Cologne Academy Mathematics Department Grade 3H Math (Aligned Text: Math in Focus Singapore Math Common Core Ed.) Curriculum 100% Aligned Adopted: 08/2014 Board Approved: 07/24/2014 Updated: 07/13/2015 Page 0
Table of Contents Math Department Lesson Plan Essentials... 2 Units and Pacing Charts Unit 1 Overview: Ordering & Comparing, Rounding, and Adding & Subtracting Numbers to 100,000... 3 Essential Vocabulary... 5 Pacing Chart... 6 Unit 2 Overview: Multiplication & Division & Real World Problems... 7 Essential Vocabulary... 9 Pacing Chart... 10 Unit 3 Overview: Input-Output, Number Sentences & Fractions... 11 Essential Vocabulary... 13 Pacing Chart... 14 Unit 4 Overview: Time, Temperature, Data Analysis & Geometry... 15 Essential Vocabulary... 16 Pacing Chart... 17 Highlighted items indicate overlap of MN State Standards and the Sequence. Boxed items indicate content to be introduced post-mcas. Page 1
Math Department Lesson Plan Essentials Topic: Title of lesson. *Objective: Academic goal for students to achieve by end of lesson. *Benchmark Reference: MN State Standard or Sequence reference. Agenda: Sequence of instruction and activities Closure: Brief summary/overview of lesson. May include formative assessment. Homework: Continued practice of lesson. May be used as formative assessment. *Indicates required components. Note: The text has been as closely aligned with MN State Standards but additional resources may be required to include all skills (including within the Sequence). Resources may be located on the s: drive under Mathematics Resources and by grade level. Further research/exploration may be required to locate additional resources. Page 2
Overview Strand(s): Numbers & Operations, Geometry & Measurement Unit 1: Ordering & Comparing, Rounding, and Adding & Subtracting Numbers to 100,000 Approximate Duration of Study: 8 Weeks of Instruction MNSS Knowledge Skills Fluency Core Knowledge Number to 100,000 3.1.1.1 Place Value 3.1.1.2 3.1.1.3 Addition increases a value, subtraction decreases a value There is a relationship between addition and subtraction facts. Numbers can be represented in a variety of ways including: o Numerals, expressions with operations, words, pictures, number lines, and manipulatives. Roman numerals is a number system based on seven different symbols. o I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000 A digit represents a place value in a whole number. o The digit 4 in 4,327 has a value of 4,000 because 4,000 + 300 + 20 + 7 = 4,327 Demonstrate fluency with basic addition facts and related subtraction facts. Read, write and represent (in digits and words) whole numbers up to 100,000 using a variety of methods. Review dozen, half-dozen and pair. Identify Roman numerals from 1 to 20 (I - XX). Recognize and use place value to describe and write whole numbers between 1000 and 100,000 in terms of ten thousands, thousands, hundreds, tens and ones. Write numbers in expanded form. Find 10,000, 1000, 100 more or less than a given 4- or 5-digit number. Rounding, Estimating and Comparing 3.1.1.4 3.1.1.5 Non-exact values can be used to make predictions/decisions/confirm if an answer is reasonable or not. o $4,357 can be rounded to $4,400 (hundreds place) to estimate the amount of savings needed to make a $4,357purchase. Place value can be used to make comparisons and order numbers from least to greatest and vice versa. o Greater than: > (e.g. 6 > 2) o Less than: < (e.g. 2 < 6) o Equal to: = (e.g. 6 = 6) Round a number to the nearest 10,000, 1000, 100, 10. Round numbers to estimate sums and differences. Use a number line to round numbers to the nearest tens, hundreds or thousands. Compare whole numbers up to 100,000. Order whole numbers up to 100,000. Use a number line to compare and order numbers. Locate positive and negative whole numbers on a number line. Unit 1 Page 3
