Number Sense Is the Key to Success in Math!

Jan 3, 2021 | Location Maple Valley

Regardless of age or skill level, there are almost always gaps in a child’s foundational understanding that, if addressed, would boost their success in math.

When we give assessments to children in our math learning centers, we see that a high proportion of their knowledge gaps stems from a lack of number sense. Number sense is “the ability to appreciate the size and scale of numbers in the context of the question at hand.” In essence, it’s the understanding of what numbers mean, how they work together and how they connect to real life. It’s critical that children have a firm grasp of number sense, because it underlies all mathematical comprehension and ability. Typical math tutoring does not teach number sense, acting as a bandage rather than a cure for the problem.

How do I know if my child has number sense?

Context provides a framework of ideas and information that can be used in a meaningful way. If a child doesn’t understand the context of a mathematical concept or principle when it’s taught to them, they’re likely to say they “don’t get it” or that it “doesn’t make sense.” Sound familiar?

Without number sense, a child feels increasingly lost as they move up through the school grades. Year after year, the disparity grows between what they are being taught and what they truly understand. Children who lack number sense work longer and harder than they should have to in order to solve math problems. Students in middle- and high-school-level math courses — even if they seem to be doing OK — can still lack number sense, because they never got a good grip on it when they were younger. This is part of why so many children need a math tutor.

Children who have good number sense are able to solve problems like these quickly in their heads:

What is 7% of 250?
99 + 99 + 99 = ?
Which is the largest? 

Whether it’s in the early or later years, eventually, the child without number sense will “hit a wall.” This can manifest as the inability to understand new material, do certain types of problems, low grades on timed tests, homework frustration, or the mistaken belief that they “can’t do math.” In fact, it’s often problems with number sense that cause children to give up on math. It’s a pity, because it doesn’t have to be that way. Anyone, of any age, can be taught number sense! It’s never too late to learn.

How do we learn number sense?

The important thing to realize is that number sense doesn’t just come naturally. It’s a learned skill. Teachers can instill number sense if they have the right materials (curriculum and tools) and use the right instruction. This is why Mathnasium invested 40+ years and millions of dollars refining the Mathnasium Method. By teaching number sense in a way that makes sense to children, Mathnasium supports children’s classroom education.

In addition to teachers, parents and other caregivers also play a role in children’s mathematical growth. It’s often as simple as spending a few minutes each day asking number sense-related questions. You can do this on the way to and from school, at the market, or even when enjoying a sporting event together. It’s a great way to instill in your child that math is an important part of everyday life. For great tips on how to do this, see this article.

What are the components of number sense?

Generally, we break down number sense into three basics: counting, wholes and parts, and proportional thinking. But there are three other principles/skills that are important to fully possess number sense. We’ll break them all down here:

Counting

When children fully understand counting, they can count from any number, to any number, by any number, both forward and backward. This may sound basic — like any child would eventually learn this ability, but truly, it’s not. That’s why so many children are still using their fingers to count long past when they should be doing the math in their head (mental math).

Wholes and Parts

We all know the principle “The whole equals the sum of its parts.” A full comprehension of this principle leads to success with problem-solving and fractions — the nemesis of many children (and many adults, too).

Proportional Thinking

Proportional thinking is thinking “according to amount.” It’s a sense of scale. It helps children to understand problems such as: Five is what part of 15? If you can buy 3 candies with $2, how many candies can you buy with $10? Children who have learned proportional thinking can answer these questions quickly and easily.

Quantity and Denomination

The quantity is the amount of something — the number of things. The denomination is the name-value of that thing. In order to solve math problems, you need to know both.

The “Law of SAMEness”

This leads to Mathnasium’s “Law of SAMEness”: We can add and subtract only things that have the same name (same denomination). Here’s the classic Mathnasium example: When you add two bananas and three apples, do you get five banapples? Of course not. You can, however, get five pieces of fruit. “Fruit” is the denomination (name) that both apples and bananas share.

Numerical-Computational Fluency

Numerical fluency is the ability to “effortlessly recall — to know by heart.” While memorization is the way that many of us learned, it does notteach the mathematical thinking and problem-solving skills that are needed to build higher-order math skills. A student may memorize their 12 times tables, but a numerically fluent student uses computational strategies to quickly and efficiently answer questions beyond what is considered normal. For example, a student with numerical fluency can solve problems like 14 x 12 = ? without the need for pencil and paper. 

We like to say: “It is fairly easy to forget that which you have memorized, and it’s nearly impossible to forget that which you have learned.”

Mathnasium places enormous emphasis on number sense because it truly is the key to mathematical understanding. In partnership with schoolteachers and parents, the expert math instructors in our centers grow and build upon the power of number sense to foster true conceptual understanding in children. That critical understanding leads to math mastery and to a love and appreciation of math that will positively impact their entire lives.

