1-1. Enrichment. Using a Reference Point

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Kevin Nicholson
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1 1-1 Using a Reference Point There are many times when you need to make an estimate in relation to a reference point. For example, at the right there are prices listed for some school supplies. You might wonder if $5 is enough money to buy a small spiral notebook and a pen. This is how you might estimate, using $5 as the reference point. The notebook costs $1.59 and the pen costs $3.69. $1 $3 $4. I have $5 $4, or $1, left. $0.59 and $0.69 are each more than $0.50, so $0.59 $0.69 is more than $1. So $5 will not be enough money. Use the prices at the right to answer each question. 1. Jamaal has $5. Will that be enough money to buy a large spiral notebook and a pack of pencils? 2. Andreas wants to buy a three-ring binder and two packs of filler paper. Will $7 be enough money? Spiral Notebook Large $2.29 Small $1.59 Three-Ring Binder $4.75 Filler Paper Pack of 100 $ Rosita has $10. Can she buy a large spiral notebook and a pen and still have $5 left? 4. Kevin has $10 and has to buy a pen and two small spiral notebooks. Will he have $2.50 left to buy lunch? 5. What is the greatest number of erasers you can buy with $2? 6. What is the greatest amount of filler paper that you can buy with $5? 3 packs, or 300 sheets 7. Lee bought three items and spent exactly $8.99. What were the items? three-ring binder, pen, eraser 8. Select five items whose total cost is as close as possible to $10, but not more than $10. Sample answer: one pen, three packs of filler paper, one pack of pencils. Ball-Point Pen $3.69 Pencils Pack of 10 $2.39 Eraser $0.55 Glencoe/McGraw-Hill 1 and Connections, Course 1

2 1-2 Number Puzzles The puzzles on this page will help you sharpen your arithmetic and logical reasoning skills. Even when you solve a puzzle, you should think about the best method of computation to use mental math, paper and pencil, or a calculator. Solve each puzzle. Then identify the method of computation that you think is most appropriate. Methods of computation will vary. 1. Arrange the digits 5, 6, 7, 8, and 9 in this multiplication so that you get the greatest possible product. 2. Each letter in this addition problem represents a different digit. What is the value of each letter? S E N D M O R E M O N E Y 9,567 1,085 10, Suppose each equation is true. What does 8 l equal? 5. Draw two straight lines across the face of this clock so that the sum of the numbers in each region is the same Find the pattern , What does 12,345, equal? 111,111, Arrange the counting numbers from 1 through 6 in the circles so that the sum of the numbers along each side of the triangle is 10. Answers will vary Glencoe/McGraw-Hill 2 and Connections, Course 1

3 1-3 Newspaper Numbers Many stories that you read in newspapers contain numbers. Sometimes these numbers are exact, and sometimes they are rounded. Do you know which is which? In the headline at the right, the score of the game, 5 2, certainly is exact. However, the attendance probably was just a little more than 40,000 or little less than 40,000. So 40,000 is most likely a rounded number. The Benton Bugle 40,000 attend home opener Tigers beat Twins, 5 2 Tell whether the number in each headline is more likely to be rounded or exact. 1. Road construction 2. Developer to build to cost $3 million 65-story skyscraper local families take part in national survey 5. One thousand homes without electricity 7. Maris hits 61st home run 4. Census: population increased by 8, students honored at awards banquet 8. Alvarez wins by 7,000 votes Circle the letter of the correct answer. 9. For a newspaper headline, the population of a country was rounded to 74 million. Which could be the actual population of this country? a. 73,098,500 b. 73,908,500 c. 74,598,500 d. 74,908, The actual amount of a city budget is $4,150,000. Which is the most appropriate way to round this amount for a headline? a. $4.1 million b. $4.2 million c. $4.5 million d. $45 million 11. CHALLENGE The attendance at a concert was reported to be 6,000. If the number was rounded correctly to the nearest thousand, what is the least that the actual attendance could be? the greatest? Glencoe/McGraw-Hill 3 and Connections, Course 1

