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Numbers, Number Sense & Number Operations

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Vocabulary List Sum- the answer to an addition problem Difference- the answer to a subtraction problem Product- the answer to a multiplication problem Quotient- the answer to a division problem Exponent- a number that tells how many times a base is used as a factor Order of Operations- 1. ( ) 2. exponents 3. multiply or divide (left to right) 4. add or subtract (left to right) GCF- the greatest factor that two or more numbers have in common LCM- the least common multiple of two or more denominators Factor- a number that is multiplied by another number to find a product Multiple- the product of a given whole number and another whole number Percent- the ratio of a number to 100, per hundred Ratio- a comparison of two numbers, a and b, written as a fraction Proportion- an equation that shows that two ratios are equal Decimal- a number with one or more digits to the right of the decimal point Improper fraction- a fraction whose top number is bigger than the bottom number Equivalent- the same amount, equal Mixed number- a number represented by a whole number and a fraction Simplest form-the numerator & denominator of a fraction have no common factors other than 1 Numerator- the part of the fraction that tells how many parts are being used (the top number) Denominator- the part of the fraction that tells how many equal parts are in the whole (the bottom number)

FRACTIONS (Graphic organizer) Explain below how to solve fractions. List the steps in order 1-6.

Prime and Composite Numbers (Hands-On Activity) Learn what prime and composite numbers are and how to identify them. Materials Needed: Have several square cards (or tiles). At least 20 cards would be useful. You can even use "Post-It" notes. Each card (tile) is assumed to have one square unit area for simplicity. If you can’t make these cards, you can draw them on the board and complete the lesson. Teacher Instructions: Take 4 cards and ask the students to arrange them into possible areas. Students will easily figure out that only the following two configurations are possible. In both cases, area is 4 square units. In the first case, 4 tiles arranged in 1 row form the area. It is a 4 x 1 rectangle. In the second case, 2 tiles arranged in 2 rows form the area. It is a 2 x 2 square. Both figures represent the same area. This means number 4 can be written as 4 x 1 or 2 x 2. Tell the students, in such cases, we can say numbers 1, 2 and 4 are factors of 4. Draw students’ attention to the fact that number 4 can be divided by 1, 2 and 4. Ask the students to do another example with 6 tiles. In the first case, 6 tiles arranged in 1 row form the area. It is a 6 x 1 rectangle. In the second case, 3 tiles arranged in 2 rows form the area (2 tiles arranged in 3 rows will be the same). It is a 3 x 2 rectangle (or 2 x 3 rectangle). All figures represent the same area. This means number 6 can be written as 6 x 1, 3 x 2 or 2 x 3. So, 1, 2 and 3 are factors of 6. Draw students’ attention to the fact that number 6 can be divided by 1, 2 and 3. If necessary do more examples with numbers such as 8 and 10 until all the students understand this concept.

Now tell them, when a number such as 4, 6, and 8 has more than two factors, it is called a composite number. Now ask the students to do the same exercise with 3 tiles. In this case, there is only one option and that is 3 tiles arranged in 1 row. There are no other configurations available. So number 3 can only be written as 3 x 1. This means there are only two factors for 3, and they are 1 and 3. Draw the students’ attention to the fact 3 can be divided only by 1 and 3 (itself). Ask the students to do another example with number 5. Here again, 5 x 1 is the only option. This means there are only two factors for 5, and they are 1 and 5. Draw the students’ attention to the fact 3 can be divided only by 1 and 3 (itself). If necessary do more examples with numbers such as 7 and 11 until all the students understand this concept. Now tell them, when a number such as 3, 5 and 7 has only two factors (1 and itself), it is called a prime number.

1 is neither a prime nor a composite. Most students think 1 is a prime number. 2 is NOT a composite number. It is a prime number. Ask students, why? Don’t confuse odd numbers and even numbers. Many students tend to believe odd numbers are prime. Give them some examples such as an odd number 9, which is a composite. Ask students to use the tiles approach to find and list all the prime and composite numbers from 2 to 20 (Answer: The prime numbers between 2 and 19 are: 2, 3, 5, 7, 11, 13, 17 and 19) Adapted from: http://www.lessonplanspage.com/printables/PMathPrimeAndCompositeNumberTiles67.htm

FINDING PERCENT (Writing Activity) Name __________________________

Date __________________

In each group, state which one does not belong. Explain your reasoning. Group 1 20% of 50 0.5% of 200 50% of 20 ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________

Group 2 4% of 600 60% of 40 40% of 6 ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________

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Product Game Rules (Game) http://illuminations.nctm.org/LessonDetail.aspx?ID=L273

1. Player 1 puts a paper clip on a number in the factor list. No square on the product grid is marked with Player 1’s color because only one factor has been marked; it takes two factors to make a product. 2. Player 2 puts the other paper clip on any number in the factor list (including the same number marked by Player 1) and then shades or covers the product of the two factors on the product grid. 3. Player 1 moves either one of the paper clips to another number and then shades or covers the new product. 4. Each player, in turn, moves a paper clip and marks a product. If a product is already marked, the player does not get a mark for that turn. The winner is the first player to mark four squares in a row – up and down, across or diagonally.

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Product Game Follow up activities TASK 1: Play the Product Game several times with a partner. Look for interesting patterns and winning strategies. Make notes of your observations.

TASK 1 Follow-up Suppose one of the paper clips is on 5. What products can you make by moving the other paper clip? The products you listed in question 1 are multiples of 5. A multiple of a number is the product of that number and another whole number. If a number is a multiple of 5, then 5 is a factor of that number. These four sentences are all ways of expressing 5 x 3 = 15. 5 is a factor of 15. 3 is a factor of 15. 15 is a multiple of 5. 15 is a multiple of 3. List five multiples of 5 that are not on the game board.

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The Product Game Game board 1

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MINUTE DAILY REVIEW Numbers, Number Sense and Number Operations 1. The simplest form of 12/18 is ____________________. 2. 3.2 x 102 __________________ 0.32 x 103 Use ‹, › or = 3. What is the greatest common factor of 15 and 33? ___________ 4. Write 24/64 in lowest terms. ______________________ 5. Write the decimal for 7%. _________________________ 6. Is thirty three prime or composite? ____________________ 7. The sum of 8 and 9 is __________________________ 8. Write what comes next in the pattern. 1.2, 2.4, 4.8, 9.6 _________ 9. Circle the answer that is equal to 3 • 3 • 3 • 3 ________________ 10. Name a prime number between 12 and 16. _________________