Module 1: Place Value, Rounding, and Algorithms for Addition and Subtraction

• Use the four operations with whole numbers to solve problems.
• 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. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
• Generalize place value understanding for multi-digit whole numbers. (Grade 4 expectations are limited to whole numbers less than or equal to 1,000,000.)
• 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. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
• Place Value, Rounding, and Algorithms for Addition and Subtraction
• Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
•  Use place value understanding to round multi-digit whole numbers to any place.
• Use place value understanding and properties of operations to perform multi-digit arithmetic. Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Foundational Standards

• Solve two-step word problems using the four operationsRepresent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. 4
• Use place value understanding to round whole numbers to the nearest 10 or 100.
• 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.
• Focus Standards for Mathematical Practice
• Make sense of problems and persevere in solving them. Students use the place value chart to draw diagrams of the relationship between a digit’s value and what it would be one place to its right, for instance, by representing 3 thousands as 30 hundreds. Students also use the place value chart to compare very large numbers.
• Reason abstractly and quantitatively. Students make sense of quantities and their relationships as they use both special strategies and the standard addition algorithm to add and subtract multi-digit numbers. Students also decontextualize when they represent problems symbolically and contextualize when they consider the value of the units used and understand the meaning of the quantities as they compute.
•  Construct viable arguments and critique the reasoning of others. Students construct arguments as they use the place value chart and model single- and multi-step problems. Students also use the standard algorithm as a general strategy to add and subtract multi-digit numbers when a special strategy is not suitable.
•  Use appropriate tools strategically. Students decide on the appropriatness of using special strategies or the standard algorithm when adding and subtracting multi-digit numbers.
•  Attend to precision. Students use the place value chart to represent digits and their values as they compose and decompose base ten units.

Module 2

Unit Conversions and Problem Solving with Metric Measurement

• Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.[1]
• Know relative sizes of measurement units within one
• system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec.  Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit.  Record measurement equivalents in a two-column table.  For example, know that 1 ft is 12 times as long as 1 in.  Express the length of a 4 ft snake as 48 in.  Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), …
• 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.  Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale
• Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.  Understand the following as special cases: 100 can be thought of as a bundle of ten tens — called a “hundred.”
• Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (L). (Excludes compound units such as cm3 and finding the geometric volume of a container.)  Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. (Excludes multiplicative comparison problems, i.e., problems involving notions of “times as much.”)
• 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.  Represent these problems using equations with a letter standing for the unknown quantity.  Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
• Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Focus Standards for Mathematical Practice

• Make sense of problems and persevere in solving them.  Students use place value knowledge to convert larger units to smaller units before adding and subtracting.  They are able to fluently add and subtract metric units of length, weight, and capacity using the standard algorithm.  Tape diagrams and number lines conceptualize a problem before it is solved and are used to find the reasonableness of an answer.
• Look for and make use of structure.  Students use place value and mixed units knowledge to find similarities and patterns when converting from a larger unit to a smaller unit.  Making use of parts and wholes allows for seamless conversion.  They recognize that 1 thousand equals 1,000 ones relates to 1 kilometer equals 1,000 meters.  Using this pattern, they might extend thinking to convert smaller to larger units when making a conversion chart.
• Look for and express regularity in repeated reasoning.  Students find metric unit conversions share a relationship on the place value chart.  1,000 ones equals 1 thousand, 1,000 g equals 1 kg, 1,000 mL equals 1 L, and 1,000 m equals 1 km.  Knowing and using these conversions and similarities allows for quick and easy conversion and calculation.

Module 3:

Multi-Digit Multiplication and Division

Use the four operations with whole numbers to solve problems.

• Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
• Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. (See CCLS Glossary, Table 2.)
• 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. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Gain familiarity with factors and multiples.

• Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. 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.
• Use place value understanding and properties of operations to perform multi-digit arithmetic.[2]
• 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. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
• 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. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
• Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.[3]
• Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

Foundational Standards

• Represent and solve problems involving 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. (See CCLS Glossary, Table 2.)
• 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 x ? = 48, 5 = _ ÷ 3, 6 x 6 = ?.
• Understand properties of multiplication and the relationship between multiplication and division.
• Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
• Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
• Multiply and divide within 100.
• 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. By the end of Grade 3, know from memory all products of two one-digit numbers.
• 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. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order, i.e., Order of Operations.

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

• 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.

Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

• Relate area to the operations of multiplication and addition.

Geometric measurement:  recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

• 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.

