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Math Unit 4

 

Study Guide

Unit 4: Multiplying Tables of 6, 7, 8, and 9

 

 

Chapter 1- Examples of test questions:

  • Have all 6, 7, 8, and 9 multiplication (and division) problems memorized.
  • Be able to answer multiplication and division problems in various ways:
    • ___ x 9 = 54
    • What is 8 x 6?
    • 63 % 9 =
    • Divide 49 by 7.
    • Write two multiplication sentences for a picture.  For example, if there were 20 objects, example sentences would be:
      • 2x10=20
      • 10x2=20
      • 1x20=20
      • 20x1=20
      • 4x4=20
      • 5x4=20
    • 4x9 = 40-__ = ___  (if four times nine is 36, the final blank is 36; 40-4 is equal to 36 so the second blank is 4)
    • 7x7 is ___ more than 7x4 (7x7 is 49 and 7x4 is 28; 49-28 is 21, so the blank is 21)
  • There are 63 eggs put equally in 7 bowls.  How many eggs are there in each bowl?
  • Multiply 437 by 8.
  • What is 527 x 9? (4,743)  Also be able to use estimation to see if an answer is reasonable. (500x10 = 5,000)
  • Be able to do long division with remainders.
  • What is the remainder when you divide 741 by 7?
  • How would you check if the following is correct?  357 % 7 = 51 (you would show your work by multiplying 51x7)
  • Two step word problems:
    • Alex has $4,876.  He gives $31 to each of his 9 family members.  How much does he have left? ($31x9 = $279) ($4,876-279=$4,597)
    • There are 357 apples and oranges altogether.  There are 6 times as many apples as oranges.  How many oranges are there?  (If there are 6 times as many apples as oranges, you need 7 equal groups.  Divide the total number by 7 to find out how many oranges there are: 357 % 7 = 51 oranges)

 

Chapter 2 - Examples of test questions:

  • Patterns: 6, 12, 18, ___, 30, ___, 42, 48, 54, ____
  • See examples in Chapter 1:
    • Write two multiplication sentences for a picture
    • Be able to answer multiplication and division problems in various ways
    • How would you check if a division problem was correct?
  • How many days are there in 9 weeks?
  • The store sold 584 items each day.  How many items were sold in a week?
  • Two step problems:
    • 7,358 carrots were placed in bags of 9.  How many bags were needed?  How many carrots were left?
    • There are 18 balloons in 3 bags.  Each balloon cost $7.  How much does a bag of balloons cost? (18%3=6 balloons in each bag) (6x$7=$42 a bag)
    • 9 boxes cost $558.  How much do 6 such boxes cost? ($558%9 = $62) ($62x6 = $372)
    • There are 558 people in the store.  There are 8 times as many women as men.  How many men are there? (If there are 8 times as many women as men, you need 9 equal groups.  Divide the total number by 9 to find out how many men there are)

 

Chapter 3 - Examples of test questions:

  • Patterns: be able to use variable – instead of having blanks to fill in, there will be letters of the alphabet.
    • 2, 4, 6, A, 8, 10, 12, 14
    • 6, 12, 18, 24, 30, B, 42, 48, 54,
    • A is ____
    • B is ____
  • There will be a picture of objects broken into groups.  Be able to write both multiplication and division sentences.  If there were 72 objects in 8 groups:
    • 8x9=72
    • 72%8=9
  • Write 8x9 as a repeated addition sentence. (8+8+8+8+8+8+8+8+8=72)
  • Long division problems with remainders.
  • <, >, =
    • 558 % 9 ___ 6x8 (558%9 is 62) (6x8 is 48) (62 > 48)
  • Sherry ate 4 strawberries in a day.  She ate the same number of strawberries each day for 9 days.  How many strawberries did she eat in all?
  • Find an answer and use estimation to check if an answer is reasonable.  42x7=____ (294) (Estimation: 40x10=400)
  • How would you check if a division problem was correct? (multiply the two smaller numbers to see if it equals the larger number)
    • 6,712 % 7 = _______ (the answer is 958 R6; to check the problem, multiply 958 by 7 and add the remainder)
  • Each week Eric has $62 left over after he paid his bills.  How much will he have after 9 weeks?
  • Two Step Problems:
    • Marsha purchased 52 baskets for $9 a piece.  She paid $600.  How much does she have left? (52x$9 = $468) ($600-468 = $132)
    • 504 liters of soda were being poured into 6 smaller containers.  Sally asked for her container to have only 77 liters.  How many liters were left in Sally’s container? (504 % 6 = 84 liters in each smaller container) (84-77 = 7 liters)
    • Alice asked for 4,074 yards of cloth.  7 yards cost $6.  How much did she pay? (4,074%7 yards = 582 yards) (582 x $6 = $3,492)
    • The cloth cost $3,492.  Alice paid $401 every month for 6 months.  How much more will she have to pay after 6 months? ($401x6 = $2,406) ($3,492 - $2,406 = $1,086)

