# Chapter 1: Number Relationships

This is the 2014 version of this unit. For the 2015 version, go here.

Whether you're teaching or studying a unit for the first time, one of the first questions that always pops up is "What are we going to learn?". It is usually followed very closely by "Why should I learn that?" In this post, I hope to answer both those questions within the context of the Ontario grade 8 curriculum. As a teacher, this chapter will be most useful to other teachers, since the lesson plans are written from that perspective. However, the lessons could be just as useful as review for students who have already covered the material with a teacher, tutor or some other mentor.

**Year at a Glance.** In the context of the overall year, this is chapter 1, "Number Relationships". Links will become active as chapters come online. All links should be up by the end of 2014. Here is the post I wrote on my year-long lesson plans. And here's the list of chapters:

- Chapter 1: Number Relationships
- Chapter 2: Proportional Relationships
- Chapter 3: Collecting, Organizing and Displaying Data
- Chapter 4: Patterns and Relationships
- Chapter 5: Measurement of Circles
- Chapter 6: Integer Operations
- Chapter 7: Transformations
- Chapter 8: Equations and Relationships
- Chapter 9: Fraction Operations
- Chapter 10: Angles and Triangles
- Chapter 11: Geometry and Measurement Relationships
- Chapter 12: Probability

**Chapter Overview / Table of contents.** In this chapter, students will learn how to ...

- Chapter 1: Number Relationships
- Identify prime and composite numbers (1.1)
- Express numbers through their prime factors (1.2)
- Find common factors and common multiples (1.3)
- Calculate powers / exponents (1.4)
- Express numbers in expanded form and scientific notation (1.5)
- Mid-Chapter Quiz: Lessons 1.1 - 1.5: Mid-Chapter Review and Quiz
- Calculate square roots (1.6)
- Explore square roots and squares (1.7)
- Use the order of operations (1.8)
- Chapter Test: Lessons 1.1 - 1.8: Chapter Self-Test, Review and Test Questions (Click to view/print PDF)

**Vocabulary.** For the final test, students should be comfortable with the following vocabulary:

- Factor (1.1)
- Multiple (1.1)
- Prime (1.1)
- Composite (1.1)
- Prime factorization (1.2)
- Greatest common factor (1.3)
- Least common multiple (1.3)
- Factor tree (1.3)
- Venn diagram (1.3)
- Power, exponent (1.4)
- Scientific notation (1.5)
- Expanded form (1.5)
- Square root (1.6)
- Brackets (1.8)
- Order of operations (1.8)

**Support Questions.** At the end of the chapter, students should be able to answer the following questions from Nelson Mathematics 8. If you are using a different textbook, the questions will of course be different.

- Nelson Mathematics 8, p. 43, Practice Questions # 1, 2, 6, 8, 9, 10
- Workbook, p. 13, # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12

**Jump Math Support.** If you are looking for additional support, either for your students or for yourself, the following units from the grade 8 Jump Math program will help you (teachers can login on the left at that link for additional free teacher resources).

- NS8-1 Factors and Multiples
- NS8-2 LCMs and GCFs
- NS8-3 Prime Numbers
- NS8-4 Prime Factorization
- NS8-5 Prime Factorizations and GCFs
- NS8-6 Prime Factorizations and LCMs
- NS8-7 Order of Operations
- NS8-58 Perfect Squares
- NS8-59 Factors of Perfect Squares
- NS8-60 Square Roots of Perfects Squares
- NS8-61 Prime Factorizations of Perfect Squares
- NS8-62 Square Roots of Non-Perfect Squares
- NS8-63 Estimating Square Roots
- NS8-104 Introduction to Powers
- NS8-105 Investigating Powers
- NS8-106 Powers and Expanded Form

**Test Questions.** Lessons 1.1 - 1.8.

- Match vocabulary with definitions
- True-or-false, based on the vocabulary
- Variants on the Support Questions listed above
- Selected questions from Jump Math (these can be accessed by creating a free teacher account here)
- Part 1, Unit 1, Quiz 1 - 7
- Part 1, Unit 3, Test 58 - 63
- Part 2, Unit 5, Test 104 - 110

**Table of contents.** Not what you're looking for? Try the main Grade 8 Nelson Mathematics Lesson Plans.