DIVISION REVIEW. Math Grade 6 Review Lesson 4 Information Organized by Beckey Townsend

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1 DIVISION REVIEW Math Grade 6 Review Lesson 4 Information Organized by Beckey Townsend

2 Divisibility Rules 2 A number is divisible by 2 if it ends in a zero or an even number. Example: The number 2,784 is divisible by 2 since 4 is an even number. The number 1,813 is NOT divisible by 2 since 3 is an odd number A number is divisible by 3 if the sum of its digits is divisible by 3. Example: The number 813 is divisible by 3 since the sum of its digits (8+1+3) equals 12, and 12 is a multiple of 3 (3 x 4 = 12). The number 617 is NOT divisible by 3 since = 14 and does not divide equally into three groups A number is divisible by 4 if the last two digits are both zeros or if they are multiples of 4. Example: The numbers 400 and 436 are both divisible by 4 since the last two digits in 400 are zeroes, and the last two digits in 436 are a multiple of 4 (4 x 9 = 36) A number is divisible by 5 if it ends in 0 or 5. Example: The number 105 is divisible by 5 since it ends with a 5. The number 640 is divisible by 5 since it ends with a A number is divisible by 6 if it is even and is also divisible by 3. Example: The number 618 is divisible by six since it is both even and the sum of its digits (6+1+8=15) is a multiple of 3 (3 x 5 = 15) A number is divisible by 9 if the sum of its digits is divisible by 9. Example: The number 711 is divisible by 9 since = 9. (9x1=9) The number 693 is divisible by 9 since = A number is divisible by 10 if it ends with zero. Example: 370 ends with 0 so it is divisible by 10 Keep the divisibility card listing these rules with your other fact cards and multiplication table. Store in a place that is within reach at all times.

3 Practice Divisibility Rules Thumbs up or down if the number is 1. divisible by divisible by , divisible by 4 32, divisible by divisible by divisible by divisible by

4 Have you tried any of these methods? DIVISION: Demonstrations with Base 10 Blocks and Area Models 1. Single-Digit Divisor: (7:01 min) Watch video clips (1:56 min) Two-Digit Divisor: Watch video clip (13:42 min) 3. Rectangle Method: (2:53 min) 4. Area Model Method: (5:57 min) (4:31 min)

5 Standard Method to Divide (Algorithm) Watch video clip (6:11 min) BONUS = short division!!! Use your own words to describe division in the base ten number system

6 Practice Division: Use divisibility rules & favorite method Vocabulary Review 1-Digit Divisor 2-Digit Divisor 3-Digit Divisor =? , Dividend Divisor Quotient TIP: For 1-digit divisors the distributive property allows for quick mental math computation. Divisor x Quotient Dividend Answer Key

7 What about Remainders? remainder Two Choices: Fraction? or Decimal? remainder divisor Fraction Write remainder over divisor and simplify if needed = numerator denominator See Fraction Tower & Decimal Chart given in class. Decimal 1. Write decimal point at the end of dividend and on top of quotient line. (Place in the house & raise it to the roof.) 2. Write one zero at a time, bring down and continue dividing. You can keep adding zeroes as needed

8 Step-by-Step Bar Modeling for Simple Division Word Problems Tips for Division Model Drawing 1. For both division and subtraction start with longer bars. Compare part to whole unit bars. 2. Show units by dividing one long unit bar into its parts. 3. If the question asks for the value of a missing part, then place question mark inside that section of the bar. 4. Simple division problems often don t have a WHO variable. Step 1: READ 28 chairs are arranged equally in 4 rows. How many chairs are there in each row?* * NOTE: no WHO variable Step 2: Write Step 3: List Steps 4-5: Draw & Adjust There are chairs in each row. Chairs Chairs = 28 Total Practice this problem in journal. 18 cookies are arranged equally in 6 piles. How many cookies are there in each pile? Steps 6 & 7: Compute & Answer 4 units = = 1 unit =? (20 4) + (8 4) = 7 There are 7 chairs in each row.

9 Practice Multi-Step Division: Model & Guided Practice Part-Whole A man divided his fortune of $92,000 into 8 equal parts. He gave 4 portions to his wife, 1 portion to his son, and divided the remaining portions equally among three charities. How much more money did the wife receive than the son? Part-Whole A woman divided her collection of 1,200 books into 10 equal parts. She gave 3 portions to her husband, 4 portions to her daughter, and the rest equally to three nieces. How many books did her daughter receive? The wife received $ more than the son. Her daughter received books. Man s Total fortune = 8 Portions = w $92,000 w w w s c c c Woman s Total Books = 10 Portions = 1,200 H H H D D D D N1 N2 N3 1 Portion =?? wife s? son s remain? Difference NOTICE: There are 4 question marks = 4 steps 1 Portion =? Husband? Daughter Nieces NOTICE: There are 2 question marks = 2 steps 92,000 8 = 1 unit 8 units = $92,000 (64,000 8) + (24,000 8) + (4,000 8) 1 unit =? 8, , , = 11,500 Wife s Portion Son s Portion Difference 4 x 11,500 1 x 11,500 46, (46,500) (4 x 11,000) + (4 x 500) - 11, (12,000) 44, ,000 34,500 46,000 The wife received $34,500 more than the son. 10 units = 1,200 1 unit =? 1 Portion Daughter s Portion 1, = 1 unit Daughter = 4 units 1 unit = x 120 = 4( ) = 480 The daughter received 480 books.

10 Practice Multi-Step Division: Model & Guided Practice Before & After Eric had 3 times as many cookies as Sean. After* Eric ate 50 cookies, he had half as many cookies as Sean. How many cookies did Eric have left? * After = trigger word to set-up before & after models Eric had cookies left. Before & After Brenda had 3 times as many dresses as Cathy. After Brenda gave away 75 dresses, she had half as many dresses as Cathy. How man dresses did Brenda have left? Brenda had dresses left. Before 1x 2x 3x Eric s cookies Sean s cookies After Left 50 missing (ate half) Eric s cookies Sean s cookies Before 1x 2x 3x Brenda s dresses Cathy s dresses After Left 50 missing (ate half) Brenda s dresses Cathy s dresses After 6 half-units total, 5 are missing 5 half-units = = 10 1 half-unit =? Each half-unit = 10 cookies Eric had 10 cookies left. After 6 half-units total, 5 are missing 5 half-units = = 10 1 half-unit =? (50 5) + (25 5) = 15 Brenda had 15 dresses left.

11 TODAY WE LEARNED 1. to use both divisibility rules & the distributive property as an easy mental math division strategy. 2. tell HOW to use the standard division algorithm and explain WHY it works. 3. to practice fluency for multiplication using both the standard algorithm & distributive method. 4. how to use bar modeling to solve division word problems and justify solutions. Before leaving class read all of these steps and complete them: 1. Math Journal notes should be completed. If you did not have time to write everything, then grab a Lesson 4 Math Journal Slip and finish writing all of the information in your journal. 2. Complete ALL Guided Practice problems and Step-by-Step Bar Modeling word problems in your journal. 3. Complete the Independent Practice student assignment. If it is not finished in class, then it must be completed for homework.

12 Today s handouts given in class and available online.

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