Vocabulary: Digits Place Value Standard form Expanded Form Word Form Compare Commutative Property of Addition Associative Property of Addition Identity Property of Addition Breaking apart Compensation Inverse operations Standard algorithm Addend Sum Estimate Rectangular Array Area model Product Multiples Compatible numbers Factor(s) Rounding Remainder Quotient Dividend Prime number Composite number Partial product Ohio s New Learning Standards Grade 4 Gifted Math Number and Operations in Base Ten 1
Generalize place value understanding for multi-digit whole numbers. 1. 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. How can you prove that in a multi-digit whole number that the digit in the ones place represents ten times what it represents in the place to its right? 2. 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. How do you read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form? How do you compare two multi-digit numbers based on meanings of the digits in each place using >, =, and < symbols to record the results of comparisons? 3. Use place value understanding to round multi-digit whole numbers to any place. How do you use place value understanding to round multi-digit numbers? Use place value understanding and properties of operations to perform multi-digit arithmetic. 4. Fluently add and subtract multi-digit whole numbers using the standard algorithm. How do you add and subtract multi-digit numbers using the standard algorithm? 5. 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. How do you multiply a whole number of up to four digits by a one-digit whole number? How do you multiply 2 two-digit numbers, using strategies based on place value and the properties of operations? How do you explain multiplication problems using equations, rectangular arrays, and/or area models? 6. 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. How do you 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? How do you explain division problems by using equations rectangular arrays, equations, and/or area models? 2
Activities: Differentiating With Instruction Menus v Place Value List Menu v Prime/Composite 2-5-8 Menu v Whole Numbers Baseball: Singles, Doubles, Triples, Homeruns p. 57 Math Art v Numbers and Computations Wanted Posters p. 34-45 3
Number and Operations Fractions Vocabulary: Fraction Numerator Denominator Factors Equivalent Fractions Common denominator Benchmark Fraction Unit Fraction Mixed Number Improper Fraction Extend understanding of fraction equivalence and ordering. 1.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. How do you explain why two fractions are equivalent if both the numerator and the denominator have been multiplied or divided by the same number? How do you explain why two fractions are equivalent by using visual fraction models? How do you generate equivalent fractions? 2. 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. How do you compare two fractions with different numerators and denominators? How do you explain that comparisons are only valid when the two fractions refer to the same whole? How do you record the results of the comparisons with the symbols: >, =, <? How do you justify your conclusions by using a visual fraction model? Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. 3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. How can you understand a fraction a/b with a>1 as a sum of fractions 1/b? 4
a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. How do 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. How do you decompose a fraction into a sum of fractions with the same denominator in more than one way? How do you record each decomposition by using an equation? How do you justify the decomposition by using a visual fraction model? c.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. How do you add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction? How do you add and subtract mixed numbers with like denominators by using the relationship between addition and subtraction? d. 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. How do you solve real world problems involving the addition and subtraction of fractions that refer to the same whole and have like denominators? How do you use visual fraction models and equations to represent and solve the problem? 4. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. How do multiply a fraction by a whole number? a. 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). How can you understand fraction a/b as a multiple of 1/b? 5
b. 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.) How do you understand a multiple of a/b as multiple of 1/b? How do you use this understanding to multiply a fraction by a whole number? c. 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? How do you solve word problems involving a fraction and a whole number? How do you use visual fraction models and equations to represent the problem? Understand decimal notation for fractions, and compare decimal fractions. 5. 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. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. How do you express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100? How do you use this technique to add two fractions with denominators of 10 and 100? 6. 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. How can you use decimal notation for fractions with denominators of 10 and 100? 7. 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. How do you compare two decimals to the hundredths by reasoning about their size? How do you know the comparisons are valid only when the two decimals refer to the same whole? How do you record the results of the comparisons using the symbols >,<, =? 6