Ordinal Position Core Knowledge Place Value: Add & Subtract There is a name for numerical positions. Place value is used to add and subtract multi-digit numbers. o Algorithm: add/subtract from right to left (i.e. ones, tens, hundreds, etc.). Identify ordinal positions, 1 st to 100 th. Add and subtract multi-digit numbers using place value as a guide. Add and subtract with and without regrouping up to 10,000. 3.1.2.1 Addition and subtraction are inverse (opposite) operations. Use addition to check subtraction and vice versa. Addition & Subtract in the Real World 3.1.2.2 Money: Making Change 3.3.3.3 Measuring Time 3.3.3.1 Addition and subtraction of whole numbers can be applied to real-world situations. Multiple strategies can be applied to assess the reasonableness of results. Different coin combinations can sum to the same amount of money. o E.g. 10 pennies and 4 dimes = 2 quarters = 4 nickels and 3 dimes. A digital or analog clock can be used to measure time. o Hours, minutes, seconds. Time can be measured linearly. o Use duration, start time, and end time to find missing information and/or make decisions. Use addition and subtraction of whole numbers to solve real-world problems. Solve two-step word problems. Make sense of solutions using: o The relationship between addition and subtraction. o Technology o Context of the problem Make change, up to one dollar, using as few coins as possible and in more than one way. Write amounts of money using $ and signs, and the decimal point. Add and subtract amounts of money. Read and write decimals to the hundredths. Tell and determine elapsed time to the minute as either A.M. or P.M. o If you left the movie theater at 3 pm and the movie was 1 hour and 45 minutes long, what time did the movie begin? Tell time in terms of both minutes before and minutes after the hour. Solve problems on elapsed time (how much time has passed). A calendar is used to measure time. Identify the date, day of the week, month, and year. Write the date using words (for name of month) and numbers, and only numbers. Unit 1 Page 4
Converting Time 3.3.3.2 There is a relationship between measurements of time (i.e. minutes, hour, days in a week, and months in a year). Convert between units of time. Represent lengths of time using different units. Temperature 3.3.3.4 Temperature can be measured in Fahrenheit and Celsius. O : degree symbol. Determine temperature to the nearest degree, using an analog thermometer, in Fahrenheit and Celsius. Identify freezing point of water as 32 O F = 0 O C. Use negative numbers can be used to describe temperature. o Temperatures below zero. Essential Vocabulary: Value, Dozen, Half-Dozen, Pair, Roman Numerals (I, II, III, IV, V, VI, VII, VII, IX, X, XI, XII, XII, XIV, XV, XVI, XVII, XVIII, XIX, XX), Digit, Place Value, Ten Thousands, Thousands, Hundreds, Tens, Ones, Expanded Form, Estimate, Rounding, About, Sum, Difference, Number Line, Greater Than (>), Less Than (<), Equal To (=), Positive, Negative, Ordinal Position, Inverse Operations, Decimal, Hundredth, Digital, Analog (Clock Face), Hours, Minutes, Seconds, Linearly, Duration, Calendar, Elapsed Time, A.M., P.M., Date, Day, Week, Month, Year, Fahrenheit, Celsius, O Degree Symbol, Thermometer, Freezing Point. Interim 1 Unit 1 Page 5
Pacing Chart Unit 1: Ordering & Comparing, Rounding, and Adding & Subtracting Numbers to 100,000 Time Frame Topic Suggested Performance Tasks/Projects/ Activities/Assessments Resources & Text Alignment Week 1 Pre-test & Routines BrainPop.com Week 2 Numbers to 100,000 DiscoveryEducation.com Text section: 1.1 Week 2 Place Value Text section: 1.2 Week 3 Week 4 Week 5 Rounding, Estimating and Comparing Text section: 1.3 Place Value: Add & Subtract Text: Ch. 3, Ch. 4 Week 6 Addition & Subtraction in the Real World Text: Ch. 5 Week 7 Money: Making Change Need resource Week 8 Measuring Time Text Sections: 16.1, 16.3 to 16.5 Week 8 Converting Time Text Section: 16.2 Week 8 Temperature Text Sections: 16.6, 16.7 Week 9 Review Week 10 Interim 1 Unit 1 Page 6
