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Mrs. Marshall & Mr. Liberato’s Math Class Study Guide MATH TOPIC 1 TEST: REVIEW PACKET Directions: This packet covers ALL of Topic 1. Take a lesson or two a night and review. Do not try to study it all in one night. The packet provides MANY examples of each lesson and some for you to try as well. You should complete EVERY “You Try It” section – do a little each night. Vocabulary Dividend – The number that is divided. Example: 32 ÷ 4 = 8. 32 is the dividend Divisor - The number by which another number is divided. Example: 32 ÷ 4 = 8. 4 is the divisor Quotient – The answer to a division problem Example: 32 ÷ 4 = 8. 8 is the quotient. Fact Family - A group of related facts using the same set of numbers. Example: 2 x 5 = 10 5 x 2 = 10 10 ÷ 5 = 2 10 ÷ 2 = 5 2, 5, 10 LESSON 1-1: “Meanings of Multiplication” Array: A way of displaying objects in equal rows and columns. Example: The multiplication sentence for this array is 3 x 6 because there are 3 groups of 6 The multiplication sentence for this array is 2 x 4 because there are 2 groups of 4 Factor: The numbers multiplied together to find the product. Example: 8 x 2 = 16 (8 and 2 are both the factors) 6 x 9 = 54 (6 and 9 are both the factors) Product: The answer to a multiplication problem Example: 9 x 4 = 36 (36 is the product) Repeated Addition: A way of writing a multiplication problem into an addition problem. Example: 3 x 9 = 27 (think of this as 3 groups of 9) Repeated Addition= 9 + 9 + 9 = 27 6 x 2 = 12 (think of this as 6 groups of 2) Repeated Addition= 2 + 2 + 2 + 2 + 2 + 2 = 12 You Try It: 1. What is the multiplication sentence for this repeated addition sentence? 4 + 4 + 4 = 12 2. What is the repeated addition sentence for this multiplication problem? 9 x 4 = 36 LESSON 1-2 & 1-5: “Patterns for Facts”; “Problem Solving: Look for a Pattern” Multiple: The product of any two whole numbers. Example: Multiples of 2 are the products in bold. 2x1=2 2x2=4 2x3=6 2x4=8 2 x 5 = 10 2 x 6 = 12 (The Multiples of 2 are the products). Quick Tip: When looking at multiples of two, the ones digit is always even When multiplying you can SKIP COUNT. This means counting up by the specific number: Example: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 Example: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 You Try It: What are the multiples of 6 up to 6 x 10? 1. What comes next in the sequence: 18, 27, 36, _____ 5, 10, 15, ______ LESSON 1-3: “Multiplication Properties” Commutative Property of Multiplication: Numbers can be multiplied in any order and the product remains the same. Example: 7x2=2x7 9x3=3x9 Identity Property of Multiplication: The product of any number and 1 is the number. Example: 7x1=7 3x1=3 Zero Property of Multiplication: The product of any number and 0 is zero. Example: 6x0=0 5x0=0 You Try It: Name the Property being used and give another example of each. 1. 9,000,000 x 0 = 0 Property: Give another example: 2. 15 x 1 = 15 Property: Give another example: 3. 4 x 8 = 8 x 4 Property: Lesson 1-4 Distributive Property: Breaking apart problems into 2 simpler problems. Example: 4 x 32 STEP 1: We can break apart 32 into an easier addition problem (30 + 2) STEP 2: Multiply 4 by each of the numbers INSIDE the parentheses= (4 x 30) + (4 x 2) STEP 3: Add both of the parentheses together (120) + (8) = 128 You Try It: 9 x 22 LESSON 1-6 & 1-7: “Meanings of Division” & “Relating Multiplication and Division” You can use multiplication to help you solve division problems. You can also use division to help you solve multiplication problems. Fact Families are very helpful for this. Fact Family - A group of related facts using the same set of numbers. Example: 2 x 5 = 10 5 x 2 = 10 10 ÷ 5 = 2 10 ÷ 2 = 5 2, 5, 10 Example: 6 x 6 = 36 6, 36 ÷ 6 = 6 6, 36 You only need to write 2 number sentences for this fact because two of your factors are the same. LESSON 1-8: “Special Quotients” Any number divided by itself is 1. o Example: 8 /8 = 1 Zero divided by any number is zero. o Example: 0 / 5 = 0 You cannot divide by 0. o There is no such number. You will need to solve problems like these. Compare. Use >, <, or = for each 6÷6 3÷3 7 ÷7 7÷7 0÷4 0÷9 0 ÷ 11 0 ÷ 15 LESSON 1-10: . “Problem Solving: Draw a picture and write an equation” Bar Diagrams can help us to solve multiplication and division problems. Example: There are 10 students in each row at the assembly. There are 8 rows of students. Which number sentence shows the total number of students? -------------------------------------------- ? (Total students) -----------------------10 10 A. B. C. D. 10 5 x 6= 30 8 x 10 = 80 8 x 8 = 64 10 x 10 = 100 10 10 10 10 10 You Try It: Carmen’s recipe calls for three times as many carrots as peas. If Carmen uses 2 cups of peas, how many cups of carrots will she use? ----- ? (# of carrots in all) ---2 2 2 Multiplication Sentence: ________ x ________ = _________ Practice some word problems.... I am going shopping for 10 students who want sandwiches. Each sandwich needs 2 pieces of cheese. How many pieces of cheese should I buy? Jimmy has 5 pairs of shoes. How many total shoes does Jimmy have? 5 students want to buy 2 brand new shirts each. How many shirts will they buy altogether? Using Bar Graphs with Division A classroom has 26 chairs. The teacher wants to arrange the chairs in 4 rows. Write a number sentence that shows how many desks the teacher can have in each row if each row has the same number of chairs? 26 ? chairs chairs