Tables and Coordinate Graphs

• Notebook
• ACE Questions
• Text 1.1 (Tuesday - 9/07)
• Text 1.2 (Wednesday - 9/08)
• Text 1.3 (Thursday - 9/09)
• Text 1.4 (Friday - 9/10)
• Text 1.5 (Monday - 9/13)

Investigation 2: Analyzing Graphs and Tables

• Notebook
• ACE Questions
• Text 2.1 (Tuesday - 9/14)
• Text 2.2 (Monday - 9/20)
• Text 2.3 (Tues 9/20 and Weds 9/21)

Investigation 3: Rules and Equations

• Notebook
• ACE Questions
• Text 3.1 (Monday 9/27 and Tues. 9/28)
• Text 3.2 (Wednesday 9/29)
• Text 3.3 (Thursday 9/30)

Variables and Patterns Project

• Metric Conversion and Unit Conversion Practice (Mon. 10/04)
• Grand Canyon Problem (Tues 10/05) For Distance Interval Trail Map Click Here and for Sample of Data Table and Graph Comparing Distance and Elevation Against Time Click Here.
• My Me Mobile Project Notebook (Wednesday 10/06 through 10/15 . . . possibly longer)
• Click Here to View Slideshow of Some Awesome Mobiles.
• Sample of how to convert weight to force.
• Sample Calculations Page

Unit 4: Accentuate the Negative: Positive and Negative Thinking

The next unit in your child’s course of study in mathematics class this year is Accentuate the Negative: Positive and Negative Numbers. Although students have intuitively used operations on integers to make sense of some situations in their everyday world, this unit looks at formal ways to compute with these numbers.

UNIT GOALS

In this unit, the focus is on understanding and developing systematic ways to add, subtract, multiply, and divide positive and negative numbers. Students will develop algorithms for computations and will use the order of operations, the Commutative Property, and the Distributive Property to solve problems.

Unit 6: Filling and Wrapping: Three Dimensional Measurement

The next unit in your child’s mathematics class this year is Filling and Wrapping: Three-Dimensional Measurement. Its focus is volume (filling) and surface area (wrapping) of objects, especially rectangular prisms, cylinders, cones, and spheres. In addition, students extend their understanding of similarity and scale factors to three-dimensional figures.

UNIT GOALS

Students develop strategies for measuring the surface area and volume. Their strategies are discussed and used to formulate rules for finding the surface area and volume of rectangular prisms and cylinders. They also investigate other solids—including cones and spheres—to develop volume relationships.

Ideas from previous units will be revisited and extended in this unit. For example, from the Stretching and Shrinking unit, the connection of how changing the scale of a box affects its surface area and volume will be studied.

Unit 7: What Do You Expect? Probability and Expected Value

The next unit in your child’s mathematics class this year is What Do You Expect?: Probability and Expected Value. This unit is about the concepts of probability and will help students understand common ideas that they read or hear about every day. They will explore long-range expectations in probability situations and learn how to make better predictions.

UNIT GOALS

Students will learn to find probabilities in two ways: by conducting trials and collecting experimental data, also by analyzing situations to determine theoretical probabilities. As they work, students will be using fractions, decimals, and percents to describe how likely events are.

Unit 8:Data Distributions: Describing Variability and Comparing Groups

The next unit in your child’s mathematics class this year is Data Distributions: Describing Variability and Comparing Groups. Students will learn to choose among a variety of representations to display distributions and will analyze, describe, and compare sets of data.

UNIT GOALS

Exploring statistics as a process of data investigation involves a set of four interrelated components (Graham, 1987).

• Posing the question: formulating the key question(s) to explore and deciding what data to collect to address the question(s);

• Collecting the data: deciding how to collect the data as well as actually collecting it;

• Analyzing the data: organizing, representing, summarizing, and describing the data and looking for patterns in the data; and

• Interpreting the results: predicting, comparing, and identifying relationships and using the results from the analyses to make decisions about the original question(s).

This dynamic process often involves moving back and forth among the four components.