Focus Standards for Mathematical Practice

• Reason abstractly and quantitatively.  Students solve multi-step word problems using the four operations by writing equations with a letter standing in for the unknown quantity.
• Model with mathematics.  Students apply their understanding of place value to create area models and rectangular arrays when performing multi-digit multiplication and division.  They use these models to illustrate and explain calculations.
• Use appropriate tools strategically.  Students use mental computation and estimation strategies to assess the reasonableness of their answers when solving multi-step word problems.  They draw and label bar and area models to solve problems as part of the RDW process.  Additionally, students select an appropriate place value strategy when solving multiplication and division problems.
• Look for and express regularity in repeated reasoning.  Students express the regularity they notice in repeated reasoning when they apply place value strategies in solving multiplication and division problems.  They move systematically through the place values, decomposing or composing units as necessary, applying the same reasoning to each successive unit.

MODULE 4: Angle Measure and Plane Figures

Geometric measurement:  understand concepts of angle and measure angles.

• Recognize angles as geometric shapes that are formed whenever two rays share a common endpoint, and understand concepts of angle measurement:
1. 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.
2. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.
• Measure angles in whole-number degrees using a protractor.  Sketch angles of specified measure.
• 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.  Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

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 these in two-dimensional figures.
• 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.  Recognize right triangles as a category, and identify right triangles.
• 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.  Identify line-symmetric figures and draw lines of symmetry.

Foundational Standards

• Solve two-step word problems using the four operations.  Represent these problems using equations with a letter standing in for the unknown quantity.  Assess the reasonableness of answers using mental computation and estimation strategies including rounding.  (This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order, i.e., Order of Operations.)
• Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals).  Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

Focus Standards for Mathematical Practice

• Reason abstractly and quantitatively.  Students represent angle measures within equations, and when determining the measure of an unknown angle, they represent the

Number and Operations—Fractions3 4.NF

• Extend understanding of fraction equivalence and ordering.
• Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × 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. Use this principle to recognize and generate equivalent fractions.
• 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. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
• 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. b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 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.
• 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.
• 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.
• 4. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
• Understand a fraction a/b as a multiple of 1/b. For example, use
• a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).
• Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)
• 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. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

Understand decimal notation for fractions, and compare decimal fractions.

•  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 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
•  Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. 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. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

Module 1: Place Value, Rounding, and Algorithms for Addition and Subtraction

• Use the four operations with whole numbers to solve problems.
• 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. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
• Generalize place value understanding for multi-digit whole numbers. (Grade 4 expectations are limited to whole numbers less than or equal to 1,000,000.)
• 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. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
• Place Value, Rounding, and Algorithms for Addition and Subtraction
• Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
•  Use place value understanding to round multi-digit whole numbers to any place.
• Use place value understanding and properties of operations to perform multi-digit arithmetic. Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Foundational Standards

• Solve two-step word problems using the four operationsRepresent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. 4
• Use place value understanding to round whole numbers to the nearest 10 or 100.
• 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.
• Focus Standards for Mathematical Practice
• Make sense of problems and persevere in solving them. Students use the place value chart to draw diagrams of the relationship between a digit’s value and what it would be one place to its right, for instance, by representing 3 thousands as 30 hundreds. Students also use the place value chart to compare very large numbers.
• Reason abstractly and quantitatively. Students make sense of quantities and their relationships as they use both special strategies and the standard addition algorithm to add and subtract multi-digit numbers. Students also decontextualize when they represent problems symbolically and contextualize when they consider the value of the units used and understand the meaning of the quantities as they compute.
•  Construct viable arguments and critique the reasoning of others. Students construct arguments as they use the place value chart and model single- and multi-step problems. Students also use the standard algorithm as a general strategy to add and subtract multi-digit numbers when a special strategy is not suitable.
•  Use appropriate tools strategically. Students decide on the appropriatness of using special strategies or the standard algorithm when adding and subtracting multi-digit numbers.
•  Attend to precision. Students use the place value chart to represent digits and their values as they compose and decompose base ten units.

