Grade 6 Standards For Mathematical Practice

The K-12 Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. This page gives examples of what the practice standards look like at Grade 6.

Information taken from Connecticut State Department of Education.


Explanations and Examples

1. Make sense of problems and persevere in solving them.

In grade 6, students solveproblems involving ratios andrates and discuss how theysolved them. Students solvereal world problems throughthe application of algebraicand geometric concepts.Students seek the meaning of aproblem and look for efficientways to represent and solve it.They may check their thinkingby asking themselves, “Whatis the most efficient way tosolve the problem?”, “Doesthis make sense?”, and “Can Isolve the problem in adifferent way?”

2. Reason abstractly and quantitatively.

In grade 6, students represent awide variety of real worldcontexts through the use ofreal numbers and variables inmathematical expressions,equations, and inequalities.Students contextualize tounderstand the meaning of thenumber or variable as relatedto the problem and decontextualize to manipulatesymbolic representations byapplying properties ofoperations.

3. Construct viable arguments and critique the reasoning of others.

In grade 6, students constructarguments using verbal orwritten explanationsaccompanied by expressions,equations, inequalities,models, and graphs, tables,and other data displays (i.e. box plots, dot plots,histograms, etc.). They furtherrefine their mathematicalcommunication skills throughmathematical discussions in which they critically evaluatetheir own thinking and thethinking of other students.They pose questions like“How did you get that?”,“Why is that true?” “Does thatalways work?” They explaintheir thinking to others andrespond to others’ thinking.

4. Model with mathematics.

In grade 6, students modelproblem situationssymbolically, graphically,tabularly, and contextually.Students form expressions,equations, or inequalities fromreal world contexts and connect symbolic andgraphical representations.Students begin to explorecovariance and represent twoquantities simultaneously.Students use number lines tocompare numbers and represent inequalities. Theyuse measures of center andvariability and data displays(i.e. box plots and histograms)to draw inferences about andmake comparisons betweendata sets. Students need manyopportunities to connect andexplain the connectionsbetween the different representations. They shouldbe able to use all of theserepresentations as appropriateto a problem context.

5. Use appropriate tools strategically.

Students consider availabletools (including estimation andtechnology) when solving amathematical problem anddecide when certain toolsmight be helpful. For instance,students in grade 6 may decideto represent similar data setsusing dot plots with the samescale to visually compare thecenter and variability of thedata. Additionally, studentsmight use physical objects orapplets to construct nets andcalculate the surface area ofthree-dimensional figures.

6. Attend to precision.

In grade 6, students continueto refine their mathematicalcommunication skills by using clear and precise language intheir discussions with othersand in their own reasoning.Students use appropriateterminology when referring torates, ratios, geometric figures,data displays, and componentsof expressions, equations orinequalities.

7. Look for and make use of structure.

Students routinely seekpatterns or structures to modeland solve problems. Forinstance, students recognizepatterns that exist in ratiotables recognizing both theadditive and multiplicativeproperties. Students applyproperties to generateequivalent expressions (i.e. 6 + 2x = 3(2 + x) bydistributive property) andsolve equations (i.e. 2c + 3 =15, 2c = 12 by subtractionproperty of equality), c = 6 bydivision property of equality).Students compose anddecompose two- and three-dimensionalfigures to solvereal world problems involvingarea and volume.

8. Look for and express regularity in repeated reasoning.

In grade 6, students userepeated reasoning tounderstand algorithms andmake generalizations aboutpatterns. During multipleopportunities to solve andmodel problems, they maynotice that a/b ÷ c/d = ad/bcand construct other examplesand models that confirm theirgeneralization. Studentsconnect place value and theirprior work with operations tounderstand algorithms to fluently divide multi-digitnumbers and perform alloperations with multi-digitdecimals. Students informallybegin to make connectionsbetween covariance, rates, andrepresentations showing therelationships betweenquantities.

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