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.
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.”
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?”
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.
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.
- 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?”
“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?”
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.