Hampton School District
Math Competencies and Standards for Grade 3
OPERATIONS AND ALGEBRAIC THINKING
▪ Apply properties of operations as strategies to multiply and divide. Ex. 6×4=24, so then 4×6=24 (Commutative), 3x5×2 can be found by 3×5=15 then 15×2=30, or by 5x2=10, then 3×10=30 (Associative), since 8×5=40 and 8×2=16, solve 8×7 as 8×(5+2) = (8×5)+(8x2) = 40+16= 56 (Distributive)
▪ Assess the reasonableness of answers to two-step word problems using mental computation and estimation strategies including rounding.
▪ By the end of Grade 3, know from memory all products of two one-digit numbers.
▪ Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8×=48, 5=÷3, 6×6=_.
▪ Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8×5=40, one knows 40÷5=8) or properties of operations.
▪ Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. Ex.4 times a number is always even; explain why 4 times a number can be decomposed into two equal addends.
▪ Interpret products of whole numbers, e.g., interpret 5×7 as the total number of objects in 5 groups of 7 objects each; describe a context in which a total number of objects can be expressed as 5×7.
▪ Interpret whole-number quotients of whole numbers, e.g., interpret 56÷8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each.
▪ Multiply and divide within 100.
▪ Represent and solve problems involving multiplication and division.
▪ Solve problems involving the four operations, and identify and explain patterns in arithmetic.
▪ Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity.
▪ Understand division as an unknown-factor problem. For example, find 32÷8 by finding the number that makes 32 when multiplied by 8.
▪ Understand properties of multiplication and the relationship between multiplication and division.
▪ Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent
NUMBER AND OPERATIONS IN BASE TEN
▪ Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
▪ Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.
▪ Use place value understanding and properties of operations to perform multi-digit arithmetic
▪ Use place value understanding to round whole numbers to the nearest 10 or 100.
NUMBER AND OPERATIONS – FRACTIONS
▪ Compare two fractions with the same numerator or the same denominator, by reasoning about their size. Recognize that valid comparisons rely on the two fractions referring to the same whole.
▪ Develop understanding of fractions as numbers.
▪ Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
▪ Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
▪ Recognize and generate simple equivalent fractions, e.g., 1/2=2/4, 4/6=2/3). Explain why the fractions are equivalent.
▪ Record the results of comparisons with the symbols >, =, or <, and justify the conclusions.
▪ Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts; each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
▪ Represent a fraction a/b on a number line diagram by marking off a length 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.
▪ Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
▪ Understand a fraction as a number on the number line; represent fractions on a number line diagram.
▪ Understand two fractions as equivalent if they are the same size, or the same point on a number line.
MEASUREMENT AND DATA
▪ A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.
▪ A square with side length 1 unit, called "a unit square," is said to have "one square unit" of area, and can be used to measure area.
▪ Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes in the same units.
▪ Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories.
▪ Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
▪ Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch.
▪ Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
▪ Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
▪ Measure and estimate liquid volumes and masses of objects using standard units of grams(g), kilograms(kg), and liters(l).
▪ Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
▪ Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
▪ Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems
▪ Recognize area as an attribute of plane figures and understand concepts of area measurement.
▪ Relate area to the operations of multiplication and addition.
▪ Represent and interpret data.
▪ Show the data by making a line plot, where the horizontal scale is marked off in appropriate units - whole numbers, halves, or quarters.
▪ Solve one- and two-step "how many more" and "how many less" problems using information presented in bar graphs.
▪ Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
▪ Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
▪ Solve word problems involving addition and subtraction of time intervals in minutes.
▪ Tell and write time to the nearest minute and measure time intervals in minutes.
▪ Use area models to represent the distributive property in mathematical reasoning.
▪ Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b+c is the sum
of ab and ac.
▪ Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape
▪ Partition shapes into parts with equal areas.
▪ Reason with shapes and their attributes.
▪ Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
▪ Understand that shapes in different categories may share attributes, and that the shared attributes can define a larger category (e.g., rhombuses and rectangles are also quadrilaterals).
Hampton School District
Math Competencies and Standards for Grade 3
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