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Math 7

Math 7 . Unit 1 Patterns and Relations. What does it mean when I say, A number is divisible by 2? A number is divisible by 5? A number is divisible by 10?. Lesson 1.1 Patterns in Division. A number is divisible by 2 when 2 divides even into the number with no remainder.

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Math 7

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  1. Math 7 Unit 1 Patterns and Relations

  2. What does it mean when I say, • A number is divisible by 2? • A number is divisible by 5? • A number is divisible by 10? Lesson 1.1 Patterns in Division

  3. A number is divisible by 2 when • 2 divides even into the number with no remainder. Ex. 8 is divisible by 2 because 2 divides into 8, 4 times with no remainder.

  4. A number is divisible by 5 when • 5 divides even into the number with no remainder. Ex. 15 is divisible by 5 because 5 divides into 15, 3 times with no remainder.

  5. A number is divisible by 10 when • 10 divides even into the number with no remainder. Ex. 40 is divisible by 10 because 10 divides into 40, 4 times with no remainder.

  6. We can use counters to show divisibility? Is 12 divisible by 2? 5? 10? (Use counters here!)

  7. What numbers are divisible by 2? Even numbers, numbers that end 0, 2, 4, 6, 8. • What numbers are divisible by 5? Numbers ending with 0 or 5. • What numbers are divisible by 10? Divisibility Rules Numbers ending with 0.

  8. How do you know if a number is divisible by 4? Check the last two digits to see if it is divisible by 4. Is 412 divisible by 4? • How do you know if a number is divisible by 8? Check the last three digits to see if it is divisible by 8. Divisibility Rules Is 2168 divisible by 8?

  9. Hidden number exercise.

  10. Venn Diagrams. • Create a Venn Diagram for “Divisible by 4” and Divisible by 5”, using the number 16, 95, 20, 132, 248, 341

  11. Exercises: • Page 8-9 # 1, 2, 3, 4, 5, 6, 7 Finish for homework if not finished. Pass in exercise book before start of classes tomorrow.

  12. Are there any numbers that are divisible by 0? • Can you divide a number by zero? Example: Is 12 divisible by 0? Try taking 12 counters and putting them into 0 groups. Can you do it? Try taking 12 counters and putting them into groups of zero? Can you do it? So is 12 divisible by 0? No! Lesson 1.2 More Patterns in Division Is any number divisible by 0? No!

  13. Explore Activity: Divisible by 3 and 9. (Handout: lesson1-2-explore.doc)

  14. Lets make a rule for divisible by 6. We know that 2 x 3 = 6. So any number that is divisible by 6 is also divisible by 2 and 3. Rule: A number is divisible by 6 if it is divisible by 2 and 3. Divisible by 6:

  15. Rule: A number is divisible by 6 if it is divisible by 2 and 3. Is 432 divisible by 6? Is 128 divisible by 6? Divisible by 6:

  16. Create a Carroll diagram for “Divisible by 3” and “Divisible by 4” using the data below: 128, 420, 531, 122, 816, 702, 315, 636 Carroll Diagram (Page 12)

  17. Page 12-13: 1, 2 (explain), 3, 5, 6, 7 (explain), 8, 9 (Omit #4 and 10) Exercises:

  18. Go over homework (look at difficult questions) • Worksheet – Practice all divisibility rules.

  19. Find the factors of each number using divisibility rules. A) 116 B) 135 Exercises: Page 12, #4 Using Divisibility Rules to Factor

  20. Journal Entry #1 • Worksheet 2 – Extra Divisible Rules • Worksheet 3 – Factoring with Div. Rules Quiz 1.1 to 1.2

  21. The basis of algebra is the variable. It is a letter used to represent some quantity that can change. • Example: Suppose you work at McDonald’s and you get paid by the hour. The number of hours you work in a week could be represented by the variable h. If you get paid $10 an hour, then 10h would represent the amount of pay you would get when you work hhours. The 10h is an algebraic expression. Complete the table to show how much you would make if you worked each number of hours. Algebra – Algebraic Expressions

  22. 10h = 10 x h

  23. The algebraic expressions we will be working with will contain 3 parts: the variable, the numerical coefficient and the constant. • The variable is the letter being used, the numerical coefficient is the number in front of the variable (use a 1 if there is none) and the constant is the number which has no variable with it (use 0 if there is none).

  24. Complete the table.

  25. Identify some words that indicate each operation. Writing algebraic expressions for phrases.

  26. Write an algebraic expression for each phrase. • 3 more than a number • 4 times a number • a number decrease by 5 • double a number • a number divided by 6 • a number subtracted from 11 • twice a number increased by 8 • the sum of 3 times a number and 12 Writing algebraic expressions for phrases.

  27. Exercises: Page 18, #1 to 6

  28. Evaluating an expression means to find the value of the expression for a certain value of the variable. • To evaluate an algebraic expression you substitute a value in for the variable and simplify. Example: Evaluate each expression when n = 6 A. 2x – 5 B. C. 20 – 3n Evaluating Algebraic Expressions

  29. Exercises: Page 19 #7, 8, 9 Evaluating Algebraic Expressions

  30. We can create an input/output table for any algebraic expression. • Ex. Input/Output Tables

  31. A linear relation is a relation in which the output values increase or decrease by the same amount each time. • Ex: Does this input/output show a linear relation. • Write a linear relation for the input/output table. Writing Linear Relations for Input/Output Tables

  32. Exercises Page 27-28 • #1, 2, 3, 4

  33. Writing algebraic expressions for word problems.

  34. Exercises Page 23 & 24 #2, 3, 4, 5, 6, 7, 8 Mid-Unit Review Page 29 #1, 2, 3, 4, 5, 6, 7, 8

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