Module 2

Unit Conversions and Problem Solving with Metric Measurement

• Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.[1]
• Know relative sizes of measurement units within one
• system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec.  Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit.  Record measurement equivalents in a two-column table.  For example, know that 1 ft is 12 times as long as 1 in.  Express the length of a 4 ft snake as 48 in.  Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), …
• 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.  Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale
• Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.  Understand the following as special cases: 100 can be thought of as a bundle of ten tens — called a “hundred.”
• Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (L). (Excludes compound units such as cm3 and finding the geometric volume of a container.)  Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. (Excludes multiplicative comparison problems, i.e., problems involving notions of “times as much.”)
• 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.  Represent these problems using equations with a letter standing for the unknown quantity.  Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
• Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Focus Standards for Mathematical Practice

• Make sense of problems and persevere in solving them.  Students use place value knowledge to convert larger units to smaller units before adding and subtracting.  They are able to fluently add and subtract metric units of length, weight, and capacity using the standard algorithm.  Tape diagrams and number lines conceptualize a problem before it is solved and are used to find the reasonableness of an answer.
• Look for and make use of structure.  Students use place value and mixed units knowledge to find similarities and patterns when converting from a larger unit to a smaller unit.  Making use of parts and wholes allows for seamless conversion.  They recognize that 1 thousand equals 1,000 ones relates to 1 kilometer equals 1,000 meters.  Using this pattern, they might extend thinking to convert smaller to larger units when making a conversion chart.
• Look for and express regularity in repeated reasoning.  Students find metric unit conversions share a relationship on the place value chart.  1,000 ones equals 1 thousand, 1,000 g equals 1 kg, 1,000 mL equals 1 L, and 1,000 m equals 1 km.  Knowing and using these conversions and similarities allows for quick and easy conversion and calculation.

Module 3:

Multi-Digit Multiplication and Division

Use the four operations with whole numbers to solve problems.

• Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
• Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. (See CCLS Glossary, Table 2.)
• 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. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Gain familiarity with factors and multiples.

• Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. 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.
• Use place value understanding and properties of operations to perform multi-digit arithmetic.[2]
• 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. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
• 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. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
• Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.[3]
• Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

Foundational Standards

• Represent and solve problems involving 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. (See CCLS Glossary, Table 2.)
• 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 x ? = 48, 5 = _ ÷ 3, 6 x 6 = ?.
• Understand properties of multiplication and the relationship between multiplication and division.
• Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
• Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
• Multiply and divide within 100.
• 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. By the end of Grade 3, know from memory all products of two one-digit numbers.
• 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. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order, i.e., Order of Operations.

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

• 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.

Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

• Relate area to the operations of multiplication and addition.

Geometric measurement:  recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

• 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.

Focus Standards for Mathematical Practice

• Reason abstractly and quantitatively.  Students solve multi-step word problems using the four operations by writing equations with a letter standing in for the unknown quantity.
• Model with mathematics.  Students apply their understanding of place value to create area models and rectangular arrays when performing multi-digit multiplication and division.  They use these models to illustrate and explain calculations.
• Use appropriate tools strategically.  Students use mental computation and estimation strategies to assess the reasonableness of their answers when solving multi-step word problems.  They draw and label bar and area models to solve problems as part of the RDW process.  Additionally, students select an appropriate place value strategy when solving multiplication and division problems.
• Look for and express regularity in repeated reasoning.  Students express the regularity they notice in repeated reasoning when they apply place value strategies in solving multiplication and division problems.  They move systematically through the place values, decomposing or composing units as necessary, applying the same reasoning to each successive unit.

MODULE 4: Angle Measure and Plane Figures

Geometric measurement:  understand concepts of angle and measure angles.

• Recognize angles as geometric shapes that are formed whenever two rays share a common endpoint, and understand concepts of angle measurement:
1. 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.
2. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.
• Measure angles in whole-number degrees using a protractor.  Sketch angles of specified measure.
• 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.  Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

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 these in two-dimensional figures.
• 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.  Recognize right triangles as a category, and identify right triangles.
• 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.  Identify line-symmetric figures and draw lines of symmetry.

Foundational Standards

• Solve two-step word problems using the four operations.  Represent these problems using equations with a letter standing in for the unknown quantity.  Assess the reasonableness of answers using mental computation and estimation strategies including rounding.  (This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order, i.e., Order of Operations.)
• Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals).  Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

Focus Standards for Mathematical Practice

• Reason abstractly and quantitatively.  Students represent angle measures within equations, and when determining the measure of an unknown angle, they represent the

Number and Operations—Fractions3 4.NF

• Extend understanding of fraction equivalence and ordering.
• Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × 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. Use this principle to recognize and generate equivalent fractions.
• 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. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
• 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. b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 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.
• 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.
• 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.
• 4. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
• Understand a fraction a/b as a multiple of 1/b. For example, use
• a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).
• Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)
• 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. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

Understand decimal notation for fractions, and compare decimal fractions.

