## Math

**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

the problem.

**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

▪ 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

▪ 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

▪ 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 a*b and a*c.

**GEOMETRY**

▪ 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

This report was created with tools provided by Revolutionary Schools.

To learn more, visit www.RevolutionarySchools.com.