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2- Digit Divisor

Journal Prompt

How would you explain using base-ten pieces to divide with a 2-digit divisor to a younger student? Use an example and place value drawings to help support your answer.

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2-Digit Divisor Practice

Directions: Model each problem using base-ten pieces. Record your work in the space provided using place value drawings. Use the other box to check the quotient using multiplication.

935 ÷ 11

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1,230 ÷ 15

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2-Digit Divisor Practice (Page 2)

1,504 ÷ 16

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1,932 ÷ 12

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2-Digit Divisor Practice – ANSWER KEY

935 ÷ 11

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|935 ÷ 11 = 85 |8 5 |

| |x 1 1 |

|Students should show 11 groups and divide the 935 evenly among the 11 groups. |8 5 |

| |8 5 0 |

| |9 3 5 |

1,230 ÷ 15

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|1,230 ÷ 15 = 82 |8 2 |

| |x 1 5 |

|Students should show 15 groups and divide the 1,230 evenly among the 15 groups. |4 1 0 |

| |8 2 0 |

| |1 2 3 0 |

1,504 ÷ 16

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|1,504 ÷ 16 = 94 |9 4 |

| |x 1 6 |

|Students should show 16 groups and divide the 1,504 evenly among the 16 groups. |5 6 4 |

| |9 4 0 |

| |1 5 0 4 |

1,932 ÷ 12

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|1,932 ÷ 12 = 161 |1 6 1 |

| |x 1 2 |

|Student should show 12 groups and divide the 1,932 evenly among the 12 groups. |3 2 2 |

| |1 6 1 0 |

| |1 9 3 2 |

2-Digit Divisor Introduction

Mrs. Canton realized she added 2,142 miles to her car’s mileage in two weeks. If she drove the same amount each day, how many miles did she drive on a given day?

To model this, Joe used base-ten pieces. He started with 2 base-ten cubes (thousands), 1 base-ten flat (hundreds), 4 base-ten rods (tens), and 2 base-ten blocks (ones) (shown here using place value drawings).

Joe knew Mrs. Canton traveled on 14 days so he has to split the 2,142 miles into 14 groups.

2-Digit Divisor Introduction (page 2)

Joe realized that the two thousands could not be divided evenly by the 14 days so he traded them for hundreds.

Now Joe has 21 hundreds, 4 tens and 2 ones.

Joe saw he could distribute one hundred to each day. Meaning Mrs. Canton drove at least 100 miles a day.

Now Joe has 7 hundreds, 4 tens and 2 ones.

2-Digit Divisor Introduction (Page 3)

Joe realized that the 7 hundreds could not be divided evenly by the 14 days so he traded them for tens.

Now Joe has 74 tens and 2 ones.

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Joe saw that he could distribute 5 tens to each day. Meaning Mrs. Canton drove at least 150 miles a day.

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Now Joe has 4 tens and 2 ones.

Joe realized that the 4 tens could not be divided evenly by the 14 days so he traded them for ones.

2-Digit Divisor Introduction (Page 4)

Now Joe has 42 ones.

Joe knows distributes one to each day until he has distributed all of the ones. He distributes 3 ones to each day and has no ones leftover. This means 42 ÷ 14 = 3.

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Joe checks to see that an equal amount of miles has been distributed to each day and sees that Mrs. Canton drove 153 miles each day.

This means 2,142 ÷ 14 = 153.

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Mathematics Alignment Lesson

Grade 5 Quarter 1 Day 8

Alignment Lesson

Modeling Divison with 2-Digit Divisor

1. Explain to students that today you will extend what they learned yesterday about dividing to include 2-digit divisors. Display Transparency “2-Digit Divisor Introduction”, displaying only the problem at the top. Have a student leader read the problem aloud and lead a discussion about what you are asked to determine.

2. Have students work in groups and use base-ten pieces to model the division problem. (If necessary, review the value of each base-ten pieces prior to beginning.) When most or all groups have found a solution, call the class back together and ask for a student leader to share what their group did to model and solve the problem. Through the use of math talk, focus the discussion on the rationale for trading base-ten pieces and what you are discovering about the quotient with each step.

3. Use Transparency, “2-Digit Divisor Introduction” to show how to use place value drawings to record what the students modeled using the base-ten pieces. Use the base-ten pieces to support if needed or you can use virtual manipulatives from this site:

4. Pose the question, “How can we check to make sure our quotient is correct?” Have a student leader lead the class through checking the quotient. (Students should suggest by multiplying the quotient and the divisor; the result should be the dividend. (153 x 14 = 2,142))

5. Distribute Blackline Master, “2-Digit Divisor Practice”. Explain to students that they will work in small groups to model each problem with base-ten pieces in order to solve. Students will also record their work on the worksheet using the place value drawings used in the introduction. They will also check their quotient. Review the answers using multiple student leaders as time permits.

6. Assign Blackline Master “2-Digit Divisor Journal Prompt” for homework. Use student responses on Day 8 to lead into dividing with 2-digit divisors without concrete modeling.

NOTE: No Formal Algorithm Required.

NOTE: Base-ten pieces (cubes, flats, rods, and blocks) are needed for small groups. You may need to borrow from teachers at another grade level to have enough for all students. Students could use virtual manipulatives as well.

Note:

Common Core State Standard(s)

|5.NBT.6 Find whole-number quotients of whole |

|numbers with up to four-digit dividends |

|and two-digit divisors, using strategies |

|based on place value, the properties of |

|operations, and/or the relationship |

|between multiplication and division. |

|Illustrate and explain the calculation by |

|using equations, rectangular arrays and/ |

|or area models. |

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Standards for Mathematical Practice

|Standard 6: Attend to precision. |

|Standard 7: Look for and make use of |

|structure. |

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Materials Needed:

• Blackline Master-, “2-Digit Divisor

Practice”

• Transparency- “2-Digit Divisor

Introduction”

• Base ten pieces

Assessment

Ask students: “Explain to me why you made that trade with the base-ten pieces.” “How does each step build to the quotient?”

Homework

Blackline Master, “2-Digit Divisor Journal Prompt”

WCPSS/PROJECT ACHIEVE/C&I/2001

LEARNING STRATEGIES:

Vocabulary

Dividend – the number to be divided; the number of items

Divisor – the number that divides the dividend; the number of groups

Quotient – the number, not including the remainder, that results from dividing; the number of items in each group

Remainder – the amount left over when a number cannot be divided equally

Source: Teacher Created

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Day 5

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Day 13

Day 8

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Day 11

Day 12

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