•  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 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
•  Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. 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. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

Possible but not limited to, reading passages:

Secrets of the Sea/ A Monumental Mystery

Muscle Voyage

Common Core Standards

Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text.

Determine a theme of a story, drama, or poem from details in the text; summarize the text.

Describe in depth a character, setting, or event in a story or drama, drawing on specific details in the text (e.g., a character’s thoughts, words, or actions).

Determine the meaning of words and phrases as they are used in a text, including those that allude to significant characters found in mythology (e.g., Herculean).

Explain major differences between poems, drama, and prose, and refer to the structural elements of poems (e.g., verse, rhythm, meter) and drama (e.g., casts of characters, settings, descriptions, dialogue, stage directions) when writing or speaking about a text.

Compare and contrast the point of view from which different stories are narrated, including the difference between first- and third-person narrations.

Compare and contrast the treatment of similar themes and topics (e.g., opposition of good and evil) and patterns of events (e.g., the quest) in stories, myths, and traditional literature from different cultures.

By the end of the year, read and comprehend literature, including stories, dramas, and poetry, in the grades 4–5 text complexity band proficiently, with scaffolding as needed at the high end of the range.

Read with sufficient accuracy and fluency to support comprehension.

Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacherled) with diverse partners of grade 4 topics and texts, building on others’ ideas and expressing their own clearly.

Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 4 reading and content, choosing flexibly from a range of strategies.

a. Use context (e.g., definitions, examples, or restatements in text) as a clue to the meaning of a word or phrase.

Possible Reads, but not limited to:

“Fires of Pele”

“Like Fire and Water!”

“Bridge of Fire”

“How Night Came”

Common Core Standards

Determine a theme of a story, drama, or poem from details in the text; summarize the text.

Make connections between the text of a story or drama and a visual or oral presentation of the text, identifying where each version reflects specific descriptions and directions in the text.

Compare and contrast the treatment of similar themes and topics (e.g., opposition of good and evil) and patterns of events (e.g., the quest) in stories, myths, and traditional literature from different cultures.

By the end of the year, read and comprehend literature, including stories, dramas, and poetry, in the grades 4–5 text complexity band proficiently, with scaffolding as needed at the high end of the range.

Recognize, interpret and make connections in narratives, poetry, and drama, to other texts, ideas, cultural perspectives, personal events and situations.

Read with sufficient accuracy and fluency to support comprehension.

Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 4 topics and texts, building on others’ ideas and expressing their own clearly.

Seek to understand and communicate with individuals from different perspectives and cultural background.

Possible Reads but not limited to:

This Time Was Different/excerpt from “President Roosevelt’s Fireside Chat”

Jim Lovell: Stranded in Space

A Meeting of Minds

Common Core Standards

Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text.

Determine the main idea of a text and explain how it is supported by key details; summarize the text.

Explain events, procedures, ideas, or concepts in a historical, scientific, or technical text, including what happened and why, based on specific information in the text.

Describe the overall structure (e.g., chronology,comparison, cause/effect, problem/solution) of events, ideas, concepts, or information in a text or part of a text.

Compare and contrast a firsthand and secondhand account of the same event or topic; describe the differences in focus and the information provided

By the end of year, read and comprehend informational texts, including history/social studies, science, and technical texts, in the grades 4–5 text complexity band proficiently, with scaffolding as needed at the high end of the range.

Read with sufficient accuracy and fluency to support comprehension.

Participate in collaborative conversations with diverse partners about grade 1 topics and texts with peers and adults in small and larger groups

Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 4 reading and content, choosing flexibly from a range of strategies.

Use common, grade-appropriate Greek and Latin affixes and roots as clues to the meaning of a word (e.g., telegraph, photograph, autograph).

Possible Readings, but not limited to:

“The Hare and the Hedgehog”-The Tale of Mr. Jeremy Fisher

The Pot of Gold

Taking Action

Common Core Standards

Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text.

Determine a theme of a story, drama, or poem from details in the text; summarize the text.

Describe in depth a character, setting, or event in a story or drama, drawing on specific details in the text (e.g., a character’s thoughts, words, or actions).

Determine the meaning of words and phrases as they are used in a text, including those that allude to significant characters found in mythology (e.g., Herculean).