Activities/Projects: Differentiating With Instruction Menus v Basic Fractions Tic-Tac-Toe p. 63 v Adding and Subtracting Fractions Tic-Tac-Toe Menu Math Art v Fraction Flags p.82-83 v Fraction Quilts p.84-86 7
Operations and Algebraic Thinking Vocabulary: Array Product Factors Multiple Fact family Prime Divisor Quotient Zero property Commutative property Identity property Distributive property of multiplication Inverse operations Composite Dividend Multiplicative comparison Additive comparison Remainder Rounding Estimation Factors Patterns Rule Use the four operations with whole numbers to solve problems. 1.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. Represent verbal statements of multiplicative comparisons as multiplication equations. How can you identify and explain a multiplication equation as a comparison? How can you explain multiplicative comparisons as multiplication equations? 2. 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.1 How do you multiply or divide to solve word problems involving multiplicative comparsion? How do you use drawings and equations with a symbol for the unknown to represent the problem? 8
3. 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. How do you solve multi-step word problems with whole numbers including problems in which remainders must be interpreted? How do you represent these problems using equations with a letter standing for the unknown quantity? How do you assess the reasonableness of answers using mental computation and estimation strategies such as rounding? Gain familiarity with factors and multiples. 4. 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. How do you find all the factor pairs for a whole number in the range of 1-100? How do you prove that a whole number is a multiple of each of its factors? How do you determine if a number in the 1-100 range is a multiple of a given one-digit number? How do you determine if a given number in the 1-100 range is prime or composite? Generate and analyze patterns. 5. 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. For example, given the rule Add 3 and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. How do you generate a number or shape pattern that follows a given rule? How do you identify apparent features of a pattern that were not stated in the rule? 9
Geometry Vocabulary Point Line Segment Ray Angle Right Angle Obtuse Angle Acute Angle Perpendicular Parallel Ray Angle Degrees Arc Right triangle Symmetry Line of symmetry Draw and identify lines and angles, and classify shapes by properties of their lines and angles. 1.Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. How can you draw points, line segments, rays, angles, perpendicular and parallel lines? How do you identify these in two-dimensional figures? 2. 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. How do you classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines? How do you classify two-dimensional figures based on the presence or absence of angles of a specified size? How do you identify and classify right triangles? 3. 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. 10
How do you recognize a line of symmetry for a two-dimensional figure? How do you identify line-symmetric figures? How do you draw lines of symmetry? Activities: Differentiating Instruction With Menus v Lines and Congruency 2-5-8 p. 81 v Geometry Shapes Tic-Tac-Toe p. 83 v Geometry Game Show Menu p. 87 Math Art: v Five Pointed Stars p.31-32 v Geometric Sculptures p.29-30 v Nature Symmetry Prints p.15 Students find geometry in their names: types of angles, lines etc Create polygons with spaghetti and marshmallows What s Your Angle, Pythagoras? A Math Adventure by Julie Ellis 11
Measurement and Data Vocabulary: Fraction Decimal Scale Unit Area Perimeter Formula Line-plot Ray Endpoint Angle Degrees Arc Angles Protractor 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),... How can you tell the relative sizes of measurements within one system of units? How do you express measurements in a larger unit in terms of a smaller unit? How do you record measurement equivalents in a two column table? 2. 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. How do you use the four operations to solve word problems involving distances? How do you solve word problems involving intervals of time? How do you solve word problems involving liquid volumes? How do you solve word problems involving masses of objects? How do you solve word problems involving money? How do you solve word problems including fractions or decimals? 12
