3rd grade Instructional Guide

Utah Core Standards for Mathematics Progressions

• Build fractions from unit fractions by applying and extending previous understanding of operations on whole numbers o Understand addition and subtraction of fractions as joining and separating parts referring to the same whole o Decompose a fraction into a sum of fractions with same denominator o Add and subtract mixed numbers with like denominators o Solve word problems involving addition and subtraction of fractions having like denominators o Understand a fraction a/b as a multiple of 1/b and use this understanding to multiply a fraction by a whole number o Solve word problems involving multiplication of a fraction by a whole number • Understand decimal notation for fractions and compare decimal fractions o Express a fraction with denominator 10 as an equivalent fraction with denominator 100 o Use decimal notation for fractions with denominators 10 or 100 o Compare two decimals to hundredths by reasoning about their size • Solve problems involving measurement and conversion of measurements form a larger unit to a smaller unit o Know relative sizes of measurement units within one system of units including km, m, cm; kg, g, oz; l, ml; hr, min, sec. and express measurement equivalents in terms of a smaller unit, recording measurement in a two-column table o Use the four operations to solve problems involving distances, intervals of time, liquid volumes, masses of objects, and money including problems involving simple fractions or decimals o Represent measurement quantities using diagrams such as number line diagrams such as number line diagrams that feature a measurement scale

• Apply and extend previous understandings of multiplication and division to multiply and divide fractions o Interpret a fraction as division of the numerator by the denominator o Solve word problems involving division of whole numbers o Find the are of a rectangle with fractional side lengths by tiling it with unit squares o Multiply fractional side lengths to find area of rectangle to get a rectangular areas o Interpret multiplication as scaling o Solve real world problems involving multiplication of fractions and mixed numbers o Divide a unit fraction by a whole number and whole numbers by unit fractions • Convert like measurement units within a given measurement system • Represent and Interpret data o Make a line plot to display a data set of measurements in fractions of a unit ( ! " , ! # , ! $ ) o Use operations on fractions for this grade to solve problems from information on the line plot • Recognize volume as an attribute of solid figures and understand concepts of volume measurement. o Measure volume by counting unit cubes • Relate volume to the operations of multiplication and addition and solve real world problems involving volume o Find the volume of a right triangle by packing it with unit cubes

Measurement and Data

*Links above are information regarding Progression Documents for the Utah Core State Math Standards