Explain major differences between poems, drama, and prose, and refer to the structural elements of poems (e.g., verse, rhythm, meter) and drama (e.g., casts of characters, settings, descriptions, dialogue, stage directions) when writing or speaking about a text.

By the end of the year, read and comprehend literature, including stories, dramas, and poetry, in the grades 4–5 text complexity band proficiently, with scaffolding as needed at the high end of the range.

Read with sufficient accuracy and fluency to support comprehension.

Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher led) with diverse partners on grade 4 topics and texts, building on others’ ideas and expressing their own clearly

Demonstrate understanding of figurative language, word relationships, and nuances in word meanings

Demonstrate understanding of words by relating them to their opposites (antonyms) and to words with similar but not identical meanings (synonyms).

Possible Readings, but not limited to:

“Windy Nights”

“Wind”

“The Hen”

“The Arrow and the Song”

“A Narrow Fellow in the Grass”

“I’m Nobody! Who Are You?”

“What is Pink?”

“Brown and Furry”

“Some One”

Common Core Standards

Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text.

Determine a theme of a story, drama, or poem from details in the text; summarize the text.

Determine the meaning of words and phrases as they are used in a text, including those that allude to significant characters found in mythology (e.g., Herculean).

Explain major differences between poems, drama, and prose, and refer to the structural elements of poems (e.g., verse, rhythm, meter) and drama (e.g., casts of characters, settings, descriptions, dialogue, stage directions) when writing or speaking about a text.

By the end of the year, read and comprehend literature, including stories, dramas, and poetry, in the grades 4–5 text complexity band proficiently, with scaffolding as needed at the high end of the range.

Read with sufficient accuracy and fluency to support comprehension.

Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher led) with diverse partners on grade 4 topics and texts, building on others’ ideas and expressing their own clearly

Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.

Explain the meaning of simple similes and metaphors (e.g., as pretty as a picture) in context.

Possible Readings but not limited to:

“Talking Underwater”

“Tools of the Fossil Hunter”

“Don’t Make Light of This!”

Common Core Standards

Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text.

Determine the main idea of a text and explain how it is supported by key details; summarize the text.

Explain events, procedures, ideas, or concepts in a historical, scientific, or technical text, including what happened and why, based on specific information in the text.

Determine the meaning of general academic and domain-specific words or phrases in a text relevant to a grade 4 topic or subject area.

Describe the overall structure (e.g., chronology, comparison, cause/effect, problem/solution) of events, ideas, concepts, or information in a text or part of a text.

Interpret information presented visually, orally, or quantitatively (e.g., in charts, graphs, diagrams, time lines, animations, or interactive elements on Web pages) and explain how the information contributes to an understanding of the text in which it appears.

By the end of year, read and comprehend informational texts, including history/social studies, science, and technical texts, in the grades 4–5 text complexity band proficiently, with scaffolding as needed at the high end of the range.

Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 4 topics and texts, building on others’ ideas and expressing their own clearly.

Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases, including those that signal precise actions, emotions, or states of being (e.g., quizzed, whined, stammered) and that are basic to a particular topic (e.g., wildlife, conservation, and endangered when discussing animal preservation).

Possible Readings, but not limited to:

“Nature’s Worst Storms”

Common Core Standards

Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text.

Determine the main idea of a text and explain how it is supported by key details; summarize the text.

Explain events, procedures, ideas, or concepts in a historical, scientific, or technical text, including what happened and why, based on specific information in the text.

Determine the meaning of general academic and domain-specific words or phrases in a text relevant to a grade 4 topic or subject area.

Describe the overall structure (e.g., chronology, comparison, cause/effect, problem/solution) of events, ideas, concepts, or information in a text or part of a text.

Interpret information presented visually, orally, or quantitatively (e.g., in charts, graphs, diagrams, time lines, animations, or interactive elements on Web pages) and explain how the information  Explain how an author uses reasons and evidence to support particular points in a text.

Integrate information from two texts on the same topic in order to write or speak about the subject knowledgeably.

By the end of year, read and comprehend informational texts, including history/social studies, science, and technical texts, in the grades 4–5 text complexity band proficiently, with scaffolding as needed at the high end of the range.

Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 4 topics and texts, building on others’ ideas and expressing their own clearly.

Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases, including those that signal precise actions, emotions, or states of being (e.g., quizzed, whined, stammered) and that are basic to a particular topic (e.g., wildlife, conservation, and endangered when discussing animal preservation).

