Use this Tool to Check Your Child’s Mathematical Reasoning and Numerical Fluency
Common Core Math Standards have changed the expectations for math. It requires a higher and deeper way of thinking about math concepts. Use the activities below to see if your child is on target in math and progressing adequately. The activities are aligned with Common Core Math Standards by grade level. You will see if your child has two key skills for being successful in math.
Mathematical Reasoning
Mathematical reasoning is the skill of applying concepts to figure out how to solve a problem, when no steps are given for how to do it. It is the ability to understand and apply why a set of steps works to solve a problem, when to use the steps, and how to tell if the answer is reasonable. Mathematical reasoning can’t be taught by showing the steps to solve a problem. It requires deep thought on the part of the learner and must be encouraged with dialogue, oral or in writing. Children with solid mathematical reasoning can explain the “why” and “what if” questions in math.
Numerical fluency
Numerical fluency is the skill of seeing how numbers relate to each other and being able to do computations quickly and accurately. Students develop numerical fluency by using concrete tools or manipulatives and by using numbers often and in many applications. Not every child develops numerical fluency the same way. Read What Kind of Math Learner is Your Child more information.
Math concepts are concrete in elementary school, but they get more and more abstract in the higher levels. Children who develop strong mathematical reasoning and number sense skills in elementary school are the better prepared for abstract math in secondary school. See Prepare Your Child for Calculus Starting in Second Grade. Below are activities and questions to help you get an idea of your child’s mathematical reasoning level and numerical fluency.
How to Use the Tool
The activities are geared for grades k-6 and follow the Common Core Math Standards for grade level. You can access the C.C.M.S at https://www.corestandards.org/Math/. These are goals the child should meet by the end of a grade level.
Start with a grade or two below your child’s actual grade level. Try to make it a fun conversation instead of like a test. You could say “I’ve been hearing a lot about math standards and mathematical reasoning in the news. It seems to frustrate a lot of kids, parents and teachers. Can you show me how you do these math activities? I want to see if it’s different than the way I learned.” If they are old enough, you could even show them the article, Are You a Parent in Parker Frustrated with the Common Core Math Standards.
Always ask the included follow-up questions. That’s where children really get to show their mathematical reasoning. Each activity describes what to look for to see if your children demonstrate the appropriate level of mathematical reasoning and numerical fluency.
Kindergarten
Suggest a pretend party and get out dolls, animals, and action figures to be your “guests.” Collect between 10- 20 pretend guests. Tell your child to get enough “treats” for each guest to have one. Something small like raisins or pretzels sticks would work well as the treat. She must collect the exact amount in a separate container before passing them out to each guest.
Follow up questions: Did you have the right amount of treats for every guest to have one treat? Why? Or why not? What would you have to do if 3 more guests arrived?
Look for your child’s ability to accurately count up to 20 objects and explain that the number of guests and treats are “equal” or “the same.” She should also be able to recognize that she would have to get 3 more treats, or that 3 guests wouldn’t get a treat.
1st Grade
Say you want to know the order of ages of everyone in the extended family. Make sure to include a variety of ages. Tell your child the ages of each family member and have him write down their ages. You can write their names next to the numbers. Have him put the people in order from youngest to oldest.
Follow up questions: Let’s say Grandma gave me a penny on each birthday. I am 35 years old. I traded the pennies for dimes whenever I got 10 pennies. How many dimes and how many pennies would I have now? How do you know?
Look for your child’s ability to accurately write two-digit numbers and know which numbers are bigger than others. A first grader should use the position of the digits to know that 34 is less than 43. He should also be able to explain 35 equals 3 groups of ten and 5 ones.
2nd Grade
Say: Let’s pretend you want to buy a $47 toy and $35 game. Let’s pretend you have $65. Do you have enough money? How much more do you need?
Follow up questions: How did you solve the problem? Would you solve the problem the same way if the toy was $470 and the game was $350 and you had $650? Why?
Look for your child’s ability to add two-digit numbers and to know when and how to subtract. She should also recognize that multiplying everything by 10 does not change the process.
3rd Grade
Ask: Would you rather have 6 pockets that each has $4 or 4 pockets with $6 each? What if you only had two pockets but had the same amount of money, how many dollars would be in each pocket?
Follow up question: Why can you always use addition to help figure out multiplication problems?
Look for your child knowing that 4 x 6 is the same as 6 x 4 and that 24 ÷ 2 = 12. He should also be able to explain that multiplication is a way to add groups of equal amounts quickly.
4th Grade
Ask your child to help you do the math to triple this ingredient list for making 10 popcorn balls:
1 tablespoon canola oil
3 tablespoons unpopped popcorn kernels
2 tablespoons unsalted butter
2 1/4 cups mini marshmallows
1 cup cereal
1 ounce of pretzels, broken into pieces
1/4 cup chopped nuts
Follow up question: Why would making 40 balls eliminate all the fractions in this recipe?
Look for your child’s ability to multiply fractions and mixed fractions. He should also be able to explain that to make 40 balls he must quadruple the recipe. Multiplying ¼ x 4 =1, or 4 quarters equals a whole.
5th grade
Explain that many sports such as, gymnastics, diving, and snowboarding, use judges to award points to athletes. The points from different judges must be averaged to get the actual score.
(An average means all the scores are added together and then divided by number of scores. To make it fair, the highest and lowest scores are discarded and only the middle scores are used.
As a quick example, suppose the scores were 3, 4, 2, 5, 6, and 7. The 2 and the 7 would not be used. Then add 3, 4, 5, and 6 to get 18 and divide by number of scores used (4) so: 18÷ 4= 4.5. The final score would be 4.5).
If Shaun White gets the following scores for half-pipe snowboarding, what will his actual score be?
92.55, 93.50, 93.05, 92.1, 92.60, 90.05,
Follow up questions: Why can 93.50 be written 93.5 instead? Is 93.05 the same as 93.5? Why or why not?
Look for the ability to order numbers with decimals to be able to add, subtract, and divide them. She should explain the role of zero as a placeholder and how it affects quantity after the decimal point.
6th grade
Think about starting a business like mowing lawns or dog walking. If you make $12 a day but you spend 25% of your earnings to buy supplies, how long will it take you to save $48?
Follow up question: What are two ways you save money quicker?
Look for your child’s ability to understand percentages and rates and apply them to the problem. He should be able to explain why decreasing spending or increasing revenue will increase the amount saved.
Mathnasium also has a short, 4-5 question assessment on our website where you can check if you child is on grade level.
How did Your Child Do?
If your child is right on track or even ahead, great! Keep having math conversations and sparking their love for math. If they want more math challenges, check out our tips at 6 Ways for Accelerated or Advanced Students to Get Excited About Math Again.
If your child struggled or expressed a dislike of math, read Does Your Child Show Any of the 4 Warning Signs for Imminent Math Struggles for tips on how to help.
At Parker Mathnasium, we are here to help with all types of math students from struggling to accelerated, from second grade and up. We have a unique approach https://www.mathnasium.com/parker/method that people love. Please take a moment to read our methods and testimonials. We would love to talk to you about your child.
Call us today. 303 840-1184
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This article was written by and owned by Cuttlefish Copywriting. It is copyright protected. Mathnasium of Parker has permission to use it. Other Mathnasium locations should contact Heather at [email protected] before using it.