Locations near
ME
Ashburn 0.93 mi
43330 Junction Plaza
#160
Ashburn, VA 20147
Sterling 4.07 mi
44 Pidgeon Hill Drive
#100
Sterling, VA 20165
Leesburg 5.69 mi
521 E Market St
#B
Leesburg, VA 20176
Herndon 7.66 mi
2465 Centreville Road
#J2
Herndon, VA 20171
Stone Ridge 7.88 mi
42020 Village Center Plaza
#100
Stone Ridge, VA 20105
Reston 8.62 mi
1424 North Point Village Center
Reston, VA 20194
Purcellville 12.72 mi
1020 E Main St
Ste L
Purcellville, VA 20132
North Potomac 13.58 mi
12150 Darnestown Rd
Gaithersburg, MD 20878
Centreville 14.52 mi
5959 Centreville Crest Ln
Centreville, VA 20121
Fairfax 14.67 mi
11891 Grand Commons Ave
Fairfax, VA 22030
Potomac 14.98 mi
10232 River Road
#B
Potomac, MD 20854
Germantown MD 15.03 mi
12800 Middlebrook Road
Germantown, MD 20874
Tysons 15.45 mi
328 Maple Ave E
#A
Vienna, VA 22180
Haymarket 17.87 mi
15125 Washington St
Haymarket, VA 20169
Rockville 18.19 mi
20 Courthouse Square
#106
Rockville, MD 20850
Mclean 18.23 mi
1435 Center St
McLean, VA 22101
Gaithersburg 18.71 mi
9132 Rothbury Drive
Gaithersburg, MD 20886
North Bethesda 20.42 mi
5268 Nicholson Ln
#N
Kensington, MD 20895
Falls Church 20.59 mi
6674 Arlington Blvd
Falls Church, VA 22042
Manassas 20.65 mi
9722 Liberia Ave
Manassas, VA 20110
Bristow 20.71 mi
12705 Braemar Village Pz
Bristow, VA 20136
Burke 20.82 mi
9411 Old Burke Lake Rd
#C
Burke, VA 22015
Bethesda 21.3 mi
4918 Fairmont Ave
Bethesda, MD 20814
Annandale 21.64 mi
7000 Columbia Pike
Annandale, VA 22003
Damascus 22.77 mi
9815 Main St
Damascus, MD 20872
Arlington, VA 23.29 mi
4801 1st St N
Arlington, VA 22203
Cathedral Heights 23.51 mi
3706 Macomb St NW
Washington, D.C., DC 20016
Olney 23.96 mi
18157 Village Center Dr
Olney, MD 20832
Downtown Silver Spring 24.94 mi
1133 East West Highway
Silver Spring, MD 20910
Lorton 25.06 mi
9027 Silverbrook Rd
#A
Fairfax Station, VA 22039
West Washington 25.69 mi

Washington, DC 20009
Alexandria City 25.7 mi
4605 Duke Street
Alexandria, VA 22304
Lake Ridge 26.5 mi
12473 Dillingham Square
Lake Ridge, VA 22192
Frederick North 26.7 mi
905 W. 7th Street
Frederick, MD 21701
Northern Silver Spring 26.75 mi
732 Cloverly Street
Silver Spring, MD 20905
Alexandria 27.17 mi
6483 Old Beulah Street
Alexandria, VA 22315
Warrenton 27.42 mi
512 Fletcher Drive
Warrenton, VA 20186
Mount Airy 28.24 mi
411 E Ridgeville Blvd
Mt Airy, MD 21771
Capitol Hill DC 28.48 mi
621 Pennsylvania Ave SE
1st-floor unit
Washington, DC 20003
Dale City 28.99 mi
5512 Staples Mill Plaza
Dale City, VA 22193
Mount Vernon 29.66 mi
7696 H Richmond Hwy
Alexandria, VA 22306
Beltsville 30.89 mi
10914 Baltimore Ave
#B
Beltsville, MD 20705
Clarksville 31.56 mi
12250 Clarksville Pike
#D
Clarksville, MD 21029
Laurel 35.02 mi
10095 Washington Blvd N
#136
Laurel, MD 20723
Woodmore 35.27 mi
9101 Woodmore Centre Drive
Lanham, MD 20706
Glenn Dale 35.83 mi
10559 Greenbelt Rd
Lanham, MD 20706
Sykesville 36.57 mi
1207 Liberty Rd.
#D-104
Sykesville, MD 21784
Ellicott City 37.11 mi
3290 Pine Orchard Lane
#B
Ellicott City, MD 21042
Winchester 37.62 mi
2512 S Pleasant Valley Rd
Winchester, VA 22601
Columbia 38.19 mi
8827 Centre Park Drive
#F
Columbia, MD 21045
Stafford 39.58 mi
263 Garrisonville Road
#104
Stafford, VA 22554
Bowie 41.26 mi
15231 Hall Rd
Bowie, MD 20721
Waldorf 42.24 mi
3022 Festival Way
Waldorf, MD 20601
Crofton 42.6 mi
1153 Route 3 North
#120
Crofton, MD 21054
Owings Mills 44.15 mi
9433 Common Brook Rd #100
Owings Mills, MD 21117
Pikesville 46.84 mi
1433 Reisterstown Rd
Pikesville, MD 21208
Dunkirk 49.92 mi
10735 Town Center Blvd
#7
Dunkirk, MD 20754