Gifted students and math are a perfect fit!

I love teaching math. There's just something about logically applying rules and procedures and operations to arrive at a correct answer that kids can really understand… *if* they are infected with the teacher’s enthusiasm for the subject.

So math holds particular promise for your gifted students; it’s a subject where they can truly push ahead incrementally and gain the satisfaction of mastering a new challenge while feeling super smart in the process.

## Gifted student math strategies

There are three basic strategies for adding rigor to math instruction for gifted students. Here they are:

**1.** Use more-challenging numbers

**2.** Add additional steps by combining standards

**3.** Introduce the next-grade-level standard

Let’s go over each of those in more detail.

## Use more-challenging numbers

This is the easiest strategy of them all, and easy to apply in different grade levels, too. We’ll look at examples in two different grade levels.

#### Grade 2

Let’s start with a 2nd grade problem based on CCSS 2.NBT.6.:

Add up to four two-digit numbers using strategies based on place value and properties of operations.

Here is an example problem based on that standard:

Carl has four piles of Legos® sorted by color. The red pile has 42, blue has 64, yellow has 19 and green has 38. How many Legos® in all?

We can increase the difficulty level for an early finisher just by saying:

“Holy smokes, Janice! You zipped through those. But, what if Carl’s green pile had 538?”

See how we just bump up the rigor a bit? It takes no advance planning at all. In fact, for lower grades, you could call this strategy “just add hundreds.”

Be very cautious, however, about “adding thousands” unless you are very sure there is adequate understanding.

#### Grade 6

Let’s look at a similar situation in grade 6. We’ll use CCSS 6.EE.A.1.:

Write and evaluate numerical expressions involving whole-number exponents.

Here is an example problem based on that standard:

Trina wanted to buy carpet for her square room. Her room is 13 feet on each side. Write and solve an equation to find area using an exponent.

The answer to this problem is:

13 x 13 = Area

13² = Area

169 square feet = Area

And your directions to add additional rigor:

“Wow, Peter… you’ve got this down! What if Trina’s room was 12.5 feet long on each side?”

Using larger or more-challenging numbers (such as decimals) is a quick way to extend learning for gifted students while keeping them on the same standard you are helping the rest of the class with.

Let’s keep with the same standards while we implement the next strategy.

## Add additional steps

At any grade level, the more steps that must be completed, the more challenging the problem becomes. Any operation that the students have been exposed to in the past is fair game – even ones from prior grade levels.

Here’s how I would add steps to our second-grade math problem:

“Now that you know how many Legos® Carl has, do you think he can share them equally with two friends? Explain why or why not!”

And now for the 6th grade one:

“The carpet Trina wants is $3.64 per square foot. How much will it cost to carpet Trina’s room?”

This is another technique that requires no advanced planning. Now… let’s bump those smarties up to the next grade level.

### Video tips: adding rigor to math lessons

## Introduce the next-grade-level standard

This strategy requires that you know the next grade’s standard. It's easy to keep those at your fingertips using my Common Core Guidebooks.

#### Grade 3 → Grade 4

Let’s consider this third-grade standard… CCSS 3.NF.A.1.:

Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

After you have taught your mini-lesson, a gifted student will understand that 1/4 is one piece of a pie that is cut into four pieces. She will also know that 3/4 of a pie is when a pie is cut into 4 pieces and you take 3 of those pieces of pie.

Of course we always teach fractions with a variety of models, some of which are contextual such as using pies or pizzas. But Common Core focuses on using a *number line* to show understanding of fractions and their equivalence. Students should be able to demonstrate using a variety of models, and that is one way to challenge gifted students.

Here’s the fourth-grade standard that we want to stretch our gifted early-finisher up to. It’s CCSS 4.NF.A.1:

Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

To extend to this fourth grade standard while in third grade, you might say to your little Einstein:

“What if that pie you cut into four equal pieces was cut into eight equal pieces? How many pieces would be the same as 3/4? How do you know they are the same?”

This requires the student to draw a model to show evidence that 6/8 is the same as 3/4 and a number line is the best choice. To challenge further, you might ask her if she can show the same thing on a tape diagram or using fraction bars.

