Constructing Times Tables Through Exploration


Objectives
Standards
Assessment
Students can articulate the relationship between addition and multiplication

Students will create their own times table to use as a reference
__CCSS.Math.Content.3.OA.A.1__ Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each.
Formative assessments
Monitor student work on writing down the products for the number they are working on with their partner


Summative assessment-
Complete entry in column of times table


Exit questions using times table used to transition students to next activity

Learning goal to post:
I can show how multiplication is adding together groups of numbers

Instructional plan (timing and activities):

Introduction
~10 min
Students will have blank times tables in front of them. Instruct them to use only pencil at this point

Present pattern of adding 2s with unifix cubes and record it on blank times table
Ask students what I am doing.

Teacher: Is there a quicker way to express 2 + 2 + 2 + 2 = 8?

Discuss multiplication as repeated addition and fill out 2's column through to 12 demonstrating amounts with unifix cubes as students follow along on their personal times tables

Guided Practice
~15 min

Teacher: Why did I start in the 2 column instead of over here? (indicate columns to the left) What might these columns be for?

Give each student 12 unifix cubes to use for modeling the amounts fin these columns for themselves

Guide students through filling out the columns for 0 demonstrate this by removing the unifix cube of the corresponding number and covering it with my hand

Have them do the same by covering the amount of unifix cubes being multiplied by zero with a hand

Teacher: How can you show one group of 1 with your cubes? How can you show 1 group of 2 with your cubes?

Continue to ask questions to prompt students to demonstrate groups of 1 with their cubes and filling out their times table

Exploration and Creation
~30

Teacher: Now, you and a partner are going to pick a number to fill out the column for on your times table. You can use unifix cubes to help show the groups you are creating and the products created by multiplying these numbers.
You can also use your white boards to help do your work with addition. If you run out of unifix cubes, keep adding from where you left off on your whiteboard.

Have students get with their designated math partner for the week and pick a number from popsicle sticks

Facilitate everyone receiving whiteboards, markers, and unifix cubes

Monitor students progress and assist and support where needed

When students finish their column, have them check their work using a master copy of the column for their number and make any necessary corrections.

When partner groups are done and have checked their work there are two more things for them to do:

1. Find a group of objects in the classroom that corresponds to their number (so if they have five, find a place where there are at least five of something like, crayons) and record that object on the back of their times table paper. They will use this idea in future lessons.

2. Begin decorating their times table, starting with just the outside border (have an example that has only this portion decorated on display)

In future lessons they will get to add all of the numbers on to their times table and once it is complete will get to finish decorating it.


Review/Closure

As an exit ticket to transition to the next activity, each group will consult their completed column to answer a multiplication word problem about the number they have been working on


Materials:
Unifix cubes, whiteboards and markers, blank times tables, crayons and colored pencils.



Future Extension of this Lesson in the Classroom

This lesson would be added to over following days. A large class anchor chart multiplication table would be created and added to as each student parte3nership would get a chance to present the numbers for their column of the table. As each student partnership presented, and added their numbers to the class table, students would add these numbers to their personal multiplication charts and continue decorating them. Students would use their personal multiplication charts to go on scavenger hunts, finding groups of items that could be represented by multiplication problems within the classroom and within the school.