UNIT 2: RATIONAL NUMBER CONCEPTS WEEK 5: Student Packet

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1 Name Period Date UNIT 2: RATIONAL NUMBER CONCEPTS WEEK 5: Student Packet 5.1 Fractions: Parts and Wholes Identify the whole and its parts. Find and compare areas of different shapes. Identify congruent figures. Add fractions. 5.2 Fourfold Way: Growing Shapes Use variables, parentheses, and exponents in expressions. Use formulas to find perimeter and area of rectangles. Describe geometric patterns numerically, symbolically, graphically, and mentally. Plot ordered pairs that satisfy a specified condition. Connect the slope of a line to its context in a graph. 5.3 Factorization Write natural numbers as products of prime numbers. Review math concepts from prior lessons. Demonstrate competency in division algorithm of whole numbers (highlighted review) Week 5 SP

2 FOCUS ON VOCABULARY 5 Fill in the crossword puzzle using the clues below Across Down 3. = is called the sign. 1. Three and 5 are both of A natural number with more than two factors (two words). 2. The distance around the outside of a two-dimensional shape or a figure. 9. The formula for the of a rectangle is length times width. 4. figures have exactly the same size and shape. 10. The set of natural numbers and zero. 11. Counting numbers are also called numbers. 5. A natural number greater than 1 that has exactly two factors, itself and 1 (two words). 7. Two fractions are if they name the same number. 8. A of 16 is 64. Word Bank equal natural factors multiple composite number perimeter equivalent area whole congruent prime number Week 5 SP0

3 5.1 Fractions: Parts and Wholes FRACTIONS: PARTS AND WHOLES Ready (Summary) We will find fractional parts of a whole using an area model and find the areas of different shapes. We will add fractions using the model. Set (Goals) Identify the whole and its parts. Find and compare areas of different shapes. Identify congruent figures. Add fractions. Go (Warmup) Show different ways to divide a unit square into fourths. Week 5 SP1

4 5.1 Fractions: Parts and Wholes SQUARES PROBLEM 1. If each of the five congruent squares is equal to 1 square unit, find the area of each piece below. A : F: K: B: G: L: C: H: M: D: I: N: E: J: P: 2. What would happen to the areas of the other shapes if the area of N was 1 square unit? 3. What would happen to the areas of the other shapes if the area of B was 1 square unit? 4. The value of the word MAN (that is, the sum of the areas of M + A + N) is has a value of. Find the value of these words: MAP : FLEA : BEAN : 5. Create a word value that has value Challenge: Create a word that has as large a value as possible. Week 5 SP2

5 5.1 Fractions: Parts and Wholes ANOTHER SQUARES PROBLEM Q R T S U V 1. In the picture above, what fraction of the whole do the following pieces represent? Q: S: U: R: T: V: 2. If the area of piece R (in the picture above) was 1 square unit, what would happen to the areas of the other pieces? 3. If the area of piece Q (in the picture above) was 1 square unit, what would happen to the areas of the other pieces? 4. The value of the word US (that is U + S) is 1. Find the value of 8 RV : TV : SUV : Week 5 SP3

6 5.2 Fourfold Way: Growing Shapes FOURFOLD WAY: GROWING SHAPES Ready (Summary) We will extend square and rectangle patterns. Then we will represent geometric measures in the pattern using an input output table, a graph, with symbols, and with words. Set (Goals) Use variables, parentheses, and exponents in expressions. Use formulas to find perimeter and area of rectangles. Describe geometric patterns numerically, symbolically, graphically, and mentally. Plot ordered pairs that satisfy a specified condition. Connect the slope of a line to its context in a graph. Go (Warmup) Complete each table. Find a rule that will give the output for any input. Table 1 Table 2 Table 3 Input Output Input Output Input Output Rule: If the input is x, then the output will be Rule: If the input is x, then the output will be Rule: If the input is x, then the output will be Week 5 SP4

