Grade 7 - Chapter 1 -Recall Prior Knowledge

Transcription

1 MATH IN FOCUS Grade 7 - Chapter 1 -Recall Prior Knowledge REFRESH YOUR MEMORY!

2 CHAPTER 1 Recall Prior Knowledge In order to be successful with the new information in Chapter 1, it is necessary to remember the important facts from previous learnings. The following pages will provide some reminders and examples of the important information.

3 SECTION 1 Recognizing Types of Numbers Starting with the whole number zero in the middle of our number line, all positive whole numbers appear to the right of zero. All negative whole numbers appear to the left of zero. Remember: The further left of zero a number is, the less value it represents. i.e. -4 is smaller than -3. IMPORTANT FACTS 1. A horizontal number line can show where all numbers should be placed. 1. Whole numbers 2. Negative numbers 3. Fractions 4. Decimals All have a home on a number line. All positive proper fractions (the numerator is smaller than the denominator) occur between zero and one on a number line. All negaitve proper fractions (the numerator is smaller than the denominator) occur between negative one and zero on a number line. The decimal part of a number places the number between two integers. The larger the decimal, the closer to the larger interger the number lives. 5.3 occurs between 5 and 6 but closer to the five than the 6 because of the.3 part is less than lives between 6 and 7 but very close to the appears between -2 and -3 but closer to -2. Check out page 3 in your textbook to make sure you understand these concepts. 2

4 MOVIE 1.1 See and hear Mr. Hampshire talk about this topic. Chapter 1 Recall Prior Knowledge - Recognizing types of numbers. Click here to view a lesson created on Educreation about recognizing types of numbers.

5 REVIEW 1.1 Using the < sign, order the numbers from least to greatest: REVIEW 1.2 Using the < sign, order the numbers from least to greatest: 11/17, 1 ⅗, 0.3, 1.7, 19/10 ½, 6/9, ⅓, 4/7, ⅗ A. 11/17 < 1 ⅗ < 0.3 < 1.7 < 19/10 B. 0.3 < 11/17 < 1 ⅗ < 1.7 <19/10 C. 0.3 < 19/10 < 11/17 < 1.7 < 1 ⅗ D. 19/10 < 1.7 <0.3 < 1 ⅗ < 11/17 A. 1/2 < ⅗ < 6/9 < ⅓ < 4/7 B. ⅗ < ½ < 4/7 < 6/9 <⅓ C. ⅓ < ½ <4/7 <⅗ < 6/9 D. ½ <⅓ < ⅗ < 4/7 <6/9 4

6 SECTION 2 Comparing Decimals Place Value Chart: 1. Start by comparing the highest value that both numbers have, if one is larger than the other, then that number is larger. 2. If they are the same, look at the next highest value that both numbers have, if one is larger than the other, then that number is larger. IMPORTANT FACTS 1. There are two ways to compare decimals: 3. If they are still the same, look at the next highest value... Continue this until the values are different and if one is larger than the other, then that number is larger. 1. Use a place value chart 2. Use a number line Use a Number Line: 1. Place both decimals accurately on a number line. 2. Whichever decimal lies to the right of the other is the larger decimal. Review the section on page 3 of your text called Comparing decimals to see some examples of these processes. 5

7 MOVIE 1.2 See and hear Mr. Hampshire talk about this topic. Chapter 1 Recall Prior Knowledge - Comparing Decimals Click here to view a lesson created on Educreation about Comparing Decimals.

8 REVIEW 1.3 Compare the following decimals: REVIEW 1.4 Compare the following decimals: REVIEW 1.5 Compare the following decimals: A. = B. < C. > A. = B. < C. > A. = B. < C. > 7

9 SECTION 3 Rounding Numbers Knowing the place value of the number is very important: GALLERY 1.1 Place Value Chart IMPORTANT FACTS 1. When we round a number we have to know to which place we are rounding. 2. After we are sure of the place, we look to the right of that place and follow the following rules: 1. If the number to the right of the place we are rounding is 0, 1, 2, 3, or a 4, then we drop it and everything else to the right. 2. If the number to the right of the place we are rounding is a 5 or above (5, 6, 7, 8, or 9), we increase the number to which we are rounding by 1 and drop everything else to the right. 3. You can then replace any of the dropped numbers with zeroes. Notice the decimal point first and then remind yourself of the columns and their value. Example: What is rounded to the hundredths place? Since 6 is in the hundredths place, we look at the 8. Since it is greater than 5 we round the 6 to a seven and drop all other numbers: We can put zeroes in if need be:

10 Round to the indicated place: to the hundredths place to the thousandths place to the tenths place to the hundredths place (Underlined place value) (Hint: 1.99 rounds to 2.00)

11 MOVIE 1.3 See and hear Mr. Hampshire talk about this topic. Chapter 1 Recall Prior Knowledge - Rounding Numbers Click here to view this as a Educreation.

