Can your child truly count?

1. “Start counting at 6!”

Lots of kids sound like they can count, but have just memorized the number names in order, like song lyrics. By starting to count somewhere other than 1, you can assess their understanding.

When kids can “count on” from any number as quickly as saying their name, then they’ve achieved what is known as “automaticity.” If they have to start at 1 and whisper their way up to 6 first, they’ve memorized lyrics instead of understanding quantities. 

If you don’t know what comes after 6, you can’t yet add 1. So practice true counting with your child to lay groundwork for addition!

2. “Quick, without counting: How many cookies are on the plate?”

When you see a few objects, we can tell instinctively whether there are 3, 4 or 5 without counting each individual one. That gut reaction is called “subitizing.” 

Multiple studies have found that the ability to subitize up to five predicts which kids will succeed or struggle with first-grade math skills like addition and subtraction.  One group found that students who couldn’t estimate were 2.4 times more likely to face math learning disabilities later.

Offer this challenge to your child using cookies, Cheerios, LEGO pieces or other small objects. Your child will likely get the right answer every time — but the key is to build that instinct.

Can your child “read” numbers?

“What does the ‘1’ in ‘14’ mean?”

A lot of kids memorize number names but don’t understand place value. It’s the math equivalent of illiteracy: The lines are just meaningless squiggles. We want our kids to be numerate.

Ask your child to explain what the “1” in “14” means, and to line up that number of objects to show what it means. We’ve seen kids insist that the “1” in “14” just means “1,” not “10”… if that were true, wouldn’t the value of the number just be 1 + 4? Why don’t we call that number “5”? 

It’s a fun way to ensure your child grasps place value, which is critical for any future computation. If your child struggles, try these steps:

• Grab your child’s favorite snack involving small items, like Cheerios or M&Ms.

• Invite your child to write any number between 12 and 19.

• Ask your child to count out that many pieces. Ask: “How would you split these into two groups to match the number you wrote?” They should end up making one group that matches the last digit – e.g. 7 to match the 7 in 17 – which will leave 10 in the other group. 

• Discuss how the 1 in the number represents that 10.

• Once they succeed at this, try numbers above 20!

The numbers behind friends and family.

1. “If you went to camp every summer from when you were age 7 to the summer you were 10, how many summers did you go to camp?”

The answer is actually 4, not 3. Yes, count it out: you were 7 the first summer, 8 in the second summer, 9 in the third summer, and 10 in the fourth summer. That’s four summers. Why does this happen? 

Because when you count numbered items, including the very first one, it’s like including zero. You are effectively subtracting out all the years you didn’t go to camp. So, if you started at the summer of age 7, you carve out all the summers from age 6 downward.

This is great mind-building logic – and you’ll have lots of excuses to ask this!

2. “How many years in total has everyone in our family lived?”

This intriguing question shows whether your child can add two-digit numbers and remember an interim total while adding more numbers. We do math like this daily without noticing, such as adding purchases in our head, or the number of minutes left to squeeze in tasks before our next Zoom call. 

If your child struggles, you can break it down into steps:

• Choose a favorite small uniform snack, like raisins, goldfish or chocolate chips.

• Lay out each person’s age with that number of snacks. Group each age in sets of 10 followed by the remaining single-digit number of snacks.

• Let your child add up the piles however they want to. start with the biggest age and add the smaller numbers, or add the smallest to largest, or in random order. Your child could add up all the tens, then all the ones, then peel off sets of 10 from the new big singles pile. As long as it’s logical and gets the right answer, it’s all good!

If needed, discuss the interim steps, and how 21 + 13 is really “twenty-fourteen,” which is thirty-four.  James Tanton’s “Exploding Dots” series shows regrouping in a very engaging and tactile way.

1. “How long is your hair, to an eighth of an inch?” 

Ask this question, then hand over a ruler.

Even in the age of video games and social media, we still live in three dimensions. Basic spatial skills are critical, and using a ruler is one of them. It’s also a great opportunity to practice working with fractions. Measuring to the quarter of an inch is a third-grade standard, as is understanding eighths. See if your child can combine the two skills!

2. “The first candy bar ever was not invented by Mr. Hershey — it was invented by Joseph Fry in 1866! How long ago was that?”

Or for the more gadget-oriented: “How long have we had phones? Alexander Bell invented the phone in 1876.” Pick any favorite 1800s fact!

These fun factoids are actually sneaking in four-digit subtraction. Subtraction is harder for kids than addition, just like division is harder than multiplication; something about reducing numbers is more challenging. 

Many students fake their way through two-digit subtraction, memorizing that they “carry a 1” to the singles place. But if they lack true understanding, the wheels come off the cart when they tackle three digits. 

