Students use multiple representations and real-world contexts to continue to support their development of fraction concepts and operations. They use graphs, tables, and stories to interpret ratios—a fraction as a multiplicative relationship between two numbers. Students use these relationships to make generalizations, problem solve, and compare units of measure. Students continue to develop and apply a variety of strategies for solving multistep problems involving addition, subtraction, multiplication, and division. They extend these whole number and fractional representations, strategies, and procedures to models of decimals. Students classify two-dimensional shapes using properties.
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UNIT 1 Populations and Samples
This unit provides a review of the TIMS laboratory method, a simplified version of the scientific method. Using the context of populations and samples, students explore the relationship between variables. They represent these relationships using tables, graphs, and averages (median and mode). Students solve problems by analyzing data. They use averages, data tables, and graphs to make generalizations and predications about a data set.
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UNIT 2 Fractions
Students use multiple representations and real-world contexts to support their development of the concepts related to fractions. Students review the use of circle pieces, number lines, and symbols to represent and identify fractions, including proper fractions, improper fractions, and mixed numbers. Students make connections and translate between these representations to compare, order, and find equivalent fractions. Students develop multiplication and division strategies for finding common denominators. Students develop strategies to add and subtract with like and unlike denominators.
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UNIT 3 Big Numbers
Students use multiple representations and real-world contexts to support their development of number sense for large numbers. Students use place value charts, number lines, and number sentences to represent numbers to the billions. Students make connections and translate between these representations to compose, decompose, compare, and order large numbers. Students use strategies to estimate quantities and products. They represent numbers with exponents and multiply numbers that are multiples of ten represented as powers of ten.
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UNIT 4 Estimation and Efficient Computation
Students further develop strategies for multidigit addition, subtraction, and two-digit by two-digit multiplication. They explore both mental math and paper-and-pencil methods, solving problems that require exact answers as well as those where estimation is appropriate. Students use computational strategies to develop formulas for finding the area of rectangle and triangles, and the volume of rectangular prisms.
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UNIT 5 Fractions and Ratios
Students use multiple representations and real-world contexts to extend their understanding of fractions to include ratios. Students review the use of circle pieces, number lines, and symbols to represent and identify fractions and ratios. Students use multiplication and division strategies for finding the simplest form of a fraction. Students solve problems involving ratios that include converting between units of measure within a standard measurement system.
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UNIT 6 Locations and Shapes
Students begin this unit exploring negative numbers. They then use this understanding as they plot points in all four quadrants of a grid. Students describe locations on a grid using ordered pairs. They construct two-dimensional shapes by plotting points on a grid and then classify shapes using their properties.
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UNIT 7 Division and Data
Students use models to divide multidigit numbers by one- and two-digit divisors. They develop strategies for estimation, mental math, and paper-and-pencil methods to divide multidigit numbers. Students complete an investigation in which they find the area of shapes with curved sides. They organize their data in a table and on a graph and then solve problems and make generalizations about their data using these tools.
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UNIT 8 Decimals
Students represent and identify numbers to the thousandths place using area models, number lines, words, symbols, and expanded form number sentences. They make connections and translate among these representations. Students connect representations of fractions and decimals and use them to represent the same quantity. Students use their understanding of place value to compare and order decimals to the thousandths place. They extend their understanding of place value and operations to develop strategies to add, subtract, multiply and divide decimals.
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UNIT 9 Factors and Multiples
Students identify and categorize numbers as prime, composite, and square. They identify and find multiples and factors of a number. Students find the prime factorization of a number. They identify, describe, and represent number patterns. Students use order of operations to make calculations that involve exponents and the use of parentheses.
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UNIT 10 Fraction Operations
Students solve problems that involve adding and subtracting fractions and mixed numbers using models. They develop and use strategies that include finding a common denominator. Students develop procedures for multiplying a fraction times a whole number. Student use patterns to multiply fractions. They use multiplication to bridge division of fractions.
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UNIT 11 Equivalent Fractions using Proportions
Students use ratios and strategies for finding equivalent fractions to solve problems and make comparisons. Students convert recipes, determine the ratio between the circumference and diameter of a circle, and use ratios to compare the density of objects. They also use ratios to describe a population using a sample of the population.
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