Can your child truly count?

1. “Start counting at 6!”

Lots of kids sound like they can count, but many have simply 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.” Whereas if they have to start at 1 and whisper their way up to 6 first, they’ve memorized lyrics instead of understanding quantities. 

This is critical, because if you don’t know what comes after 6, you can’t yet add 1. Practice true counting with your kid by starting from different numbers to lay groundwork for addition.

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

When you see a few objects, you 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 objects at once predicts which kids will succeed or struggle with first-grade math skills like addition and subtraction.  One group found that students who could not estimate were 2.4 times more likely to face math learning disabilities later.

We use this skill all the time without realizing it. For example, you don’t have to count to recognize a table of four people. 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 over time will become faster and faster.

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 demonstrate 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 choose a number between 12 and 19 and write it on scrap paper.

• Ask your child to count out that many pieces. As your child lays them out, 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 a 10.

• Once there’s success with 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 scenarios where you can ask this!

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

This intriguing but simple question reveals 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 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 wish. One can start with the biggest age and add progressively 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 a logically sound method that arrives at 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 presents 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 like Minecraft, and social media, we still live in three dimensions. It’s critical that kids can still gauge basic spatial tasks based on their physical space. 

Using a ruler is an essential life skill, and a great opportunity to practice working with fractions. Measuring to the quarter of an inch is standard for third-grade math, but so is understanding fractions to 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!

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

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 — one that may pique your child’s curiosity. 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 floor 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, but a 2-by-4 rectangle has an area of 8 square feet, and 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, suddenly this becomes 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 reveals 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. Ask this simple, real-life scenario and watch how your child figures it out.

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, search your child’s favorite video game, click Images and open one at random. 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, it’s still critical to have a solid understanding of place value to multiply, say, 4 digits by 4 digits successfully. 

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

This quick question puts those skills to test on a real-life challenge that could be relevant to their careers later. And before you tell us that we can just use a calculator, remember: the person who can estimate will always be faster than the calculator users. Solving these problems trains the brain to see what products look like.

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, too. 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 accumulate. 

Instead, we want kids to grasp intuitively 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 actually 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. That means 3 cups of chips, 6 cups of walnuts and 12 cups of almonds.

What is 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.