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Understanding equal groups is foundational to understanding multiplication and division. This set of equal groups multiplication and division tasks allows students to explore equal groups and the language around equal groups so that they will be successful moving into the new operations of multiplication and division.
The 5 examples listed are certainly not an exhaustive list of tools and lessons that could be used to teach this skill.
They are rather a sample progression from hands-on to abstract thinking!
Which step represents your students’ current level of understanding?
When introducing equal groups, it is also important to introduce the idea of even vs. odd to your students.
Try this activity: Provide students with a small pile of counters, cubes or mini erasers. Ask your students to distribute the pile evenly- are they able to do it? Sort the piles based on whether or not they were able to be split evenly an introduce the terms even and odd to describe these groupings.
After sorting many piles and numbers under the headings of even and odd, ask your students what they notice about the number under each heading. Are there any patterns they can find?
Context is key! When introducing a brand new concept such as multiplication and division, a context or simple story can guide your students to understand.
Try this: state a simple story such as “I have 12 friends coming over for dinner and I have tables large enough to seat 4 people each. How many tables will I need to put out so that everyone has a seat?” Then allow your students to use a wide variety of math tools to model the story problem.
Take a gallery walk around the room and allow your students to describe how their model matches the story problem. What were their findings?
As your students show a level of confidence modeling equal groups with hands-on materials, introduce the idea that you can draw equal groups using either dots and circles or a number bond.
As in the preview step, provide a story context for your students to explore and ask them to model using hands-on manipulatives. Ask your students to then draw a picture or use a number bond to model the same problem. How is their picture similar to their model? How does their picture show the parts in the story? How does their picture match the whole in the story and in their hands-on materials?
The language of arrays, rows and columns may be new to your students- but contexts including arrays, rows and columns are all around!
Use simple story problems to provide a context to your students as they explore arrays and use this math vocabulary for the first time.
For example, “I have a bookshelf. The bookshelf has 4 shelves. I want to put 3 books on each shelf. How many books will I be able to fit on my bookshelf in all?
Provide your students with hands-on materials such as counters, mini erasers or even cut outs of small books and a small bookshelf (as seen in the picture).
As your students are working, continue to use and encourage the use of words such as array, row and column.
Moving your students from hands-on models to representational models is as simple as asking linking questions.
Provide your students with a new context around rows and columns such as students standing on risers at a choir concert. Ask your students to model the scenario using hands-on tools but then ask them to also draw a picture or fill in a number bond to match this same scenario.
Ask linking questions:
Where are the rows in your model? And where did you show that in your picture?
How many were in each row in your model? And where did you show that in your drawing?
How many total items were there in your model? Where did you show that total in your drawing?