7 5.2 Fourfold Way: Growing Shapes GROWING SQUARES Complete the pattern, tables, and questions below. Stage # Stage number (n) Table 1 Table 2 Table 3 Length of Stage Stage Perimeter side number number (P) (L) (n) (n) Area (A) n n n Rule: L = Rule: P = Rule: A = 1. What is the perimeter of the figure obtained in stage #10? rule: substitute: perimeter: 2. If the perimeter of the figure is 84, what is the stage number? rule: substitute: stage number: 3. Use words or diagrams to explain how the length of the side and the perimeter of a square are related. 4. Use words or diagrams to explain how the length of the side and the area of a square are related. Week 5 SP5

8 5.2 Fourfold Way: Growing Shapes GROWING SQUARES GRAPHS Two Graphs on the Left (Use Tables 1 and 2) One Graph on the Right (Use Table 3) Lengths in units L (one color) Perimeter in units P (a second color) Area in square units A (a third color) Stage number n Stage number n 1. Compare the two graphs on the left axes. Which is steeper? Why? 2. How is the graph on the right different from the two graphs on the left? Week 5 SP6

9 5.2 Fourfold Way: Growing Shapes GROWING RECTANGLES This is a pattern of growing rectangles. Continue the pattern for stage 4 and stage 5. Then complete the tables and the questions, and make graphs on the following page. Stage # Table 1 Table 2 Table 3 Stage # (n) base (b) Stage # (n) height (h) Stage # (n) Perimeter (P) n n n Rule: b = Rule: h = Rule: P = 1. What is the base of the rectangle for stage #12? 2. What is the height of the rectangle for stage #14? 3. What is the perimeter of the rectangle for stage #10? 4. If the base of the rectangle is 36, what is the stage number? Week 5 SP7

10 5.2 Fourfold Way: Growing Shapes GROWING RECTANGLES GRAPHS All of the tables on the previous page compare the stage number to a length. This is because base, height, and perimeter are all linear measurements. Draw a vertical axis at the right and label it length. Draw a horizontal axis at the right and label it stage number. Use three different colors. For each table on the previous page, graph the stage number and length as coordinates. Then draw a trend line to show each pattern, and label each line. Finally, give your graph a title. 1. How are the graphs the same? 2. How are the graphs different? Week 5 SP8

11 SKILL BUILDER 1A 1. What is the set of natural numbers? 2. What is the set of whole numbers? 3. What is different about whole numbers compared to natural numbers? 4. What is the set of integers? 5. What is different about integers compared to whole numbers? 6. List all the factors of Describe in words what it means for a number to be a factor of another number. 8. List the first seven multiples of 9. Week 5 SP9

12 SKILL BUILDER 1B 9. Describe in words what it means for a number to be a multiple of another number. 10. All even numbers are divisible by. 11. Even numbers end in,,,,. 12. List all the even numbers greater than 10 but less than Odd numbers end in,,,,. 14. List all the odd numbers between 10 and What are prime numbers? 16. What are composite numbers? 17. What natural number has exactly one factor? Week 5 SP10

13 SKILL BUILDER 1C 18. Use grid lines to draw all possible rectangles with the areas given below: a. 12 square units b. 7 square units c. 16 square units Example of a rectangle with 12 square units 19. What are the dimensions of the rectangles above? a. for 12 square units b. for 7 square units c. for 16 square units Week 5 SP11

14 SKILL BUILDER 1D 20. List all of the factors of a. 12 b. 7 c What is the relationship between the dimensions of the rectangles above and the factors of the numbers that describe their areas? 22. Is 7 a prime or composite number? Explain. 23. How many rectangles can be drawn with 7 square units? 24. Is 12 a prime or composite number? Explain. 25. How many rectangles can be drawn with 12 square units? 26. Is 16 a prime or composite number? Explain. 27. How many rectangles can be drawn with 16 square units? 28. Why do you think 16 is called a square number, while 7 and 12 are not? Find the prime factorization of each number. In other words, write each number as the product of primes. Example: = = 125 = Week 5 SP12

15 SKILL BUILDER 2A 1. Circle the even numbers , Circle the odd numbers , Circle the prime numbers Circle the composite numbers What are the factors of 31? 6. If a number is greater than 1, and it is not composite, then it is 7. List the first ten prime numbers. 8. List the first ten composite numbers. 9. List the first ten square numbers. Find the prime factorization of each number , = 250 = 1,000 = Week 5 SP13

