Warwick School District

Course Description

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Math instruction in the primary grades focuses on numeracy and mastery of basic facts. As the mathematical concepts become more advanced through the intermediate grades the focus shifts to the application of basic skills.

Core Curriculum Content Standards

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PA Common Core: Mathematics (2013)

• Numbers and Operations

• GRADE 4

• Apply place value concepts to show an understanding of multi-digit whole numbers.(2.1.4.B1)
• Extend the understanding of fractions to show equivalence and ordering.(2.1.4.C1)
• Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.(2.1.4.C2)
• Connect decimal notation to fractions, and compare decimal fractions (base 10 denominator, e.g, 19/100).(2.1.4.C3)

• Algebraic Concepts

• GRADE 4

• Represent and solve problems involving the four operations.(2.2.4.A1)
• Develop and/or apply number theory concepts to find factors and multiples.(2.2.4.A2)
• Generate and analyze patterns using one rule.(2.2.4.A4)

• Geometry

• GRADE 4

• Draw lines and angles and identify these in two-dimensional figures.(2.3.4.A1)
• Classify two-dimensional figures by properties of their lines and angles.(2.3.4.A2)
• Recognize symmetric shapes and draw lines of symmetry.(2.3.4.A3)

• Measurement, Data and Probability

• GRADE 4

• Solve problems involving measurement and conversions from a larger unit to a smaller unit.(2.4.4.A1)
• Represent and interpret data involving fractions using information provided in a line plot.(2.4.4.A4)

Mathematics

• Grade 4

• Number and Operations in Base Ten

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

• Apply place-value andnumeration concepts tocompare, find equivalencies,and round.(M.04.A-T.1.1)
• Demonstrate an understanding that in a multi-digitwhole number (through 1,000,000), a digit in oneplace represents ten times what it represents in theplace to its right.Example: Recognize that in the number 770, the 7in the hundreds place is ten times the 7 in the tensplace.(M.04.A-T.1.1.1)
• Read and write whole numbers in expanded,standard and word form through 1,000,000.(M.04.A-T.1.1.2)
• Compare two multi-digit numbers through1,000,000 based on meanings of the digits in eachplace, using >, =, and < symbols.(M.04.A-T.1.1.3)
• Round multi-digit whole numbers (through1,000,000) to any place.(M.04.A-T.1.1.4)

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

• Use operations to solveproblems.(M.04.A-T.2.1)
• Add and subtract multi-digit whole numbers (limitsums and subtrahends up to and including1,000,000).(M.04.A-T.2.1.1)
• Estimate the answer to addition, subtraction, andmultiplication problems using whole numbersthrough six digits (for multiplication, no more than2 digits × 1 digit, excluding powers of 10).(M.04.A-T.2.1.4)

• Number and Operations – Fractions

• Extend understanding of fraction equivalence and ordering.

• Find equivalencies and comparefractions.(M.04.A-F.1.1)
• Recognize and generate equivalent fractions.(M.04.A-F.1.1.1)
• Compare two fractions with different numeratorsand different denominators (denominators limitedto 2, 3, 4, 5, 6, 8, 10, 12, and 100) using thesymbols >, =, or <, and justify the conclusions.(M.04.A-F.1.1.2)

• Build fractions from unit fractions by applying and extending previous understandings ofoperations on whole numbers.

• Solve problems involvingfractions and whole numbers(straight computation or wordproblems).(M.04.A-F.2.1)
• Add and subtract fractions with a commondenominator (denominators limited to 2, 3, 4, 5, 6,8, 10, 12, and 100; answers do not need to bereduced; no improper fractions as the finalanswer).(M.04.A-F.2.1.1)
• Decompose a fraction or a mixed number into asum of fractions with the same denominator(denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and100), recording the decomposition by an equation.Justify decompositions (for example, by using avisual fraction model).Example 1: 3/8 = 1/8 + 1/8 + 1/8 OR 3/8 = 1/8 + 2/8Example 2: 2 1/12 = 1 + 1 + 1/12 =12/12 + 12/12 + 1/12(M.04.A-F.2.1.2)
• Add and subtract mixed numbers with a commondenominator (denominators limited to 2, 3, 4, 5, 6,8, 10, 12, and 100; no regrouping with subtraction;fractions do not need to be reduced; no improperfractions as the final answers).(M.04.A-F.2.1.3)
• Solve word problems involving addition andsubtraction of fractions referring to the same wholeor set and having like denominators (denominatorslimited to 2, 3, 4, 5, 6, 8, 10, 12, and 100).(M.04.A-F.2.1.4)
• Multiply a whole number by a unit fraction(denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and100; final answers do not need to be reduced orwritten as a mixed number).Example: 5 × (1/4) = 5/4(M.04.A-F.2.1.5)
• Multiply a whole number by a non-unit fraction(denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and100; final answers do not need to be reduced orwritten as a mixed number).Example: 3 × (5/6) = 15/6(M.04.A-F.2.1.6)
• Solve word problems involving multiplication of awhole number by a fraction (denominators limitedto 2, 3, 4, 5, 6, 8, 10, 12, and 100).(M.04.A-F.2.1.7)

