Standards
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Explanations and Examples
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1. Make sense of problems and persevere in solving them.
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In grade 8, students solve realworld problems through theapplication of algebraic andgeometric concepts. Studentsseek the meaning of a problemand look for efficient ways torepresent and solve it. Theymay check their thinking byasking themselves, “What isthe most efficient way to solvethe problem?”, “Does thismake sense?”, and “Can Isolve the problem in adifferent way?”
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2. Reason abstractly and quantitatively.
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In grade 8, students represent awide variety of real worldcontexts through the use ofreal numbers and variables inmathematical expressions,equations, and inequalities.They examine patterns in dataand assess the degree oflinearity of functions. Studentscontextualize to understand themeaning of the number orvariable as related to theproblem and decontextualize to manipulate symbolicrepresentations by applyingproperties of operations.
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3. Construct viable arguments and critique the reasoning of others.
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In grade 8, 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 inwhich 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.
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4. Model with mathematics.
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In grade 8, students modelproblem situationssymbolically, graphically,tabularly, and contextually.Students form expressions,equations, or inequalities fromreal world contexts and connect symbolic andgraphical representations.Students solve systems oflinear equations and compareproperties of functionsprovided in different forms.Students use scatterplots torepresent data and describeassociations betweenvariables. Students need manyopportunities to connect andexplain the connectionsbetween the differentrepresentations. They shouldbe able to use all of theserepresentations as appropriateto a problem context.
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5. Use appropriate tools strategically.
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Students consider availabletools (including estimation andtechnology) when solving amathematical problem anddecide when certain toolsmight be helpful. For instance,students in grade 8 maytranslate a set of data given intabular form to a graphicalrepresentation to compare it toanother data set. Studentsmight draw pictures, use applets, or write equations toshow the relationshipsbetween the angles created bya transversal.
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6. Attend to precision.
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In grade 8, students continue to refine their mathematicalcommunication skills by usingclear and precise language intheir discussions with othersand in their own reasoning.Students use appropriateterminology when referring tothe number system, functions,geometric figures, and datadisplays.
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7. Look for and make use of structure.
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Students routinely seekpatterns or structures to modeland solve problems. In grade8, students apply properties togenerate equivalentexpressions and solveequations. Students examine patterns in tables and graphs togenerate equations anddescribe relationships.Additionally, studentsexperimentally verify theeffects of transformations anddescribe them in terms ofcongruence and similarity.
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8. Look for and express regularity in repeated reasoning.
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In grade 8, students userepeated reasoning tounderstand algorithms andmake generalizations aboutpatterns. Students use iterativeprocesses to determine moreprecise rationalapproximations for irrationalnumbers. During multipleopportunities to solve andmodel problems, they noticethat the slope of a line and rateof change are the same value.Students flexibly makeconnections betweencovariance, rates, andrepresentations showing therelationships betweenquantities.
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