Arranging Numbers in Multiple Ways

Lesson Plan:

# Arranging Numbers in Multiple Ways

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October 7, 2015

by Angela Fiorille

October 7, 2015

by Angela Fiorille

### Learning Objectives

Students will be able to find all of the factors pairs of whole numbers up to 100 and decide whether a given whole number, within 100, is a multiple of a given one-digit number.

### Lesson

#### Introduction
*
(5 minutes)
*

- To begin, tell students that this lesson focuses on multiplication.
- Ask students to share what they already know about multiplication. If you have already been studying multiplication, build on that, but if you have not, just let students share what they generally know.
- Explain that today's lesson will involve pairs, which you will introduce in a moment. Ask students to give examples of pairs.

#### Explicit Instruction/Teacher Modeling
*
(5 minutes)
*

- Write the number 14 on the board.
- Ask students if they know what a
**factor pair**is. Explain that a factor pair is two numbers multiplied together to get a product. - Explain that in today's lesson, students will work together to find factor pairs of
**whole numbers**. Ask students what a whole number is. Remind them that a whole number is a number without fractional or decimal parts.

#### Guided Practice/Interactive Modeling
*
(15 minutes)
*

- Tell students that you will practice finding factor pairs together, before trying it in pairs.
- Point out the number 14 on the board. To check for understanding, ask students if 14 is a whole number and how they know.
- Model pulling out 14 cubes.
- Tell students that now we will need to make an
**array**using the cubes. Ask students to define array. Remind them that an array is an arrangement in a particular way. - Model making a 2 row by 7 column array. Write 2 x 7 on the board. Explain that you made a 2 x 7 array, which means that 2 and 7 are a factor pair of 14.
- Ask students other ways that we could arrange the cubes in a rectangle, to make an array. Make sure to show 7 x 2, 14 x 1, and 1 x 14, recording the factor pairs as they are made.
- Explain that they can use factor pairs to help understand
*multiples*. Ask students if they know what a multiple is. Define multiple as the number found when multiplying one number by another. - Explain that 14 is a multiple of 1, 2, and 7. Model skip counting by those numbers to reach 14.
- If needed, go through this process again, using 21 as the whole number.

#### Independent Working Time
*
(25 minutes)
*

- Explain to students that they will now work in pairs to find all of the factor pairs of various whole numbers under 100.
- Pair students up and hand out the How Many Ways Can You Arrange My Number? worksheet.
- Remind students to use cubes if they need to. They may also draw arrays on their papers.
- As students work, check in with pairs to make sure they are finding all of the factor pairs for each number.
- Encourage the use of cubes for students who need visual support.
- Students who finish early can work on the How Many Ways Can You Arrange 100? worksheet.

### Extend

#### Differentiation

**Enrichment:**Students who finish early can work on the How Many Ways Can You Arrange 100? worksheet. If they are also able to complete this, have them work on finding factor pairs of multiples of 100.**Support:**Students who need extra support can either work with partners or in a small group with teacher guidance. Make sure they use the cubes and understand how to make rectangular arrays.

### Review

#### Assessment
*
(5 minutes)
*

- Take note of student participation in the different parts of the lesson.
- Check the worksheet and index card answers for mastery.

#### Review and Closing
*
(10 minutes)
*

- Ten minutes before the end of the lesson, ask students to stop working and have them come together.
- Write the number 36 on the board.
- Hand out an index card to each student.
- Tell students to write: "1. One factor pair of 36 is..." and "2. 36 is a multiple of..."
- Tell students to think back over the lesson and fill in the answers on their index card.
- As this is an assessment of student understanding, students who are unable to give an answer will need more practice.

Start Lesson
Guided Lesson: Number Sense 3

Guided Lessons are a sequence of interactive digital games, worksheets, and other activities
that guide learners through different concepts and skills.
They keep track of your progress and help you study smarter, step by step.

Guided Lessons are digital games and exercises that keep track of your progress and help you study smarter, step by step.

Understanding how our ten number system works enables students to see interesting and useful patterns and relationships in these math activities. These patterns allow students to develop more efficient mental math strategies when multiplying by multiples of 10 or 100. Students will also review rounding and apply this skill to larger numbers - up to 100,000â€™s place.

Understanding how our ten number system works enables students to see interesting and useful patterns and relationships in these math activities.

This lesson includes printable activities:
Download All (5)

Exercise: Find the Factors of Prime and Composite Numbers

Exercise: Place Value and the Thousands Place

Exercise: Comparing Multi-Digit Numbers

Exercise: Place Value and Multiplicative Comparisons

Exercise: Multiply by Multiples of Ten

Exercise: Place Value Up to Hundred Thousands Place

Exercise: Place Value Up to Ten Thousands Place

Exercise: Place Value and Numbers in Expanded Form

Exercise: Rounding Multi-Digit Numbers to the Nearest 1,000

Exercise: Rounding Multi-Digit Numbers to the Nearest 10000

Exercise: Rounding Multi-Digit Numbers to the Nearest 100,000

Exercise: Comparing Decimal Numbers

Exercise: Ordering Decimal Numbers

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