How do you solve word problems that require expressing measurements given in larger units in terms of a smaller unit? How do you represent measurement quantities using diagrams that feature a measurement scale? 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. How do you apply the area and perimeter formulas for rectangles in the real world and in math problems? Represent and interpret data. 4. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. How do you make a line plot to display a data set of measurements using fractions? How do you solve problems involving adding and subtracting of fractions by using information from the line plots? Geometric measurement: understand concepts of angle and measure angles. 5. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: How do you show angles as geometric shapes that are formed by two rays who share a common endpoint? a. 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. How can you recognize that an angle is measured with reference to a circle with its center at the common endpoint of two rays? B.An angle that turns through n one-degree angles is said to have an angle measure of n degrees. How do you recognize that an angle that turns through n one-degree angles is said to have an angle measure of n degrees? 13
6. Measure angles in whole-number degrees using a protractor. Sketch angles of specified measurement. How do you measure angles in whole-number degrees using a protractor? How do you sketch angles of specified measurements using a protractor? 7. 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. How do you recognize an angle measure as additive when the angle is decomposed into nonoverlapping parts? How do you solve addition and subtraction problems to find unknown angles on a diagram? Activities: Differentiating Instruction with Menus v Measuring Capacity Tic-Tac-Toe p. 92 v Gallon Person p. 93 v Measuring Length 2-5-8 p. 98 v Measuring Weight Tic-Tac-Toe p. 104 v Measurement Game Show p.108 Area/Perimeter cover-all game Using cm block paper, the students write and color their names in block letters, then find the area and perimeter of their names Use Cheez-Its to find area and perimeter Use straws cut into lengths of 2,4, and 6 inches, along with pipe cleaners cut into 2-inch pieces, students explore perimeter by making polygons with sides of various lengths. Perimeter and Area Books: v Perimeter, Area, and Volume by David Adler v Mighty Math by Edmark v Spaghetti and Meatballs for All! By Marilyn Burns 14
Other resources: www.education.com offers a variety of math games that coordinate with standards Envision Math Triumph online Khan Academy www.scholastic.com Brain Pop Study Island Simple Solutions 4 th Grade Common Core Math MathCore2k: Problem of the day, mental math strategies, and model lessons and student activities that are common core aligned www.teachertube.com www.pinterest.com www.corkboardconections.com 15
Third Grade Suggested Pacing Plan: This is a grade accelerated suggested pacing plan for the third grade gifted students. Due to pretesting and compacting, the teacher may need to adjust this schedule to suit the needs of the students. The teacher may also need to supplement with other resources. The Simple Solutions Common Core 4 th Grade Math, a variety of teaching and learning strategies, MathCore2k, projects, math journals, essential questions, and formative assessments will also be implemented daily into this curriculum. Quarter 1: Envision Math Topic 3: Place Value v 4.NBT.1 v 4.NBT.2 v 4.NBT.3 Envision Math Topic 1: Multiplication and Division v 4.OA.1 v 4.OA.2 v 4.OA.3 v 4.OA.4 Envision Math Topic 2: Generate and Analyze Patterns v 4.OA.5 Envision Math Topic 4: Addition and Subtraction of Whole Numbers 16
v 4.NBT.4 Envision Math Topic 5: Number Sense: Multiplying by 1 digit numbers v 4.NBT.5 Envision Math Topic 6: Developing Fluency: Multiplying by 1 digit numbers v 5.NBT.5 Quarter 2 Envision Math Topic 7: Number Sense: Multiplying by 2 digit numbers v 4.NBT.5 Envision Math Topic 8: Developing Fluency: Multiplying by 2 digit numbers v 4.NBT.5 Envision Math Topic 9: Number Sense: Dividing by 1 digit divisors v 4.NBT.6 Envision Math Topic 10: Developing Fluency: Dividing by 1 digit divisors Standards v 4.NBT.6 Envision Math Topic 11: Fraction Equivalence and Ordering v 4.NF.1 v 4.NF.2 17
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Quarter 3: Envision Math Topic 12: Adding and Subtracting Fractions with Mixed Numbers and Like Denominators v 4.NF.3 Envision Math Topic 13: Extending Fraction Concepts v 4.NF.4 v 4.NF.4a v 4.Nf.4b v 4.NF.4c v 4.NF.5 v 4.NF.6 v 4.NF.7 v 4.MD.1 v 4.MD.2 Envision Math Topic 14: Measurement and Conversions v 4.MD.1 v 4.MD.2 Envision Math Topic 15: Solving Measurement Problems v 4.MD.2 v 4.MD.3 v 4.MD.4 19
Envision Math Topic 16: Lines, Angles, and Shapes v 4.G.1 v 4.G.2 v 4.G.3 v 4.MD.5a v 4.MD.5b v 4.MD.6 v 4.MD.7 Resources to use within Envision: v Diagnostic Tests v Topic Tests v Performance Assessments v Quick Checks v Common Core Questions v Tiered Worksheets 20
Fourth Quarter Review Topics of Concern Some Test Prep Start 5 th Grade Envision 21