This lesson builds strategies for learning fundamental multiplication facts using story-problem contexts. One computation tool that can be used is a number line. Students are encouraged to use a variety of methods to represent and discuss their solutions. Students are going to:
- show off techniques like repeated addition or skip counting.
- keep track of the number of sentences to demonstrate their work.
- sketch illustrations of their ideas.
- make use of counting techniques, both forward and backward.

- How are mathematical representations of relationships made? 
- How are relationships in mathematical contexts described by patterns? 
- How do we represent, compare, quantify, and model numbers using mathematics?

- Equivalent: Equal.

- class number line, for use under a document camera or on an overhead projector (M-2-4_Number Line) 
- document camera or overhead projector 
- Equal Groups book cover page with added blank paper (M-2-4-2_Equal Groups Book) 
- Hula-hoops or large circles made from string 
- number cubes, two different colors if possible 
- chips/counters, 25 per pair 
- paper plates, six per student (It would be easiest if the plates matched one of the number-cube colors.) 
- paper and pencils or dry-erase markers and whiteboards

- As students are working in pairs on the task, keep an eye on them and grade them.
- Formative assessments can be performed with student math journals or Equal Groups books (M-2-4-2_Equal Groups Book).

Explicit instruction, modeling, scaffolding, and active engagement
W: Go over the work from the prior lesson in equal groups. Display to the students the tools (circles or hula hoops) that you will be using in class. 
H: Use the number cubes to determine the total number of groups and members within each group. 
E: Use the chips/counters, plates, and two-number cubes to play a game. 
R: Keep an eye on your students while they play to make sure they're moving correctly and writing number sentences. Go over concepts with students who need a refresher or clarification. 
E: Students will share their strategies with partners and reflect as a class. 
T: Students who require an extra challenge can use one deca-number cube and one 1–6 number cube. If a student is having trouble, they can use a number line or alternative number cubes with fewer numbers. 
O: The lesson is presented to the entire class at first, then broken up into pairs, and lastly, it is brought back to the entire class for a summary. 

Display the string circles, also known as hula hoops, to the class. Inform the students that you will be using them to work through "equal groups" problems. Remove the two colored number cubes. "The green number cube will show how many people are in each group, and the red number cube will show how many groups there will be overall." First, roll the red number cube. Give each student an equal number of consecutive Hula-Hoops. "We will set up 4 Hula-Hoops since I rolled a 4." Next, throw the green number cube and say, "It's a five, so we'll need five students in each hoop." Select 5 students for each hoop. Next, ask, "What is the total number of students in the hoops? How are you aware?" Give students enough time to react. Ask the students to take a seat again. Sketch what they modeled on the board or chart paper. In each hoop, draw four circles and then smileys. Assist students in creating the matching number sentence by using both words and numbers:

20 students are equal to 4 groups of 5 students, so 4 × 5 = 20.

                                     -or-

4 groups of 5 students equal 5 + 5 + 5 + 5 = 20, so 4 x 5 = 20.

Once again, roll each number cube (or have a student roll one) and arrange the corresponding number of hoops and students in each hoop. Once more, use words, pictures, and numerals to represent the number sentence. Continue until the majority of students appear to grasp each step.

Display the number of cubes, chips, and paper plates to the students. Show that, although using plates and chips in place of people and hoops, they will be following the same procedure as the class. In their math notebooks, on whiteboards, or in the Equal Groups Book (M-2-4-2_Equal Groups Book.docx), students can document their ideas. [Note: It could be useful to have paper plates, chips, and number cubes all the same color.]

Ask pupils to complete the task multiple times. Have a look at the techniques that students employ, like repeated addition or skip counting. Additionally, pay attention to students who are starting to grasp the idea of the commutative property of multiplication, which states that a × b = c and b × a = c.

Call the class together and give a summary of the lesson once you believe they have a firm grasp of the material. Use questions like these:

"Tell me about something you found easy."
"What did you find difficult?" 
"What caught your attention?"
"Did you notice any patterns?"
"How could you solve the problems if you didn't have plates or chips?"

Extension:

Use the activities listed below in your classroom to meet the needs of your students throughout the year.

Routine: As needed, have students assist in resolving class grouping issues. "We have 7 groups of 2 students, so how many students are there here today?" You can use them to assist you in finding equal groups, which is a challenge. "There are twenty students present today. How many four-person groups are we able to form?"

Workstation or Small Group: Keep an eye out for students who are using the 1s to count when solving equal-group problems. To encourage skips or even stress counting, these students might benefit from additional support in the form of number lines. Alternatively, they could use number cubes with just 0–5 on them or even just 2, 3, and 5 on them. This will reduce the number of groups they initially need to become automatic with.

Expansion: Students can work with one deca-number cube (0–9) if they're prepared for a more difficult task. For problem-solving, they might also need to make sketches or take notes.