Math 6a Unit 1

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Welcome to math class! This chapter will introduce you to the mathematical practices that you will be using throughout this course and beyond. You will start by working with your classmates to make sense of and solve a series of challenging problems. These problems preview some of the mathematics that you will be learning throughout the year.

This chapter is designed to:

• Introduce students to some of the mathematical ideas on which this course is based.
• Establish class norms that will continue throughout the course, such as having students reflect in Learning Logs and using focus questions to drive learning.
• Provide an opportunity for the teacher to assess students’ skills and provide students an opportunity to review prerequisite material.
• Establish collaboration in teams of four and/or pairs.

CC1

In Section 1.1 you will work on several challenging investigations with your team. You will revisit some of the investigations later in this course. The main purpose of these problems is to introduce some of the big concepts of this math course, such as organizing data and using mathematical reasoning to make predictions.

Then in Section 1.2, you will develop multiple ways to represent (or show) mathematical ideas. You will represent your ideas using numbers, symbols, diagrams, words, and various kinds of tables.

CC2

These lessons, especially those in Section 1.1, are only meant as an introduction to the course! By no means should you expect students to have proficiency or mastery of these concepts by the end of this chapter. Instead, stress each day that students will need to apply their previous learning to solve new problems and that as they continue in this course, they will build a better understanding of these new ideas. These lessons will also allow you to informally assess your students’ prior knowledge. This will be helpful for guiding the level of scaffolding in future lessons when these topics are revisited.

Section 1.1 includes five engaging activities that set the stage for student work through the course. While these problems are not intended to bring closure to any major concept, they are intended to launch major ideas, such as identifying unknowns and the study of probability.

In this chapter it is suggested that you do not yet introduce the practices explicitly, but rather encourage students to begin engaging in these practices through your directions and your questions.

In the lesson notes for Chapter 1, six practices are identified.

Practice 1: Make sense of problems and persevere in solving them.

Practice 2: Reason abstractly and quantitatively.

Practice 3: Construct viable arguments and critique the reasoning of others.

Practice 6: Attend to precision.

Practice 7: Look for and make use of structure.

Practice 8: Look for and express regularity in repeated reasoning.

After focusing on one practice per day initially, you might begin to encourage the use of more than one if it is appropriate. More practices will be introduced in Chapter 2. It is suggested, if you plan to make these practices explicit in your classroom that you begin Chapter 3 with a formal introduction to all eight of the mathematical practices.

6.G.1. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

6.SP.4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

6.NS.4. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).

6.EE.1. Write and evaluate numerical expressions involving whole-number exponents.

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