Standards
Students apply concepts and strategies of multiplication and division to solve real-world problems. Students add and subtract unlike fractions and use visual fraction models to multiply and divide fractions and whole numbers. Students apply conceptual models and strategies to all operations with decimals to solve real-world problems and represent real-world situations within the first quadrant of the coordinate plane.
Generate resourceFind whole-number quotients and remainders with up to four-digit dividends and two-digit divisors using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning used.
Generate resourceSolve real-world problems involving addition, subtraction, multiplication, and division with decimals to hundredths including problems that involve money in decimal notation (e.g., by using equations, models or drawings, and strategies based on place value or properties of operations to represent the problem).
Generate resourceRepresent real-world problems and equations by graphing ordered pairs in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.
Generate resourceSolve real-world problems involving multiplication and division of whole numbers (e.g., by using equations to represent the problem). In division problems that involve a remainder, explain how the remainder affects the solution to the problem.
Generate resourceAdd and subtract fractions and mixed numbers with unlike denominators using strategies or the standard algorithm.
Generate resourceSolve real-world problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators (e.g., by using visual fraction models and equations to represent the problem). Use benchmark fractions and number sense of fractions to estimate mentally and assess whether the answer is reasonable.
Generate resourceUse visual fraction models to multiply a fraction by a fraction or a whole number.
Generate resourceUse visual fraction models and numbers to divide a fraction by a fraction or a whole number.
Generate resourceSolve real-world problems involving multiplication of fractions, including mixed numbers (e.g., by using visual fraction models and equations to represent the problem).
Generate resourceSolve real-world problems involving division of fractions and mixed numbers (e.g., by using visual fraction models and equations to represent the problem).
Generate resourceAdd, subtract, multiply, and divide decimals to hundredths, using models or drawings and strategies based on place value or the properties of operations. Describe the strategy and explain the reasoning.
Generate resourceStudents create questions appropriate to the data and answer the questions using multiple representations.
Generate resourceFormulate questions that can be addressed with categorical and numerical data and make predictions about the data. Collect, organize, and graph data from observations, surveys, and experiments using line plots with fractional intervals, histograms, or other graphical representations that appropriately represent the data set.
Generate resourceCalculate measures of central tendency (mean, median, and mode) to describe a data set. Analyze data sets to determine which measure of central tendency appropriately describes the distribution of data.
Generate resourceStudents use appropriate tools to investigate attributes of triangles and circles.
Generate resourceIdentify, describe, and draw triangles (right, acute, obtuse) and circles using appropriate tools (e.g., ruler or straightedge, compass, and technology). Define and model the relationship between radius and diameter.
Generate resourceStudents investigate the volume of rectangular prisms and solve real-world problems through the development and application of area formulas for rectangles, triangles, parallelograms, and trapezoids. Students investigate and convert measurements within the Customary and metric measurement systems.
Generate resourceConvert among different-sized standard measurement units within a given measurement system and use these conversions in solving multi-step, real-world problems.
Generate resourceFind the area of a rectangle with fractional side lengths by modeling with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
Generate resourceDevelop and use formulas for the area of triangles, parallelograms, and trapezoids. Solve real-world and other mathematical problems that involve perimeter and area of triangles, parallelograms, and trapezoids, using appropriate units for measures.
Generate resourceFind the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths or multiplying the height by the area of the base.
Generate resourceApply the formulas <em>V = l × w × h</em> and <em>V = B × h</em> for right rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths to solve real-world problems and other mathematical problems.
Generate resourceStudents explore place value through representing powers of 10 as exponents, modeling percents as parts of 100, and comparing and ordering fractions, mixed numbers, and decimals to the thousandth.
Generate resourceUse a number line to compare and order fractions, mixed numbers, and decimals to thousandths. Write the results using > , = , and < symbols.
Generate resourceExplain different interpretations of fractions, including as parts of a whole, parts of a set, and division of whole numbers by whole numbers.
Generate resourceExplain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
Generate resourceModel percents as parts of 100 using pictures or diagrams and identify the equivalent fraction.
Generate resource