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Summer Game #2: Math Balance Addition

So how’s the summer so far? It’s been great up here in Hazelton, North Dakota. The days are getting long – almost 16 hours of official sunlight! First light is at 5:10 am and last light is 10:09 pm, so it’s even longer when you’re outside and ... Read More

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Summer Game #1: Make 16 Cents

It’s summer time again!! School is out (or almost out), the grass is green, flowers are blooming, and the water is ready for the fun to begin! Like last year, we’re going to have a Summer Game series. These weekly games will help the kids keep ... Read More


Dr. Cotter on What 6 × 3 Means

Sometimes 6 × 3 is thought of as “6 groups of 3.” However, consistency with the other arithmetic operations requires a second look. When adding 6 + 3, we start with 6 and transform it by adding 3. When subtracting 6 – 3, we start with 6 and transform ... Read More

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Level G, Lesson 154

Susan wrote us: “Hello, my son and I are struggling with Lesson 154, with problems 9 & 10. Can we please have an explanation? Love your materials! Thank you.” Well, Susan, this took me a while to come up with a good clear explanation! Here’s ... Read More

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Dr. Cotter on Long Division

As far as long division is concerned, it no longer has the importance it had in past generations. No one today spends time on their job doing long division. Long division with that guessing component is not used higher mathematics. It is rarely on ... Read More

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Dr. Cotter on Multivides

For a child with learning disabilities doing multivides, I suggest this shorter version: Start with any 4-digit number and multiply it by 4, then 5, and 6. Then divide the final product by 4, then 5, and 6. The final quotient must be the same as ... Read More