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Factor

 

Objectives: 

·             To review the meanings of factor and product; to find all factor pairs for a number; and to assess and develop instant recall of multiplication facts.

 

                      Download as Microsoft Word Document:

Instructional Plan

 

Instructional Plan Template

Mathematics Governor’s Institute 2005

 

Names of group members:  Stacey Elliott, Donna Koval, Lina Penn, Wanda Ponder, Jodie Sauers

 

Topic/Theme:  Factors

 

Level:  Grade 5

 

Time Element:  Two class periods.

 

NCTM Standards Addressed:  Numbers and Operations, Grades 3-5:  Describe classes of numbers according to characteristics such as the nature of their factors.

 

PA Math Standards Addressed:  2.1 Numbers, Number Systems and Number Relationships:  2.1.5.G:  Develop and apply number theory concepts (e.g. primes, factors, multiples, composites) to represent numbers in various ways.

 

Math Assessment Anchors Addressed:  M 5.A.1.6:  Numbers and Operations

 

Reading Assessment Anchors Addressed:  1.1.5.D:  Identify the basic ideas and facts in texts using strategies. 1.1.5.F:  Identify, understand the meaning of and use correctly key vocabulary from various subject areas.

 

Objectives: 

  • To review the meanings of factor and product; to find all factor pairs for a number; and to assess and develop instant recall of multiplication facts.

 

Instructional Strategies and Plan (include strategies used to help different types of learners, i.e. auditory, visual, etc):

                 Strategies

  • Teacher modeling
  • Cooperative learning
  • Whole class discussion
  • Independent activity
  • Enrichment/remediation

 

                 Instructional Plan

  1. Warm-Up—Students make all possible arrays of a given number on dot paper using counters.

**Whole class discussion—sharing arrays and reflecting upon their thinking process.

  1. Whole Class Activity—Review factors, products and factor pairs.

 

               3*5=15                                                          15*1=15

                      (3 and 5 are the factors; 15 is the product)

                      (15 and 1 are the factors; 15 is the product)

  1. Independent Activity—Practice finding factors of a given product using counters, if needed.

 

                                      

Number

Number Models/2      Factors

All Possible Factors

20

 

 

16

 

 

13

 

 

27

 

 

32

 

 

 

  1. Partner Activity—Students can use fact triangles to help them recall the facts they don’t know (see attachment “Fact Triangles”).
  2. Students will draw arrays in small groups to find all of the numbers up to 20 that can be arranged into arrays with 2 rows ( relate to even and odd numbers).
  3.  Teacher introduces the game “Factor Captor” and reviews game rules (see attachment, “Factor Captor”).
    • Play a few practice rounds with the class using an overhead transparency of the “Factor Captor” grid.
    • Students break into partners to play the game on their own, discussing strategies they used.
  4. Individual Assessment—After playing several rounds have students complete an “exit slip” describing strategies that maximize scoring.
  5. Open-Ended Assessment (see attachment, “Planting Daffodils”and rubric).

 

Materials/Resources:

    • Lessons 1.3, “Factors”, 1.4, “Factor Captor” from Everyday Math series, Grade 5
    • Counters
    • Dot paper
    • Copy of chart in “Independent Activity”
    • “Factor Captor” grid
    • Overhead projector
    • TI15 Calculator
    • Paper
    • Pencil

 

Interdisciplinary Connections:

·         Reading—Reading to perform a task, reading to follow directions, expanding vocabulary, reading independently.

 

 

·         Technology—TI15 Calculator, Overhead Projector, Computer (for enrichment purpose and/or remediation).

 

 

·         Other—Science (extended activity, Garden Club)

 

 

Assessment Strategies:

·         Formative Evaluation (checking student understanding during the lesson):

 

1.      Math Games (computer games)

2.      Teacher Observation

3.      Class Participation

4.      Fact Triangles

5.      “Factor Captor”

 

 

·         Summative Evaluation (How will it be determined that the objectives were achieved?):

 

1.      Game “Exit Slip”

2.      Open-Ended Assessment (“Planting Daffodils”) and rubric

 

 

Correctives/Remediation:

·        Completion of independent activity with a partner

·        Peer tutoring

 

 

Extensions/Enrichment:

 

 

 

Special Accommodations (special needs students)

·          Description of the Special Needs student selected:

Student #4—Male—This student appears to be a disinterested learner.  He loves to draw, but it is difficult to motivate him to do other tasks.  His father says, “Well just let him draw if that is what makes him happy.”

 

·          Accommodations to use with this student:

Student will illustrate factoring by using factor rainbow or factor tree.

Student will illustrate arrays for the group

Student will illustrate definitions or examples of vocabulary

Student can work with a peer tutor

 

 

 

VOCABULARY:  factor, product, factor pair, even number, odd number,

factor rainbow, factor tree

 

Open Ended Assessment

Planting Daffodils

 

 

Rubric

 

 

4 –The student successfully illustrated all four possible arrays including 2 and 18, 6 and 6, 3 and 12, and 4 and 9.

 

 

3- The student successfully illustrated 3 of the 4 possible arrays.

 

 

2- The student successfully illustrated 2 of the 4 possible arrays.

 

 

1- The student successfully illustrated 1 of the 4 possible arrays.

 

 

0- The student did not successfully illustrate any of the 4 possible arrays, or did not attempt to complete the activity

Open Ended Assessment

 

Planting Daffodils

 

Mrs. Smith has 36 daffodil bulbs. She wants to plant them in a rectangular array consisting of at least two rows with at least two daffodils in each row. Draw as many arrays as possible.

               

  4

 

 

               

           *                        

 

 

3                                              12

 

            

                                Fact Triangles

Factor Captor

1

2

2

2

2

2

2

3

3

3

3

3

3

4

4

4

4

5

5

5

5

6

6

7

7

8

8

9

9

10

10

11

12

13

14

15

16

18

20

21

22

24

25

26

27

28

30

32

Materials         calculators for each player

 paper and pencil

 a Factor Captor grid

 48 coin-size counters

 

Players

Directions

1.  To start the first round Player 1 (James) chooses a 2-digit

      number on the number grid.  James covers it with a counter, and records the number on paper.  This is James’s score for the round.

 

2.   Player 2 (Emma) covers all of the factors of James’s number.  Emma finds the sum of the factors, and records it on paper.  This is Emma’s score for the round.

 

A factor may only be covered once during a round.

 

3.   If Emma missed any factors, James can cover them with counters and add them to his score.

 

4.   In the next round, players switch roles.  Player 2 (Emma) chooses a number that is not covered by a counter.  Player 1 (James) covers all factors of that number.

 

5.   Any number that is covered by a counter is no longer available and may not be used again.

 

6.   The first player in a round may not cover a number less than 10, unless no other numbers are available.

 

7.   Play continues with players trading roles in each round, until all numbers on the grid have been covered.  Players then use the calculators to find their total scores.  The player with the higher total score wins the game.

 

           

               

 

 

 

 

 

 

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