12 REVIEW 1.6 Round to the nearest hundred. REVIEW 1.7 Round to the nearest whole number. REVIEW 1.8 Round to the nearest 10. 1, ,923 A. 1,400 B. 1,450 C. 1,500 A. 849 B C. 850 A. 4,920 B. 4,900 C. 4,930 11

13 REVIEW 1.9 Round to 1 decimal place REVIEW 1.10 Round to the nearest hundredth REVIEW 1.11 Round to the nearest ones place , A B C. 24 A B C A. 9,909 B. 9,908 C. 9,910 12

14 SECTION 4 Finding squares, cubes, square roots, and cube roots IMPORTANT FACTS 1. The square of a number is that number multiplied by itself. 2. The cube of a number is that number multiplied by itself 3 times. 3. Square root of a number is a number that when multiplied by itself, the product equals that number. 4. Cube root of a number is a number that when multiplied by itself three times, the product equals that number (5 squared), 5 3 (5 cubed), 4 (square root of 4), 8 (cube root of 8) Finding squares: Take the number and multiply it by itself. 5 2 = 25 because 5 5 = 25, 7 2 = 49 because 7 7 = 49 Finding cubes: If you remember that a cube is a 3D (3 dimension) shape, it will be easier to remember to multiply the number three times! 5 3 = 125 because = = 8 because = 8 Finding square roots: If the number is a perfect square (the square of a whole number) then just find what whole number times itself is equal to the number in the radical Any other square root is more difficult to find. You can estimate the answer by finding which two perfect squares the number is between. For example 6 is between 2 and 3 because 2 squared is 4 and 3 squared is 9. You can guess and test to find a good estimate. There are more accurate ways of doing these skills as well. Finding cube roots: If the number is a perfect cube (the cube of a whole number) then just find what whole number times itself three times is equal to the number in the radical. 13

15 MOVIE 1.4 See and hear Mr. Hampshire talk about this topic. Chapter 1 Recall Prior Knowledge - Finding Squares, cubes, square roots, and cube roots Click here to view a lesson about this on Educreation.

16 REVIEW 1.12 Find the square. REVIEW 1.13 Find the cube A. 8 B. 16 C. 2 D. 1 A. 18 B. 2 C. 216 D

17 REVIEW 1.14 Find the square root. REVIEW 1.15 Find the cube root A B. 25 C. 125 D. 5 A. 4 B. 8 C. 6 D

18 SECTION 5 Determining Absolute Value Examples: 9 = 9 because 9 is 9 units from zero on a number line. -4 = 4 because -4 is 4 units from zero on a number line. 2 = 2 because 2 is 2 units from zero on a number line. -99 = 99 because 99 is 99 units from zero on a number line. IMPORTANT FACTS 1. The absolute value of a number may be thought of as its distance from zero on a number line. -3 = 3 because 3 is 3 units from zero on a number line. GALLERY 1.2 Absolute Value 2. The absolute value symbol is n. Two vertical lines on either side of the number. 1. Note- The number n stands for any number. Examples 17

19 MOVIE 1.5 See and hear Mr. Hampshire talk about this topic. Chapter 1 Recall Prior Knowledge - Determining Absolute Value Click here to view a lesson about this on Educreation.

20 REVIEW 1.16 Find the absolute value. -3 REVIEW 1.17 Find the absolute value. 3 REVIEW 1.18 Compare -7 7 A. -3 B. 3 C. 0 D. ⅓ A. -3 B. 3 C. 0 D. 1/3 A. < B. > C. = 19

21 Perfect square A whole number which is multiplied by itself. Related Glossary Terms Drag related terms here Index Find Term

22 Radical Sign Related Glossary Terms Drag related terms here Index Find Term