Elementary Mathematics

4th Grade Unit 1: FACTORS, MULTIPLES, AND ARRAYS

Suggested Dates: Aug. 28- Sep. 18

Estimated Duration: 15 lessons
*Investigation 1: 6 lessons (include lesson 1.6A)
*Investigation 2: 5 lessons
*Investigation 3: 4 lessons


Begin with the End in Mind: By the end of this unit, students should be able to respond to the following prompts:


* PERFORMANCE TASK!  Click the Performance task to access.

Using both a hundreds board and number lines, show multiples of 6 and 8.  What do you notice? 
How does representing multiples of 6 and 8 on a hundreds board compare to showing multiples of 6 and 8 on a number line?

Keisha claims that all odd numbers are prime numbers.  Jeremiah thinks that some odd numbers are composite. 
Who is correct?  Prove it by using an area model, number line, and a written explanation.


Common Core Clusters and Standards

Standards for Mathematical Practic

Use the four operations with whole numbers to solve problems.

4.OA.1        4.OA.2        4.OA.3      

 

Gain familiarity with factors and multiples.

 4.OA.4

During this unit, focus on MP2 (Reason abstractly and quantitatively). Facilitate
use of estimation strategies to
arrive at reasonable answers.  Emphasize using known combinations
to find unknown combinations. 
Also, encourage using context and equations to represent
multiplication situations.

During this unit, focus on MP7 (Look for and make use of structure). Once students
are able to attend to the meaning of quantity and their relationships in problem
situations, help them identify and evaluate efficient strategies for a solution.
For example, ask, "Why is multiplication more useful than repeated addition?"
Or, "How can you use 8x8 to help you find 7x8?"

Take Note! Notes about each Investigation



1
 Rectangualr arrays are used as tools to highlight important relationships and properties as well as to solve problems.
Session 1.3 introduces students to prime and composite numbers.  Look for multiple opportunities to ask
students whether or not a number from 1-100 is prime or composite and explain how they know.

Common Core Snap-In provides Session 1.6A which introduces multiplicative comparison situations
(standards 4.OA.1 and 4.OA.2).  Further development of these standards is needed as students begin translating comparative situations into equations with unknowns.

2


Quick Images will be introduced during this investigation. 
Explicit use of “prime and composite” is encouraged while attending to precision.


3

Investigation 3 extends standard 4.OA.4 by using factors of 100 to find factors of multiples of 100 (200, 300…)
and by finding factors of related numbers (introduction to concept of common multiples).


Additional experiences for proving that factors of one number always being factors of multiples of that number are
provided.
The Language of Mathematics - Words students should use precisely during mathematical conversations.
Factor, unknown, dimension, array, product, prime, multiple, composite

Routine

Corresponding Common Core State Standards and Notes

Today’s Number
4.NBT.1 and  4. NBT.2    Students work within the operations of addition and subtraction to generate
equivalent expressions that yield a given number.  Be sure to show equivalency between expressions
and have students precisely explain their strategies.
Counting Around the  Class
4.OA.3, 4.OA.4, and 4.OA.5   Students find the multiples of a given number (factor) while skip counting
(numerical pattern).   Have students occasionally provide equations to model stated multiples, e.g.,
“What equation represents what the ninth person said while counting by 4’s? (9 groups of 4 is 36 or 9 x 4 = 36).  This will help them understand the relationship between skip counting and multiplication. 

Quick Images
4.OA.5   Subitizing (quick images) promotes organizing and analyzing visual images, increases computational fluency, and allows students to model with mathematics by generating equivalent
expressions (equations).

When students struggle, have them...

When students clearly understand, have them…

- Have students use manipulatives/tools like colored tiles,
snap cubes, and grid paper to build and/or replicate
arrays (concrete models).  Also, provide real-life examples.
- Work Work with smaller numbers while representing
multiplication situations.

-Encourage students to use the distributive property to
find unknown products from known combinations.

-Ask students to write story problems that visualize
multiplication expressions.

Technology Connections



Investigation 1 Smart Board Lesson (These are updated now on the new page)

Investigation 2 Smart Board Lesson

Investigation 3 Smart Board Lesson

Professional Learning Opportunities

Why is it important for students to develop strong visual images of multiplication?  Read “Images of Multiplication,” pp. 115-116.

How does using arrays to represent multiplication increase multiplicative understanding?  Read “Representing Multiplication with Arrays,” pp. 117-119.

How can I help my students learn their multiplication combinations fluently?  Read “Learning and Assessing Multiplication Combinations,” pp. 120-122.
 
End of Unit 1 Assessment Rubric

4th Grade Vocabulary List in English and Spanish

Investigations Vocabulary

Investigations Unit Vocabulary

3-5 Literature List

Extension Projects for Investigations

Literature for Unit 1: 

All About Multiplication

One Hundred Hungry Ants

Each Orange Had Eight Slices

What Comes in 2’s, 3’s, and 4’s

Anno’s Mysterious Counting Jar.

Two Ways to Count to Ten

 

Illuminations:  All About Multiplication

Activities

-Representing Multiplicative Comparison Problems

-Multiplicative Comparison Problems

-Finding Multiples

 

Games

-Factor Game

-Prime Number Hunt

 -A Prime Numbers Math Game

-Prime Numbers Game

-Play Two-Minute Multiples






*Remember to upload files to share with others, or locate files to use, on the wiki. Be sure to join discussion posts with other colleagues to ask questions, answer questions, and discuss math.