Make Ten is a key strategy for any addition facts with an 8 or a 9. We want students to think “How many more are needed to make 10?” and then “How many are left over?”

For example: 8 + 7

How many more are needed to make 10? 2!

If the 2 is taken from the 7, how many are left over? 5!

So, 8 + 7 is 10 + 5, or 15.

Key subskills are knowing how many more are needed to make 10 (bonds of 10), and how much is left after that step (-1 or -2). The near numbers one less and two less should be practiced using ten frames and dot plates. The near number page also has other strategies.

One way to help students record their thinking is to use branch diagrams to show how they partitioned the numbers. This can also support work done in grade 2 for partitioning multidigit numbers to add.

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This ability is also used in later years for multi digit computations, such as 28 + 7. It forms a key subskill in developing jump strategies for performing multidigit addition and subtraction.

Why turn a one-step question into a 3-step problem? What is the rationale behind this strategy, how does it make things easier for the student?

Thanks for these–very good examples of using structure to learn number combinations with understanding vs. memorization like I did in elementary school!

The old way of education sorted smart students from not so smart students. This way of teaching allows the sharp/quick students to work quickly using their one or two steps and allows the student who needs additional support to have access to the learning using more steps. Memorizing use to work and still will; however, if a students doesn’t know why something works, they will not function in the world. Efficiency comes with understanding. Back in the day efficiency came because we copied what the teacher told us to do. By the way, China and India teach these concepts, techniques, and computation skills at an earlier age. America is behind because parents choose not to make or take time to help and support their kids. Learn the strategies to support your child, and if they get it, then work on efficiency.

I use bridging strategies a lot when I’m thinking about time. For instance: What year was it seventeen years ago? If I used a standard subtraction algorithm to compute 2016 minus 17, I’d need pencil and paper; but if I subtract 16 and then subtract 1, I can do it in my head. Likewise for questions like “What date was two weeks ago?”, “What time will I get home if I leave work at 5:25 and it takes 40 minutes to drive?”, etc. To cultivate the skill of bridging, it’s helpful to practice on simpler examples like 8+7, where (as Ted points out) it would be more efficient to simply consult a memorized addition table. Such examples can strike parents as pointless, but they’re about skill-formation, not the answers to particular problems. (Analogy: When you learn to ride a bike, you fall down a lot in trying to get from A to B. “Wouldn’t it be more efficient to just leave the bike and walk?” Yes, if your goal is to get to B; no, if your goal is to learn how to ride a bike.)

This makes things more complicated

My younger sibling had trouble through this and it’s way more complcated

gesuss wat

good

I taught my first grader how to add and subtract in one week this new way of doing things is plain stupid why make things harder to understand if you don’t need to hopefully Trump gets rid of this crap.

This bridging just confuses kids even more! I see my children who can add and subtract very well get seriously confused and find simple math complicated…Very poor teaching strategy…

HI

My first grader has this with his math homework. He’s a gifted math student and tests at the 5th grade math level. He never had a problem with math until they threw this at him. He struggles with this and also hates near doubles strategy. I understand bridge strategies and use them myself when doing more complicated math in my head. However, taking a simple problem and using strategies to make them more complicated is confusing because your brain almost wants to rebel against adding steps to solve something when the answer is already in your head. I honestly don’t think it’s helpful to introduce the strategy until the math gets a little more complicated.