Math 7 Unit 3

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In the first section, students simplify numeric expressions, thinking about them as groups of directions for the acrobat’s movement. They are introduced to the idea of a term, and recognize that terms must be simplified separately and then combined, thus establishing a correct Order of Operations. They also learn to see expressions with separate terms as ways to represent groups of objects.

In the second section of the chapter, students extend their thinking about integers from Chapter 2, as they work with + and – integer tiles (or tile spacers) to model subtraction of integers. Students look at the product of two negatives as repeated subtraction and learn that expressions with subtraction can be rewritten as equivalent expressions with addition.

In Section 3.3, students extend their learning about operations with portions to include dividing with fractions, mixed numbers, and decimals. Students focus on making sense of the operation of division, relying on diagrams, and reasoning before moving to an algorithm.

It is up to you how explicit you want the Mathematical Practices to be in your classroom. If you choose to discuss the Mathematical Practices in class with your students, now is a good time to stop and do so directly. This can be done as a quick whole group discussion, reflecting on the practices that they have already begun developing through the last two chapters. You might stop and have them do an entry in their Learning Logs related to their use of these Practices over the past weeks. You also might create a class poster and hang it in a prominent place in your room to keep the eight Mathematical Practices front and center in students’ minds.

Please remember, students are not expected to memorize the Mathematical Practices. Instead, developing these practices throughout the course will help students gain a more complete view of the mathematics that they are learning. Engaging in mathematics through the practices can also help students recognize the connections between the thinking skills that they learn in this class and those that they use in other areas of their lives.

In the lesson notes for Chapter 3, you are encouraged to revisit many of the Standards for Mathematical Practice. Even if they are not listed, the practices of making sense of problems and persevering to solve them, reasoning abstractly and quantitatively, and attending to precision apply to most every lesson in this course. As you circulate each day, encourage students to embrace these practices through your questioning.

7.NS.1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

c) Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

d) Apply properties of operations as strategies to add and subtract rational numbers.

7.NS.2. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

a) Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

b) Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real world contexts.

c) Apply properties of operations as strategies to multiply and divide rational numbers.

7.NS.3. Solve real-world and mathematical problems involving the four operations with rational numbers.

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