Common Core Practice Standards Part 2

Sep 14, 2019 | Location Franklin WI

September means back to school, and we’re diving into the meat of the Practice Standards! Reasoning skills have always been part of the curriculum, but they have become a prominent focus of the Common Core. These skills have also become an easy target for critics of the Standards. But why are they so important?


Reason abstractly and quantitatively

The second Practice Standard focuses on students’ reasoning skills. It encourages us to develop the ability to reason through situations and not just solve problems. Rote memorization has its place, but an ability to reason and break down situations will give opportunities for broader success.


Without a focus on reasoning skills, each problem is seen as a separate and unique algorithm. But when we utilize  reasoning skills, many problems become related. For example, three problems from our curriculum seem to be completely different on the surface:


“How many groups of 4 can you make in 16 balloons?”


“Two thirds of a pound of candy costs 60 cents. How much does a pound and a half cost?”


“â…— of ___ = 48”


But all are solved in the same manner, when reasoning is used!

  • We need 4 groups of equal amounts to make 16 balloons. We can split the whole into 4 groups by dividing, so 16/4 = 4. So there are 4 in each group.
  • If two thirds of a pound is 60 cents, then one third is 30 cents. A whole pound is three thirds, so it costs 30*3 = 90 cents. Half of a pound would be 90/2 = 45. So a pound and a half is 90+45 = 135. So $1.35
  • We have 48, and that is three groups of one-fifth of the whole. So each group is 48/3 = 16. This means that one-fifth is 16. Since they are equal parts, the whole has five of these groups. So 16*5 = 80.

We used reasoning in all three to identify that we have groups of equal parts that make a whole. While there are standard algorithms to use in solving each of these problems, when we apply reasoning skills it all becomes related. 


But beyond using reasoning skills to solve a problem, students must be able to make sense of the answer in terms of the quantities. If given different units, being able to convert to a common unit. Reasoning quantitatively also means to be able to check for reasonable answers - if they find that three baskets of 12 apples is 200 apples, they should know that they need to check their work. They should also be able to check the reasonableness of their answers - if they solve a similar figures problem and find that a man is 24 ft tall, students should be able to recognize that it’s not a realistic answer.


Part of this standard that has caused uproar of late is the increased focus on Estimation. Using estimation, students can use their reasoning skills to see if their answer would make sense. Many parents and teachers dislike this emphasis, preferring that the student goes straight to the precise answer. But estimation and checking for reasonable results is a key 21st Century skill! Everyone carries calculators, and they are being used more and more frequently in classrooms as well as real life. Being able to estimate an answer and check for reasonable results is our best check on mistakes. I know many times I’ve typed numbers wrong (112 instead of 1.12, for example), and knowing how to catch those mistakes is very valuable. 


Reasoning in mathematics is seeing the basis and connections between steps of an algorithm, and interpreting the solutions in terms of the quantities. Part of what sets the Mathnasium Method apart is rooted in the ability to lead students to connections and help them understand not just what to do, but why. Those connections form a cornerstone of Mathematical success!

Locations near
Ashburn 0.93 mi
43330 Junction Plaza
Ashburn, VA 20147
Sterling 4.07 mi
44 Pidgeon Hill Drive
Sterling, VA 20165
Leesburg 5.69 mi
521 E Market St
Leesburg, VA 20176
Herndon 7.66 mi
2465 Centreville Road
Herndon, VA 20171
Stone Ridge 7.88 mi
42020 Village Center Plaza
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
Potomac, MD 20854
Germantown MD 15.03 mi
12800 Middlebrook Road
Germantown, MD 20874
Tysons 15.45 mi
328 Maple Ave E
Vienna, VA 22180
Haymarket 17.87 mi
15125 Washington St
Haymarket, VA 20169
Rockville 18.19 mi
20 Courthouse Square
Rockville, MD 20850
Mclean 18.23 mi
1320 Old Chain Bridge Road
Suite #190
McLean, VA 22101
Gaithersburg 18.71 mi
9132 Rothbury Drive
Gaithersburg, MD 20886
North Bethesda 20.42 mi
5268 Nicholson Ln
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
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
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
Beltsville, MD 20705
Clarksville 31.56 mi
12250 Clarksville Pike
Clarksville, MD 21029
Laurel 35.02 mi
10095 Washington Blvd N
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.
Sykesville, MD 21784
Ellicott City 37.11 mi
3290 Pine Orchard Lane
Ellicott City, MD 21042
Winchester 37.62 mi
2512 S Pleasant Valley Rd
Winchester, VA 22601
Columbia 38.19 mi
8827 Centre Park Drive
Columbia, MD 21045
Stafford 39.58 mi
263 Garrisonville Road
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
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
Dunkirk, MD 20754