In recent years there has been a huge shift away from rote memorization of math facts and toward a strategy-based approach for learning math facts. There’s a big difference between memorizing and understanding. Sure, we want kiddos to have automaticity with their facts. Knowing math facts is similar to knowing sight words–it frees up the mind to solve real math problems. If a child has to struggle to solve 8 + 3, they have no mental energy (or desire) left to grapple with the types of problems that will increase their capacity as a mathematician.
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A great resource for strategy-based fact instruction is Mastering the Basic Math Facts in Addition and Subtraction: Strategies, Activities, and Interventions to Move Students Beyond Memorization. There’s one for multiplication and division facts, too.
A big problem with teaching kids facts is that we often jump to the abstract (symbolic) level of instruction too fast. This does two things: (1) produces children who can recite their math facts, but have no real understanding of what they mean, and (2) children who get left behind because they can’t memorize. I’d be hard-pressed to say which is worse.
Learning facts begins in Kindergarten (or PreK) when students are exposed to dot patterns and five-frames. When a child can see 2 dots and 3 dots on a card and know without counting (subitize) that there are 5 dots, that’s the foundation of learning math facts.
The concrete for the foundation sets (or doesn’t…) in first and second grade. Ten-frames are magical! Not only do they help students see how the ability to compose and decompose numbers helps connect facts they know with facts they are learning, but they also plant the seed for place value.
Students should have extensive exposure to the combinations that make ten using objects or drawings in Kindergarten (CCSSM K.OA.4). This skill goes by many names: friends of 10, making ten, tens partners. But it’s an absolutely essential skill–move it up to the top of your to-do list! Raise your right hand and repeat, I will not let my kinders become firsties without knowing their combinations for ten! Why is it so important? In 1st grade students are expected to add and subtract within 20 with fluency to 10 (CCSSM 1.OA.6). That means they should have automaticity of the facts within 10 by the end of 1st grade. Why? Because in 2nd grade the standard is for fluency of facts within 20 (CCSSM 2.OA.2). Do you see that beautiful progression? Do you also see, however, how critical it is that students master their grade-level standards? And what happens after 2nd grade? Multiplication, of course, but that’s a post for another day.
Which finally brings me to today’s activity, which utilizes the Using Tens strategy. We want students to be so familiar with their combinations for ten that they automatically use them. When a child is trying to add, for example, 9 + 4, a great strategy is to split (decompose) the 4 into 3 and 1, use the 1 with the 9 to make a 10, and then add on the 3 to make 13. Likewise, to add 8 + 3, split the 3 into 2 and 1, use the 2 with the 8 to make 10, and add on the extra 1. All this is a mental process, of course, but it begins with lots of work on ten-frames–first with counters and then by drawing. Look at the picture below that illustrates 9 + 4. Don’t you see the splitting of the 4 into 3 and 1?
The paper-and-pencil activity shown below is an assessment I created for my 1st-grade teachers. Note that it is an assessment to be used after students have had lots of practice with the concept.
I hope I’ve given you some food for thought today and helped you to better see the progression of fact mastery through the early grades. I’d love to hear your comments! Click here to grab the freebie assessment.