Arithmetic – Page 2 – Denise Gaskins' Let's Play Math

If Not Methods: Mixed Numbers

Posted on June 12, 2024April 29, 2024 by Denise Gaskins

$A family doing math homework together$

Continuing our series on teaching the tough topics of arithmetic…

Our own school math experiences led many of us to think that math is all about memorizing and following specific procedures to get right answers. But that kind of math is obsolete in our modern world.

The math that matters today is our ability to recognize and reason about numbers, shapes, and patterns, and to use the relationships we know to figure out something new.

But what if our children get stumped on a mixed-number calculation like 2 ⁵/₁₂ + 1 ³/₄?

Continue reading If Not Methods: Mixed Numbers

If Not Methods – Subtracting Fractions

Posted on June 5, 2024April 29, 2024 by Denise Gaskins

$Father and daughter doing math homework$

We’re continuing our series of posts on how to build robust thinking skills instead of forcing our children to walk with crutches.

When we say, “Use this method, follow these steps,” we teach kids to be mathematical cripples.

If your student’s reasoning is, “I followed the teacher’s or textbook’s steps and out popped this answer,” then they’re not doing real math. Real mathematical thinking says, “I know this and that are both true, and when I put them together, I can figure out the answer.”

But what if our kids get stumped on a fraction calculation like 7/8 − 1/6?

Continue reading If Not Methods – Subtracting Fractions

If Not Methods: Scary Division

Posted on May 29, 2024April 29, 2024 by Denise Gaskins

We’ve been exploring the many ways to help children reason about tough math problems, without giving them rules to follow.

As always, real math is not about the answers but the thinking.

But what about division with scary, big numbers? What if our kids get stumped on a calculation like 3840 ÷ 16?

When kids say, “I don’t know how”

We can teach without crippling children’s understanding if we follow the Notice-Wonder-Create cycle:

Notice everything about the problem.
Wonder about the possibilities.
Create something new: perhaps a solution or a math journal entry, or perhaps just a deeper level of understanding.

“Notice, Wonder, Create” is not a three-step method for solving math problems. It’s the natural, spiraling cycle by which our minds learn anything.

Continue reading If Not Methods: Scary Division

If Not Methods: Multi-Digit Multiplication

Posted on May 22, 2024April 29, 2024 by Denise Gaskins

$Mother helping her daughter with math homework$

As we’ve seen in earlier posts, there are more ways to solve any math problem than most people realize. Teaching children to follow memorized steps and procedures actually cripples their understanding of number relationships and patterns.

But what if our children get stumped on a multi-digit multiplication calculation like 36 × 15?

Continue reading If Not Methods: Multi-Digit Multiplication

If Not Methods: Dividing Fractions

Posted on May 15, 2024August 3, 2024 by Denise Gaskins

Mother and daughter working together on math homewrok

As I said in an earlier post, we don’t want to give our children a method because that acts as a crutch to keep them from making sense of math.

But what if our children get stumped on a tough fraction calculation like 1 ¹/₂ ÷ ³/₈?

Continue reading If Not Methods: Dividing Fractions

Musings: If Not Methods, Then What?

Posted on May 1, 2024April 29, 2024 by Denise Gaskins

Last week, I quoted Pam Harris calling out a foundational myth of math education, the idea that we need to teach kids the methods that work on even the most difficult math problems.

“We have a misconception in math education that we think we need to teach methods so that kids can answer the craziest kind of a particular problem.

“We would be far better served to teach kids to think about the most common kinds of questions WELL, and let technology handle the crankiest.”

—Pam Harris

Since many of us grew up in schools that taught these methods, they may feel like the only sensible approach to math. Without the standard procedures, how will our kids learn to do math?

If we don’t teach subtraction with borrowing/renaming, how can students figure out calculations like 431 − 86? If we don’t teach fraction rules, how will they handle problems like 1 ¹/₂ ÷ ³/₈?

Continue reading Musings: If Not Methods, Then What?

Middle School Math Proof

Posted on January 17, 2024May 5, 2024 by Denise Gaskins

Homeschool Memories…

Kitten (my daughter) and I sat on the couch sharing a whiteboard, passing it back and forth as we took turns working through our prealgebra book together.

The chapter on number theory began with some puzzles about multiples and divisibility rules.

Continue reading Middle School Math Proof

How Will You Celebrate this Epic Twosday?

Posted on February 21, 2022February 21, 2022 by Denise Gaskins

Tomorrow is Tuesday 2/22/22 (or 22/2/22, if you prefer). What a wonderfully epic Twosday!

Here’s a puzzle your family or class may enjoy…

The “All 2s” Challenge

Use only the digit 2, and try to use as few of them as you can for each calculation. You may use any math operations you know.

For example:
0 = 2 − 2
8 = 2 + 2 + 2 + 2

Can you find a way to make 8 using fewer than four 2s?
What other numbers can you make?
Can you calculate all the numbers from 1–20? 1–100?

Putting 2 in Perspective

You might enjoy practicing your math art skills with this 2-digit challenge from Steve Wyborney.

How many blocks make the digit 2? How did you count them?

Prime Factor Art on a Hundred Chart

Posted on September 2, 2020September 20, 2023 by Denise Gaskins

The best way to practice math is to play with it — to use the patterns and connections between math concepts in your pursuit of something fun or beautiful.

So this art project is a great way to practice multiplication. Use the prime factors of numbers from one to one hundred to create a colorful design.