Writing Common Core Curriculum
Writing Fictional Narratives – (Please note that each type of writing piece includes the following:

Pre-writing (brainstorming),  Organizing: Use graphic organizer to plan beginning, middle, and end, Drafting- writing the beginning, middle and end; Revising, Editing: complete sentences, capitalization, and frequently confused words;  Publishing.

Common Core Standards:

• Use context to confirm or self-correct word recognition and understanding, rereading as necessary.
• Orient the reader by establishing a situation and introducing a narrator and/or characters; organize an event sequence that unfolds naturally.
• Use dialogue and description to develop experiences and events or show the responses of characters to situations.
• Use a variety of transitional words and phrases to manage the sequence of events.
• Use concrete words and phrases and sensory details to convey experiences and events precisely.
• Provide a conclusion that follows from the narrated experiences or events.
• Produce clear and coherent writing in which the development and organization are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.)
• With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing. (Editing for conventions should demonstrate command of Language standards 1-3 up to and including grade 4 here.)
• With some guidance and support from adults, use technology, including the Internet, to produce and publish writing as well as to interact and collaborate with others; demonstrate sufficient command of keyboarding skills to type a minimum of one page in a single sitting.
• Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.
• Produce complete sentences, recognizing and correcting inappropriate fragments and run-ons.*
• Correctly use frequently confused words (e.g., to, too, two; there, their).*
• Use context (e.g., definitions, examples, or restatements in text) as a clue to the meaning of a word or phrase.
• Consult reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation and determine or clarify the precise meaning of key words and phrases.

Writing Personal Narratives:

Orient the reader by establishing a situation and introducing a narrator and/or characters; organize an event sequence that unfolds naturally.

Use a variety of transitional words and phrases to manage the sequence of events.

Provide a conclusion that follows from the narrated experiences or events.

• With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing. (Editing for conventions should demonstrate command of Language standards 1-3 up to and including grade 4 here.)
• With some guidance and support from adults, use technology, including the Internet, to produce and publish writing as well as to interact and collaborate with others; demonstrate sufficient command of
• Form and use prepositional phrases.
• Spell grade-appropriate words correctly, consulting references as needed
• Use common, grade-appropriate Greek and Latin affixes and roots as clues to the meaning of a word (e.g., telegraph, photograph, autograph).
• Recognize and explain the meaning of common idioms, adages, and proverbs.
• Demonstrate understanding of words by relating them to their opposites (antonyms) and to words with similar but not identical meanings (synonyms).

Writing Responses to Literature

• Introduce a topic or text clearly, state an opinion, and create an organizational structure in which related ideas are grouped to support the writer’s purpose
• Provide reasons that are supported by facts and details.
• Link opinion and reasons using words and phrases (e.g., for instancein order toin addition).
• Provide a concluding statement or section related to the opinion presented.
• With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing. (Editing for conventions should demonstrate command of Language standards 1-3 up to and including grade 4 here.)
• With some guidance and support from adults, use technology, including the Internet, to produce and publish writing as well as to interact and collaborate with others; demonstrate sufficient command of keyboarding skills to type a minimum of one page in a single sitting.

Research to Build and Present Knowledge

• Conduct short research projects that build knowledge through investigation of different aspects of a topic.
• Recall relevant information from experiences or gather relevant information from print and digital sources; take notes and categorize information, and provide a list of sources.
• Draw evidence from literary or informational texts to support analysis, reflection, and research.
• Apply grade 4 Reading standards to literature (e.g., “Describe in depth a character, setting, or event in a story or drama, drawing on specific details in the text [e.g., a character’s thoughts, words, or actions].”).
• Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.
• Form and use the progressive (e.g., I was walking; I am walking; I will be walking) verb tenses.
• Use modal auxiliaries (e.g., can, may, must) to convey various conditions.
• Choose words and phrases to convey ideas precisely.*
• Consult reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation and determine or clarify the precise meaning of key words and phrases.
• Explain the meaning of simple similes and metaphors (e.g., as pretty as a picture) in context.

Recognize and explain the meaning of common idioms, adages, and proverbs.

• Demonstrate understanding of words by relating them to their opposites (antonyms) and to words with similar but not identical meanings (synonyms).

Writing Informative /Explanatory Texts

Integrate information from two texts on the same topic in order to write or speak about the subject knowledgeably.

• Introduce a topic clearly and group related information in paragraphs and sections; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension.
• Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic.
• Link ideas within categories of information using words and phrases (e.g., anotherfor examplealsobecause).
• Use precise language and domain-specific vocabulary to inform about or explain the topic.
• Provide a concluding statement or section related to the information or explanation presented.