4 1-4 Operations Puzzles Now that you have learned how to evaluate an expression using the order of operations, can you work backwards? In this activity, the value of the expression will be given to you. It is your job to decide what the operations or the numbers must be in order to arrive at that value. Fill in each with,,, or to make a true statement Fill in each with one of the given numbers to make a true statement. Each number may be used only once. 9. 6, 12, , 9, , 8, 12, , 5, 10, , 4, 6, 8, , 3, 5, 7, CHALLENGE Fill in each with one of the digits from 1 through 9 to make a true statement. Each digit may be used only once. 100 Glencoe/McGraw-Hill 4 and Connections, Course 1

5 1-5 What s in a Word? Suppose you use the following code for the letters of the alphabet. A 1 B 2 C 3 D 4 E 5 F 6 G 7 H 8 I 9 J 10 K 11 L 12 M 13 N 14 O 15 P 16 Q 17 R 18 S 19 T 20 U 21 V 22 W 23 X 24 Y 25 Z 26 To evaluate a word using this code, you replace each letter with its code number, then multiply. For instance, at the right you see how to find the value of the word MATH, which is 2, (M) 1 (A) (T) (H) 2,080 Use the code above to evaluate each word. 1. BOX 2. CUBE 3. TABLE 4. CATTLE 5. VARIABLE 6. ALGEBRA Circle the word that has the greater value. (Hint: Do you have to evaluate the entire word, or is there a shortcut?) 7. PRINCIPAL or PRINCIPLE 8. MARCH or CHARM 9. THOUGHT or THROUGH 10. RIGHT or WRITE Find a three-letter word that has a value as close as possible to the given number , , , , CHALLENGE What is the least possible value that you can find for a three-letter word? the greatest possible value? Glencoe/McGraw-Hill 5 and Connections, Course 1

6 1-6 Making Models for Numbers Have you wondered why we read the number 3 2 as three squared? The reason is that a common model for 3 2 is a square with sides of length 3 units. As you see, the figure that results is made up of 9 square units. 3 units 3 units Make a model for each expression square units Since we read the expression 2 3 as two cubed, you probably have guessed that there is also a model for this number. The model, shown at the right, is a cube with sides of length 2 units. The figure that results is made up of 8 cubic units. 2 units Exercises 5 and 6 refer to the figure at the right. 5. What expression is being modeled? 6. Suppose that the entire cube is painted red. Then the cube is cut into small cubes along the lines shown. a. How many small cubes are there in all? b. How many small cubes have red paint on exactly three of their faces? c. How many small cubes have red paint on exactly two of their faces? d. How many small cubes have red paint on exactly one face? e. How many small cubes have no red paint at all? 2 units 2 units cubic units 7. CHALLENGE In the space at the right, draw a model for the expression 4 3. Glencoe/McGraw-Hill 6 and Connections, Course 1

7 1-7 Equation Chains In an equation chain, you use the solution of one equation to help you find the solution of the next equation in the chain. The last equation in the chain is used to check that you have solved the entire chain correctly. Complete each equation chain a 12, so a f 36, so f 4. ab 14, so b 2. g 13 f, so g b c, so c g h, so h d c, so d 6. h i 18, so i 11. e d 3, so e 18. j i 9, so j 20. a e 25 Check: j f 5 Check: m 4 8, so m v 12, so v 30. m n 12, so n 20. v w 3, so w 10. np 100, so p wx, so x 8. q 40 p, so q 45. w x 2y, so y 9. p q 10 r, so r 40. xy z 40, so z 32. r m 8 Check: z v 2 Check: CHALLENGE Create your own equation chain using these numbers for the variables: a 10, b 6, c 18, and d 3. Glencoe/McGraw-Hill 7 and Connections, Course 1

Essentials. Week by. Week. Calculate!

Essentials. Week by. Week. Calculate! Week by Week MATHEMATICS Essentials Grade WEEK 7 Calculate! Find two numbers whose product would be between 0 and 50. Can you find more solutions? Find two numbers whose product would be between,500 and,600.