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

• Use operations to solve problems involving decimals, including converting between fractions and decimals (may include word problems).(M.04.A-F.3.1)

• Operations and Algebraic Thinking

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

• Use numbers and symbols to model the concepts of expressions and equations.(M.04.B-O.1.1)
• Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations.Example 1: Interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5.Example 2: Know that the statement 24 is 3 times as many as 8 can be represented by the equation 24 = 3 × 8 or 24 = 8 × 3.(M.04.B-O.1.1.1)
• Multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison.Example: Know that 3 × 4 can be used to represent that Student A has 4 objects and Student B has 3 times as many objects, and not just 3 more objects.(M.04.B-O.1.1.2)
• Solve multi-step word problems posed with whole numbers using the four operations. Answers will be either whole numbers or have remainders that must be interpreted yielding a final answer that is a whole number. Represent these problems using equations with a symbol or letter standing for the unknown quantity.(M.04.B-O.1.1.3)
• Identify the missing symbol (+, –, ×, ÷, =, ) that makes a number sentence true (single-digit divisor only).(M.04.B-O.1.1.4)

• Gain familiarity with factors and multiples.

• Develop and apply number theory concepts to represent numbers in various ways.(M.04.B-O.2.1)

• Generate and analyze patterns.

• Recognize, describe, extend, create, and replicate a variety of patterns.(M.04.B-O.3.1)
• Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.Example 1: Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms alternate between odd and even numbers.Example 2: Given the rule “increase the number of sides by 1” and starting with a triangle, observe that the tops of the shapes alternate between a side and a vertex.(M.04.B-O.3.1.1)
• Determine the missing elements in a function table (limit to +, –, or × and to whole numbers or money).(M.04.B-O.3.1.2)
• Determine the rule for a function given a table (limit to +, –, or × and to whole numbers).(M.04.B-O.3.1.3)

• Geometry

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

• List properties, classify, draw, and identify geometric figures in two dimensions.(M.04.C-G.1.1)

• Measurement and Data

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

• Solve problems involving length, weight (mass), liquid volume, time, area, and perimeter.(M.04.D-M.1.1)
• Know relative sizes of measurement units within one system of units including standard units (in., ft, yd, mi; oz., lb; c, pt, qt, gal), metric units (cm, m, km; g, kg; mL, L), and time (sec, min, hr, day, wk, mo, yr). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. A table of equivalencies will be provided.Example 1: Know that 1 kg is 1,000 times as heavy as 1 g.Example 2: Express the length of a 4-foot snake as 48 in.(M.04.D-M.1.1.1)
• Use the four operations to solve word problems involving distances, intervals of time (such as elapsed time), liquid volumes, masses of objects; 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.(M.04.D-M.1.1.2)

• Represent and interpret data.

• Organize, display, and answer questions based on data.(M.04.D-M.2.1)

Units

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Unit #1 - M1: Place Value, Rounding, and Algorithms (Add/Subtract)

Unit #2 - M2: Unit Conversions

Unit #3 - M3: Multi-Digit Multiplication and Division

Unit #4 - M5: Fraction Equivalence, Ordering, and Operations

Unit #5 - M6: Decimal Fractions

Unit #6 - M4: Angle Measure and Plane Figures

Unit #7 - Module 7: Exploring Measurement with Multiplication

Course Resources

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Eureka Module Manuals
Mountain Math
Hands-on-Equations
Teacher created presentations
Teacher created assessments
Teacher created worksheets