 

Chapter 4 - Examples of test questions:

  • See examples in Chapter 1:
    • Write multiplication sentences for a picture
    • Estimate the value of multiplication problems
    • Be able to answer multiplication and division problems in various ways
      • Fill in missing numbers
        • 6x7 = 84 - ___ = _____
        • 6x__ = 84
        • 84%6 = ___
    • How would you check if a division problem was correct?
  • Find the missing number. (the center number multiplied by the number next to it equals the number on the outside: 7x1=7, 7x3=21, 7x6=42, 7x5=?) (the answer would be 35)

 

     ?

               5

42     6    7    1    7

               3

              21

 

  • When dividing know the difference between quotient and remainder.
    • 6,712 % 7 = _______ (the quotient is 958) (the remainder is 6)
  • Multi-step problems:
    • There are 7 baskets.  In each basket are 12 chocolates and 3 more fruit than chocolates. How many items altogether? (Fruit: 12+3=15) (Items in the basket: 12+15=27) (27x7=189 items altogether)
    • In the basket are 12 chocolates and 15 fruit.  Each chocolate costs $5 and a piece of fruit costs $4.  How much does the basket cost? (12x$5 = $60) (15x4 = $60) ($60+$60=$120)
    • Art painted 432 portraits and 390 landscapes.  He sold each painting for 7 cents each.  How much did he get if he sold all the paintings? (432+390=822 paintings) (822x7cents = 5,754 cents)
    • A ticket to Valley Fair costs 9 times as much as a meal.  The meal costs 4 times as much as the beverage.  If a ticket to Valley Fair costs $72, how much does the beverage cost? ($72%9 = $8) ($8%4 = $2 for a beverage)
    • When dividing a word problem, you many need to take into account a remainder:
      • The ride at Valley Fair could hold 8 people, and there were 692 people in line.  How many trips would the ride have to take so that all the people could have a turn? (692%8 = 86 R5) (It would need to take 87 trips even though the last trip would have only 5 people)

 

Chapter 5 - Examples of test questions:

  • Write a multiplication sentences for a picture:
    • There are 5 groups.  In each group are 4 rows of 6 items. ___ x ___ x ___ = ___ (4 rows x 6 items equals 24) (24 items x 5 groups = 120) (4 x 6 x 5 = 120)
  • Fill in the blanks:
    • 12 x 8 x 2 = ____ x 2 = _____ (12x8 = 96) (96x2 = 192) (the first blank would be 96 and the second blank 192)
  • When multiplying multiple numbers, a mathematical rule is to go left to right.
    • 45 x 6 x 3 = ___ (start with 45x6=270) (then multiply with the next number 270x3=810)
    • If 45 x 6 x 3 = 810, what is 3 x 45 x 6? ____ (3x45=135) (135x6=810)
  • Division problems asked in various ways:
    • 20,000 % 4 = ______
    • 20 hundreds divided by 5 ____
    • Estimate the value of 507 % 6.
      • ____ % 6 = _____ (507 rounds to 500) (on the first blank write 500) (500%6=83R2) (on the second blank write 83 R2)
      • 507%6 is about ___. (on the blank write 83: the remainder would round down)
  • When given three division problems and an estimated problem, be able to circle the problem that was estimated.
  • Multi-step problems:
    • There are 53 small marbles and 6 times as many large marbles.  How many marbles in all?
    • 9 TVs were selling for $54,918.  Estimate the cost of each TV.  How many TVs could be purchased for $12,742? (Divide 54,918 by 9 and get 6,102 and round that to $6,000) (If each TV costs approximately $12,742, then 2 TVs could be purchased)
    • There are 120 swings. There are 3 times as many children as swings.  How many children are there? (120x3 = 360 children)
      • The children were put into groups of 7.  Estimate the number of groups formed. (360%7=51 R3) (Estimate: 50 groups)

 

Unit 4 Cumulative Test:

  • Review all of Units 1 - 4
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