Production and Distribution of Writing

• Produce clear and coherent writing in which the development and organization are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.)
• With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing. (Editing for conventions should demonstrate command of Language standards 1-3 up to and including grade 4 here.)
• With some guidance and support from adults, use technology, including the Internet, to produce and publish writing as well as to interact and collaborate with others; demonstrate sufficient command of keyboarding skills to type a minimum of one page in a single sitting.

Research to Build and Present Knowledge

• Conduct short research projects that build knowledge through investigation of different aspects of a topic.
• Recall relevant information from experiences or gather relevant information from print and digital sources; take notes and categorize information, and provide a list of sources.
• Draw evidence from literary or informational texts to support analysis, reflection, and research.
• Apply grade 4 Reading standards to informational texts (e.g., “Explain how an author uses reasons and evidence to support particular points in a text”).
• Order adjectives within sentences according to conventional patterns (e.g., a small red bag rather than a red small bag).
• Use commas and quotation marks to mark direct speech and quotations from a text.
• Use a comma before a coordinating conjunction in a compound sentence.
• Choose words and phrases to convey ideas precisely.*
• Use common, grade-appropriate Greek and Latin affixes and roots as clues to the meaning of a word (e.g., telegraph, photograph, autograph).
• Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases, including those that signal precise actions, emotions, or states of being (e.g., quizzed, whined, stammered) and that are basic to a particular topic (e.g., wildlife, conservation, and endangered when discussing animal preservation).

Writing Opinion Pieces/Persuasive Essays

• Introduce a topic or text clearly, state an opinion, and create an organizational structure in which related ideas are grouped to support the writer’s purpose.
• Provide reasons that are supported by facts and details.
• Link opinion and reasons using words and phrases (e.g., for instancein order toin addition).
• Provide a concluding statement or section related to the opinion presented.

Production and Distribution of Writing

• Produce clear and coherent writing in which the development and organization are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.)
• With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing. (Editing for conventions should demonstrate command of Language standards 1-3 up to and including grade 4 here.)
• With some guidance and support from adults, use technology, including the Internet, to produce and publish writing as well as to interact and collaborate with others; demonstrate sufficient command of keyboarding skills to type a minimum of one page in a single sitting.
• Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.
• Use relative pronouns (who, whose, whom, which, that) and relative adverbs (where, when, why).

Range of Writing
Knowledge of Language

• Differentiate between contexts that call for formal English (e.g., presenting ideas) and situations where informal discourse is appropriate (e.g., small-group discussion).

Vocabulary Acquisition and Use

• Differentiate between contexts that call for formal English (e.g., presenting ideas) and situations where informal discourse is appropriate (e.g., small-group discussion).
• Recognize and explain the meaning of common idioms, adages, and proverbs.

## Science Curriculum

Unit C: Classifying Living Things

All kinds of Living Things

• How can living things be classified?
• How do vertebrates differ?
• How do the groups of Invertebrates differ?
• How are plants classified?

The Survival of Living Things

• What are the basic needs of living things?
• How do living things meet their needs?

Unit B: Properties of Matter (Describing Matter)

• Describing Matter: How can matter be described?
• How can matter be measured?

Conserving States of Matter

• What is Matter Like? –It’s physical and chemical properties
• How can matter change state

Causing Changes in Matter

• What are physical changes?
• What are chemical changes?

Unit D: Magnetism and Electricity

Magnetism

• What are Magnets?
• What are Magnetic Force Fields?

Electrical Energy

• What is Static Electricity?
• What is Current Electricity?
• How do electric circuits differ?

Electricity at Work

• What are some sources of electric current?
• How is electricity useful?

Unit A: Earth’s Land

The Shape of Land

• How does moving water shape the land?
• How do wind and Ice shape the land?

The Importance of Natural Resources

• Why is Soil and important resource?
• Why are rocks and minerals important?
• Why are energy Resources so important?

The Problem With Trash

• What do people throw away  and where does it go?
• How can trash affect resources?
• How can you help solve the trash problem?

Unit E: Weather and Climate

The Air Around Us

• What is Air?
• Why does the air move?

Observing weather

• What is air pressure?
• How can you find wind speed and direction?
• How does water in the air affect weather?

Weather Patterns

• What can clouds tell you about the weather?
• How can you stay safe during dangerous weather?