#### Grade 6 → Grade 7

Let’s consider this sixth-grade standard… CCSS 6.G.A.1:

Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

After you have taught your mini-lesson, given the following right triangle, students would first find the area of a rectangle that measures 8 inches by 5 inches. Then students would find half of that value to give the area of the right triangle:

Here’s the seventh-grade standard that we want to stretch our early-finishing sixth-graders up to. It’s CCSS 7.G.A.1.:

Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

To challenge your gifted students to start thinking about scaling figures, you might say:

“Wow! Nailed it! What if the length and width of that right triangle were nine times as big? What would be the length and width and area be? Can you draw that out and show me what you come up with?”

By the same token, you could say:

“What if that rectangle was one-fourth the size?”

This is more challenging given that five divided by four leaves you with a decimal of 1.25.

Do you still need some challenging work for these super-smart kids? No problem! Let’s combine strategies.

## Combining strategies

Taking our third-grade problem, we can combine strategies by saying this:

“How many different models can you use to show 3/4 and 6/8 are equivalent?”

Answers that include circle model, fraction bars, or number lines are all appropriate for third-graders.

This combines:

- 3.NF.A.1.: Understanding what a fraction represents

- 3.NF.A.2.: Using a number line

- 3.NF.A.3.: Explaining equivalence

And for sixth grade, we can say:

“So… can you plot the right triangle on a coordinate grid and find the coordinates for the vertices?”

And then:

“You know… you can scale a right triangle and still find its area. What would be the coordinates for the vertices if the right triangle was three times larger?”

This combines:

6.G.3.: Draw polygons in the coordinate plane

6.RP.3.: Use ratio reasoning to solve real-world and mathematical problems

The beauty of this approach is that all of these steps follow logically from the original problems that we have assigned to reinforce our mini-lesson. Your struggling math-heads are getting the individualized support they need while your gifted students are pushing their own boundaries – while both sets of kids continue to work on the same subject and nearly the same standard.

## The magic question

There’s one final technique that will add some sizzle to your extension activities. It’s the magic question:

“How do you know it’s right? Show me!”

Try it and you’ll see that it pushes students to even deeper understanding, no matter what level they are working at.

MommyJAG says

atThis is pretty much exactly how not to teach math to an actual gifted child. I’m sure it’s fine for the top half of the class though. Well mostly. Extra steps and show more work are just ways to make math less fun and more work.

My second grader (age 7) who is actually gifted and not just a good student just tested at 5th grade for both math and reading. He is able to do a lot of math beyond 5th, but he has some gaps to patch up before moving on. The idea of giving him addition with bigger numbers is ludicrous. He’s most of the way through pre-algebra and high school geometry on Khan Academy, which he does for fun at home.

His teachers have a very hard time finding anything of value to teach him, so he mostly does math on the computer/teaches himself. The idea that a student in the 98th to 99.9999+ percentile in conceptual understanding of math is served by adding an extra digit and/or one year up extension activities is beyond my ability to comprehend. School can do nothing for my son’s interest in physics, chemistry, or geography, but at least they aren’t forcing him to do second-grade math with extra steps and extra work.

Betsy says

atThere’s no doubt that your son provides a particular challenge for most teachers when trying to provide what he needs while serving the rest of the class. I think it’s great that he has the support of his parent to fill in where most teachers are unable to go due to time.

A truly advanced child is more the exception than the norm in most districts’ gifted designation parameters. For most who are “gifted,” it can be very effective to work up one or two grade levels by extending the same standard. It’s not punitive if presented correctly and NOT in addition to other work.

For those who reveal themselves to still need more challenging work, a special effort must be made. In my elementary schools, we have a senior citizen volunteer who comes in every week and will work with advanced kids as high as they are capable of going in math. Not a solution for all schools, but resourceful teachers can work to find an upper-level advanced student (e.g. from high school) to provide tutoring.

It truly takes a team approach to serve the individual needs of all students, especially if a teacher feels inadequate to provide what is needed. Thanks for commenting.

Jamie says

atWhat a wonderfully executed answer Betsy. I love your strategies and will be trying them today as I have a mother a lot like the one who commented above who doesn’t understand that it just isn’t possible for each child to have their own personalized math class everyday when you have 25-30 kids in a room of varying abilities.