Taking a CRA (Concrete-Representative-Abstract)
approach can help students to understand and generate related facts and addition and subtraction fact families.
Allow students to use a concrete manipulative such as linking cubes that they can physically put together and take apart to generate the 4 related facts.
In this example I added pictures of turtles and turtle shells to the blocks so that there is context around the number as well.
While students are using the hands-on materials, I also ask them to put their numbers into a number bond. This helps link to representative and abstract levels!
A material such as red and yellow disks is another concrete tool that can be useful for your students. The difference between the linking cubes with pictures and red and yellow disks is that the disks lack a story context making them a bit trickier to work with for students.
Additionally, it is useful to use a variety of concrete
tools so that your students have the chance to generalize what they are noticing about putting parts together and taking them apart to generate fact families.
Taking a step away from concrete materials, dice are a great representative tool. By using dice students can still see both parts (in the pips!) that they are manipulating. They can still push them together and pull them apart to simulate the action associated with addition and subtraction number sentences. However, they are no longer manipulating each individual unit. This is a step in the right direction for your students!
When your students have been successful with concrete materials and representative models such as the pips on a dice, it is time to move towards a more abstract representative model.
At this point students are working with numbers in a number bond and they don’t have any tool to manipulate the parts that are being put together and taken apart.
Your students have worked at the concrete and representative levels and, all the while, you asked them to record their equations. This was all in preparation for the abstract level! At this point, if students have worked away from needing a hands on tool or visualization, they should be able to independently generate related addition and subtraction word problems.
A fun way to practice at this level involves a partner game where each student comes up with a number 1-10 and writes that number in their candy bag. Students then show one another their numbers and write addition sentences combining their bags of candy and subtraction sentences breaking their bags back apart. I love this partner game because students can work independently to generate their fact families and then use math vocabulary to defend their responses and check their work.
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