Seasons and Climate

• What causes the seasons?
• What factors affect climate?

Unit One: New York’s Land and First People

New York’s Geography

• The Geography of New York
• New York’s landforms and waterways
• Climate and Resources of New York
• Map and Globe Skill: Using map scale and other features to find and calculate distance between two places

New York’s First People

• Prehistoric New Yorkers and; how did they arrive in North America and how they used natural resources to survive
• Algonquians and Haudenosaunee; their way of life
• The League of Five Nations; how they formed and their present life in New York today
• Reading and Thinking Skill: Summarizing

Unit 2: Colonists and Independence

The Colonial Period

• First Explorers: Discover some of the first European Explorers that journeyed through North America
• Settling New York: Settlement and Growth of New Netherland
• Colonial New York: How did Dutch and English settlement affect present day New York?
• Map and Globe Skill: Use Latitude and Longitude

American Revolution

• Causes of the Revolution: What were important events that led to the American Revolution
• Battleground New York: Explain how fighting in the American Revolution moved into New York State
• The New Nation: Explain how the Constitution of New York State and the United States became forms of government; how did the nation grow after the United States Constitution was ratified.
•  Citizenship Skill: Understanding Point of View

Unit 3: Time of Change

Growth and Expansion

• The Industrial Revolution: Investigate how the Industrial Revolution changed businesses in New York
• Immigrants and Reformers: Investigate why people immigrated to New York.
• Civil War: Learn about how the issues of state’s rights and slavery divided the country during the mid-1800s.
• Skillbuilder: Identify Primary and Secondary Sources

The Growth of Cities

• Coming to New York: Describe the reasons why immigrants came to New York, and discuss the social, economic, and cultural activities of immigrants.
• Growth of Big Business: Explain how New York State’s access to shipping routes and many natural resources helped it become a business center.
• Into the 20th Century: Describe how Franklin D. Roosevelt helped New York and the United Stantes recover from the Great Depression
• New York City: Describe how the movement of African Americans and Puerto Ricans affected New York City
• Identify Causes and Effects
• New York City: Describe how the movement of African Americans and Puerto Ricans affected New York City

Unit 4: New York Today

Life In New York

• The people of New York: Explain why New York is a multicultural state.
• A Cultural Capital: Describe New York State’s cultural life
• New Yorkers at Work: Discuss the types of work, and resources, and educational opportunities that are available in New York State

Government of New York

• State government: Discuss how the New York State Constitution sets up New York State’s plan of government
• Explain the branches of New York
• Local Government: Discuss the parts of city government
• Citizen’s Role in Government: Understand the difference between a right and a responsibility; discuss what it means to be a good cititzen

Unit 5: Living in the United States

Exploring the East

• Land and Climate: Identify and describe four major land or water features of the East.
• Explain why many towns and cities are located on rivers and coasts.
• Discuss ways the climate of the East affects the people who live there.

Resources and Economy

• List four natural resources found in the East
• Identify two ways people use natural  resources of the East
• Compare market economy and command economy/Explain private ownership
• Identiy and describe the factors of production

People of the East

• Explain how the environmnent affected American Indian culture.
• Describe two ways that American Indians have used the natural resources of the East.
• Discuss why European colonists moved to North America
• Explain why European immigrants and people from rural areas of the United States moved to the East in the early 1800s.
• Make a time line; Interpret information from a timeline

United States Government

• Discuss what it means to have a government “by the people, of the people, and for the people.”
• Identify what is a democracy
• Explain how U. S. citizens choose leaders and representatives

Many Regions, One Nation

• Identify three transportation and communication systems that link states and regions
• Describe the importance of trade between sates and regions
• Describe two ways people celebrate their heritage

North American Neighbors

• Identify three of the countries of North America
• Describe the land and climate of Canada
• Describe the land and climate of Mexico

Compare and Contrast Canada and Mexico

Prophet Ibraheem
Prophet Ishaq
Prophet Lut
Prophet Ya’qoub
Prophet Yousef
Quraaysh try to hurt the Prophet
Al Hijrah
Biuilding the Mosq
The Battle of Uhud
Surat Ul Ghashiya
I didn’t miss my prayer
Be aware of Najassah
Friday prayer
What breaks my prayer?
Al Naziah
Islamic year
Eating right
Surat Al Naziat
Islam in Africa
Muslims in South Africa
Muslims love each other
Helping others