Ideas for educating math reality fluency methods in first and second grade.
A Continuum of Math Strategies
Math methods develop alongside a continuum (see the dashboard above). We lecturers can construct college students’ mathematical energy by recognizing the place they’re on the technique continuum, and serving to them to transfer towards essentially the most environment friendly methods.The Institute for Mathematics and Education describes three ranges of methods for every operation (read extra HERE). When college students are first studying an operation, they depend on concrete representations. Eventually they be taught sooner and simpler methods.
Level 1: Counts All – Students make a concrete illustration of the issue by utilizing some type of manipulative or their fingers to present every addend. Then they depend all the objects to discover the whole. This is the least environment friendly technique however a essential beginning place for…nicely, just about everybody!
Level 2: Counts On – Rather than counting each object, college students simply say one of many addends after which depend on the quantity of the opposite addend. They will most likely hold observe of how many occasions they’ve counted on by utilizing their fingers. Once college students are snug with this technique they need to be inspired to all the time begin by saying the largest addend. It’s quite a bit sooner to depend on the smaller addend.
Level Three: Makes an Easier Problem – There are a number of methods to make a neater drawback. It helps if college students have already memorized doubles information and methods to make 10. Many of those methods contain recomposing the addends in a manner that’s simpler to work with. It might assist college students to mannequin these methods utilizing 10 frames or cubes earlier than they fight to carry out them mentally. These methods are sometimes essentially the most environment friendly however college students needs to be pushed into utilizing them till they’ve a robust understanding of addition. (Have you heard of the “in-betweens strategy”? Read about it HERE)
Knowing HOW to use a math technique is just step one. Kids additionally want to know WHEN to use every technique. I’ve a free addition methods poster and technique sorting exercise for subscribers HERE
Level 1: Takes Away- Just like with addition, the primary technique college students will develop for subtracting entails modeling the minuend (the primary quantity within the equation) utilizing cubes or fingers after which bodily taking away the subtrahend (the second quantity within the equation) to discover the reply (the distinction). It will get difficult and gradual when the minuend is larger than ten as a result of college students don’t have sufficient fingers anymore. Before they get there, assist information them towards the following technique…..
Level 2: Counts Up – The subsequent step is for college kids to begin on the subtrahend and see how many “jumps” it takes to rise up to the minuend. They might hold observe of those jumps on their fingers. This is a extra advanced technique than taking away as a result of it requires that college students perceive they’re calculating a distinction slightly than simply taking away. They start to see that subtraction matches a part-part-whole mannequin the place the minuend is the entire and they’re making an attempt to determine one of many components (extra on part-part-whole here). In some conditions counting up is essentially the most environment friendly, equivalent to 10 – eight. Sometimes although, it’s extra environment friendly to depend again like when fixing an issue like 10 – 2. It’s essential to spend time speaking along with your college students about which technique is the very best when engaged on an equation.
Level Three: Makes an Easier Problem – There are a number of methods to manipulate numbers to make a neater drawback. Students are steadily extra snug with addition information. If they perceive that addition and subtraction are associated, then they’ll use reality households (or associated information) to resolve subtraction issues. If they know that Three+Three=6, then in addition they know that 6-Three=Three. When scholar are snug with placing collectively and taking aside teen numbers, they’ll use the close to 10 technique. When they strategy an issue like 14-9 they’ll suppose, “I know that 14-10 would be 4. That would be taking away 1 too many. When I add that 1 back in, the answer is 5.” Another manner to make a neater subtraction drawback is to bridge via 10. This requires that college students already know the mixtures that make 10. It works like this: If a scholar is fixing 13-6, they break aside the subtrahend (6) in order that they’ll take the minuend (13) down to ten first, after which use their memorized mixtures of 10 to discover the distinction. They would wish to break the 6 into Three and three. Then they’ll suppose 13-Three=10, and 10-Three=7.
To make a neater drawback, college students ought to know their doubles information, mixtures of 10, and how to use 10s and 1s to construct and break aside teen numbers. With these conditions, the “make an easier problem” methods could be completed mentally and are very environment friendly.
If you’re on the lookout for a manner to assess what math methods your college students are utilizing (so you may information them towards the following, most effective ones!) take a look at my Math Running Record. It’s a short interview-style evaluation that provides you each a quantitative rating and qualitative details about your college students’ addition and subtraction expertise. The knowledge is beneficial for planning small teams, differentiated homework, objective setting at conferences, and even as an RTI evaluation.