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STEM.M.MATHEMATICS: National Council of Teachers of Mathematics (NCTM)
MATHEMATICS: National Council of Teachers of Mathematics (NCTM)
NCTM.1. Number and Operations
1.1. Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
1.1.1. Work flexibly with fractions, decimals, and percents to solve problems.
1.2.2. Use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions, and decimals.
Quiz, Flash Cards, Worksheet, Game & Study GuideUsing Integers
1.2.3. Understand and use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems.
1.3. Compute fluently and make reasonable estimates.
1.3.1. Select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods.
11.1. Number and Operations and Algebra and Geometry: Developing an understanding of and applying proportionality, including similarity
11.1.1. Students extend their work with ratios to develop an understanding of proportionality that they apply to solve single and multi-step problems in numerous contexts. They use ratio and proportionality to solve a wide variety of percent problems, including p
11.2. Measurement and Geometry and Algebra: Developing an understanding of and using formulas to determine surface areas and volumes of three-dimensional shapes
11.2.1. By decomposing two- and three-dimensional shapes into smaller, component shapes, students find surface areas and develop and justify formulas for the surface areas and volumes of prisms and cylinders. As students decompose prisms and cylinders by slicing
Quiz, Flash Cards, Worksheet, Game & Study GuideVolume
11.3. Number and Operations and Algebra: Developing an understanding of operations on all rational numbers and solving linear equations
11.3.1. Students extend understandings of addition, subtraction, multiplication, and division, together with their properties, to all rational numbers, including negative integers. By applying properties of arithmetic and considering negative numbers in everyday
Quiz, Flash Cards, Worksheet, Game & Study GuideUsing Integers
NCTM.12. Connections to the Grade 7 Focal Points
12.1. Measurement and Geometry: Students connect their work on proportionality with their work on area and volume by investigating similar objects. They understand that if a scale factor describes how corresponding lengths in two similar objects are related, th
12.2. Number and Operations: In grade 4, students used equivalent fractions to determine the decimal representations of fractions that they could represent with terminating decimals. Students now use division to express any fraction as a decimal, including frac
12.3. Data Analysis: Students use proportions to make estimates relating to a population on the basis of a sample. They apply percentages to make and interpret histograms and circle graphs.
12.4. Probability: Students understand that when all outcomes of an experiment are equally likely, the theoretical probability of an event is the fraction of outcomes in which the event occurs. Students use theoretical probability and proportions to make approx
3.1. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.
3.1.1. Precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties.
3.1.3. Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.
Quiz, Flash Cards, Worksheet, Game & Study GuideVolume
4.2.3. Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes.
5.1. Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.
5.1.1. Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population.
5.2.2. Discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots.
5.3. Develop and evaluate inferences and predictions that are based on data.
5.3.2. Make conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data and approximate lines of fit.