16 SKILL BUILDER 2B Estimate the quotient. Then use a division algorithm to find the quotient divided by ,200 Compute (-8) 19. 2(-3) (-5)(-10) divided by Which multiplication problem may be used to check that 21 divided by 3 is 7? Choose the best answer. A B C. 3 7 D Yolanda says that 2 is not a prime number because it is an even number. Is she correct? Explain. Week 5 SP14

17 SKILL BUILDER 3A 1. Circle the even numbers , Circle the odd numbers Circle the prime numbers Circle the composite numbers Circle the integers that are not natural numbers Circle the square numbers Write the prime factorization of each number = 280 = Compute (-5) 10. 6(-5) (-4) (-5)(-8) Week 5 SP15

18 SKILL BUILDER 3B 15. Flynn had 108 balloons that he wanted to give to his 12 friends. If each person got the same number, how many balloons did each person get? 16. A basketball team earned $1,400 to buy uniforms. If each uniform costs $28, how many uniforms can the team purchase? 17. Complete the table. Find a rule that will give the output for any input (x). Input (x) Output (y) ,000 x Rule: y = 18. Holly says that 45 is a prime number because it is an odd number. Is she correct? Explain. Week 5 SP16

19 TEST PREPARATION 5 Show your work on a separate sheet of paper and choose the best answer. 1. What is the product of -4 and 3? A. 12 B. -12 C. 43 D Which is the best description of the number 51? E. Prime number F. Even number G. Composite number H. Square number 3. Compute 8, A. 4,347 r1 B. 4,436 r2 C. 4,346 r1 D. 4,337 r1 4. Compute the sum of -6 and -10. E. -4 F. 4 G. -16 H What fraction of the square is shaded? A. 1 4 B. 1 2 C. 1 8 D. 3 4 Week 5 SP17

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23 KNOWLEDGE CHECK 5 Show your work on a separate sheet of paper and write your answers on this page. 5.1 Fractions: Parts and Wholes Use the figure below for #1-2. T A B C If the large square is equal to 1 whole, what fraction does each piece represent? 1. A: B: C: T: 2. What is the value of C + A + T? 5.2 Fourfold Way: Growing Shapes 3. Create one more stage for the pattern: 2 + (1 1) = (2 2) = (3 3) = 11 Stage 1 Stage 2 Stage 3 Stage 4 4. Write an equation for the pattern illustrated in # Factorization 5. List all of the even numbers greater than or equal to 58 and less than Circle the prime numbers Highlighted Review: Whole Numbers: Division Find each quotient using a division algorithm or procedure. 7. 9, , Week 5 SP21

24 Home-School Connection 5 Here are some questions from this week s lessons to review with your young mathematician. A B C 1. If the area of the entire figure is 1 square unit, then what is the value of H + E + A + D? 2. Find the prime factorization of 120. D E G F H 3. Complete the table and find a rule. Perimeter Stage # (x) (y) x Parent (or Guardian) signature Selected California Mathematics Content Standards NS Compare fractions represented by drawings or concrete materials to show equivalency and to add and subtract simple fractions in context (e.g., 1/2 of a pizza is the same amount as 2/4 of another pizza that is the same size; show that 3/8 is larger than 1/4). NS Add and subtract simple fractions (e.g., determine that 1/8 + 3/8 is the same as 1/2). NS Know that numbers such as 2, 3, 5, 7, and 11 do not have any factors except 1 and themselves and that such numbers are called prime numbers. NS Determine the prime factors of all numbers through 50 and write the numbers as the product of their prime factors by using exponents to show multiples of a factor (e.g., 24 = 2 x 2 x 2 x 3 = 2 3 x 3). MG Draw the points corresponding to linear relationships on graph paper (e.g., draw 10 points on the graph of the equation y = 3x and connect them by using a straight line). AF MR Students investigate geometric patterns and describe them algebraically. Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning. Week 5 SP22