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## Math

**MATH**

**Hampton School DistrictMath Competencies and Standards for Grade 4 **

▪ Assess the reasonableness of answers to multistep word problems using mental computation and estimation strategies including rounding.

▪ Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number.

▪ Determine whether a given whole number in the range 1-100 is prime or composite.

▪ Find all factor pairs for a whole number in the range 1-100.

▪ Gain familiarity with factors and multiples.

▪ Generate a number or shape pattern that follows a given rule.

▪ Generate and analyze patterns.

▪ Identify apparent features of the pattern that were not explicit in the rule itself. Ex. given the rule “Add 3” starting at 1, generate terms in the resulting sequence, observe that the terms alternate between odd and even. Explain why.

▪ Interpret a multiplication equation as a comparison, e.g., interpret 35=5×7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5.

▪ Multiply or divide to solve word problems involving multiplicative comparison, e.g., use drawings and equations with a symbol for the unknown number, distinguish multiplicative comparison from additive comparison.

▪ Recognize that a whole number is a multiple of each of its factors.

▪ Represent multistep word problems posed with whole numbers and having whole-number answers using equations with a letter standing for the unknown quantity.

▪ Represent verbal statements of multiplicative comparisons as multiplication equations.

▪ Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted.

▪ Use the four operations with whole numbers to solve problems.

▪ Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols.

▪ Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.

▪ Fluently add and subtract multi-digit whole numbers using the standard algorithm.

▪ Generalize place value understanding for multi-digit whole numbers.

▪ Illustrate and explain division calculations by using equations, rectangular arrays, and/or area models.

▪ Illustrate and explain multi-digit arithmetic by using equations, rectangular arrays, and/or area models.

▪ Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations.

▪ Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form.

▪ Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

▪ Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. Ex. recognize that 700÷70=10 by applying concepts of place value and division.

▪ Use place value understanding and properties of operations to perform multi-digit arithmetic

▪ Use place value understanding to round multi-digit whole numbers to any place.

▪ Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

▪ Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

▪ Build fractions from unit fractions by applying and extending

previous understandings of operations on whole numbers.

▪ Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole.

▪ Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2.

▪ Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each as an equation.

▪ Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size.

▪ Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100^4. Ex. express 3/10 as 30/100, and add 3/10+4/100=34/100.

▪ Extend understanding of fraction equivalence and ordering.

▪ Justify fraction decompositions, Ex;: 3/8=1/8+1/8+1/8; 3/8=1/8+2/8; 2 1/8 =1+1+1/8= 8/8+8/8+1/8.

▪ Recognize that comparisons are valid only when the two fractions refer to the same whole.

▪ Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

▪ Record the results of fraction comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

▪ Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

▪ Solve word problems involving multiplication of a fraction by a

whole number, e.g., by using visual fraction models and equations to represent the problem."

▪ Understand a fraction a/b as a multiple of 1/b. Use this understanding to multiply a fraction by a whole number.

▪ Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

▪ Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

▪ Understand decimal notation for fractions, and compare decimal fractions.

▪ Use decimal notation for fractions with denominators 10 or 100. Ex. rewrite 0.62 as 62/100; describe a length as 0.2”.

▪ Use the principle of fraction equivalence to recognize and generate equivalent fractions.

▪ An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle.

▪ An angle that turns through 1/360 of a circle is called a "one-degree angle," and can be used to measure angles.

▪ An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

▪ Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

▪ Geometric measurement: understand concepts of angle and measure angles.

▪ Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec.

▪ Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8).

▪ Measure angles in whole-number degrees using a protractor.

▪ Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts.

▪ Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement.

▪ Record measurement equivalents in a two-column table. Ex. 1 foot is 12 times as long as 1 inch.

▪ Represent and interpret data.

▪ Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

▪ Sketch angles of specified measure.

▪ Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems.

▪ Solve problems involving addition and subtraction of fractions by using information presented in line plots.

▪ Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

▪ Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit.

▪ Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit.

▪ Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size.

▪ Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

▪ Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines.

▪ Identify line-symmetric figures and draw lines of symmetry.

▪ Identify points, lines, line segments, rays, angles, and perpendicular and parallel lines in two-dimensional figures.

▪ Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts.

▪ Recognize right triangles as a category, and identify right triangles.

Math Competencies and Standards for Grade 4

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