If your child needs more work on this skill, watch Khan Academy’s videos on subtraction with regrouping. 

3. “How big is your room? How many square feet is the floor?”

This is a real-life example of calculating area. Measuring the edges of a rectangle and multiplying to calculate the area shows how multiplication differs from addition. Multiplication is repeated addition, so the numbers grow fast! See if your child grasps that basic concept. 

A great follow-up question: If your room’s floor was 1 foot shorter but 1 foot wider, would you have more space or less? The answer is always more — unless the room is already a perfect square! You can see this easily with a small example: 

• a 1-by-5 rectangle has an area of 5 square feet

• a 2-by-4 rectangle has an area of 8 square feet

• a 3-by-3 square has the maximum of 9 square feet!

1. “How many total years has your whole class lived?”

Because fourth graders are about 10 years old, this is a fun place value problem! Twenty-four kids have collectively lived about 240 years; 18 kids have lived 180 years; and so on.

See if your child can figure this out on the fly. This also shows whether they understand why “tacking on a zero” is the same as multiplying by 10.

2. “If those snack-size packs of M&M’s each have 34 pieces of candy, how many are in a dozen packs?”

Whether you call it “carrying” “borrowing” or “regrouping,” kids shouldn’t just move numbers around like puzzle pieces. They should grasp what’s actually going on. Watch how your child solve this real-life question.

There are lots of ways to reach the right answer. Your child might add 34 10 times followed by adding 34 twice, or they might multiply 12 by 30 in their head and then add 12 multiplied by 4. No matter what, those 34 bags hold 408 M&Ms. Any route to the answer shows math fluency.

1. On your cellphone, find an image from your child’s favorite video game. Ask: “Some animator has a really cool job drawing pictures like that. How many pixels are in that picture? It’s 1920 pixels down and 1080 pixels across.”

While multiplication is more intuitive for kids than dividing, kids still struggle when they get to the bigger numbers. 

Students need to understand why they multiply the 1s digit by the other factor, then the 10s digit by that factor, then the 100s, and add up the resulting “partial products.” Otherwise, the exercise feels like sliding puzzle pieces around the page meaninglessly. 

Bbefore you tell us that we can just use a calculator, remember: a calculator just gets you to the wrong answer faster. Solving these problems trains the brain to see what products look like. And the person who can estimate will always be faster than the button-poking calculator users. 

2. “Here’s a cookie recipe (if you need one, here’s our favorite). If you figure out how to make 1 1/2 times this, we’ll bake them!”

Fractions are the bane of many people’s existence, including adults. For decades our curricula have insisted on beginning fraction instruction with pie charts and pieces of a whole, when in real life we almost always apply fractions to numbers greater than 1, like amounts of money and numbers of people. 

Fraction instruction often decays to memorizing rules, such as “the bottoms need to be the same to add, but not to multiply.” When kids memorize the steps without understanding them, the math becomes impossible as the rules build up. 

Instead, we want kids to grasp why multiplying by 1 1/2 is the same as taking 1/2 the total, then adding it to the original — and why this reflects the same three parts (the halves) as in 3/2. 

Mastery of fractions is important in everyday life, and lays the groundwork for success in algebra. For more practice (and snacking), try making recipes with ingredients that remain visually separate, like your own trail mix.

1. “I’m thinking of a mystery number. Can’t tell you what it is, but if you double it and add 3, you get 11. What is it?”

Kids will be off and running trying to crack the code before you even ask “What is it?” Even a second or third grader will know to do the steps backwards: Subtract 3 to find out what the previous number was, then cut it in half. Little do they know, this is algebra!

Your middle schooler may be nervous about algebra, so give a “mystery number” and when they succeed, point out that it’s the exact same set of skills.

2. “Let’s make trail mix. If we mix twice as many cups of walnuts as chocolate chips, and twice as many cups of almonds as walnuts, and there are 21 cups total. How many cups of each?”

This, too, is a brain teaser that secretly uses algebra. Let your tween think it out: Each cup of chips is paired with 2 cups of walnuts, and each cup of walnuts has 2 cups of almonds — which means 4 cups of almonds in that cluster. In a sense, they’re forming “friend groups” of 7 cups. So, 21 cups total will have 3 of those sets: 3 cups of chips, 6 cups of walnuts and 12 cups of almonds.

What’s really happening is a set of 3 simultaneous equations: w = 2c (walnut amount equals double the chip amount), a = 2w, and c + w + a = 21. Imagine the excitement upon solving this brain teaser and finding out that it was algebra, after all. We can do this!

If your tween struggles with algebra, the Khan Academy website is perfectly suited to help. Check out the courses for 6th grade, 7th grade or 8th grade. You can search under each one to find the specific topic that is proving challenging.