Overview Strand(s): Numbers & Operations, Geometry & Measurement Unit 2: Multiplication & Division & Real World Problems Approximate Duration of Study: 7 Weeks of Instruction MNSS Knowledge Skills Fluency Addition increases a value, subtraction decreases a value There is a relationship between addition and subtraction facts. Multiplication is repeated addition. Demonstrate fluency with basic addition facts and related subtraction facts. Demonstrate fluency with basic multiplication facts. Division is repeated subtraction. Demonstrate fluency with basic division facts. Multiplication & Division 3.1.2.3 Multiplication can be represented using: o Repeated addition o Equal-sized groups o Arrays o Area models o Equal jumps on a number line o Skip counting Use various methods to represent multiplication facts. Count by twos, threes, fives and tens. Count by tens from any given number. Use a number line to represent multiplication. Identify perfect squares and square roots to 100. Recognize the square root sign: Mentally multiply by 10, 100, and 1,000. Estimate a product. Place value is used to write numbers in expanded form using multiplication. Write numbers in expanded form using multiplication. o 9,278 = (9 1,000) + (2 100) + (70 10) + 8 Division can be represented using: o Repeated subtraction o Equal sharing o Forming equal groups Dividend: The value being divided; Divisor: The value you divide by (indicates number of groups); Quotient: The solution to a division problem. The divisor cannot be 0. Any number divided by 1 = that number. Use various methods to represent division facts. Divide two- and three-digit dividends by one-digit divisors. Solve division problems with remainders. Check division by multiplying (and adding remainder). Unit 2 Page 7
In order for a number to be even the last digit must be a 0, 2, 4, 6, or 8. Even numbers can be split into groups, with each group containing the same amount of numbers, objects, symbols, etc. In order for a number to be odd the last digit must be a 1, 3, 5, 7, or 9. Odd numbers can be split into groups, with each group containing the same amount (of numbers, objects, symbols, etc.) but always having an unequal group remaining. o A group of 25 students can be split into 5 groups of 5 but 25 is not an even number because it does not end in 0, 2, 4, 6, or 8. Review even and odd numbers. Determine if a number is even or odd. There is a relationship between multiplication and division. Multiplication and division are inverse operations. o 9 x 6 = 54; 6 x 9 = 54, 54 9 = 6; 54 6 = 9 Use fact families to illustrate the relation between multiplication and division. Properties of Multiplication 3.1.2.5 Multiplication & Division in the Real World 3.1.2.4 Place value, equality and properties of addition/multiplication are used to multiply two- and three-digit numbers by a one-digit number. Mental strategies, partial products, standard algorithms, and the commutative, associative, and distributive properties can be used to multiply two- and three-digit numbers by a single digit number. o Commutative: 23 x 2 = 2 x 23 o Associative: (12 x 2) x 4 = 12 x (2 x 4) o Distributive: 12 x 2 = 2(10 + 2) o Partial Products: 345 x 2 = 300 x 2 = 600 40 x 2 = 80 5 x 2 = + 10 690 Multiplication and division can be applied to real-world situations. Use strategies to multiply two- and three-digit numbers by a onedigit number, with and without regrouping. (Strategies assist with creating an easier problem to solve.) Use multiplication to solve real-world problems. o There are 9 tables and each table can seat 4 people. How many people can be seated altogether? Unit 2 Page 8
Use division to solve real-world problems. o How many in each group: There are 36 people and 9 tables. If each table seats the same number of people, how many people would sit at each table? o How many groups: If there are 36 people and tables that seat 4 people, how many tables will be needed? Multiply and divide amounts of money by small whole numbers. Order of Operations There is an order of operations for solving problems with more than one operation. The order of operations follows PEMDAS from left to right: Parenthesis, Exponents, Multiplication and Division, Addition and Subtraction. Solve problems with more than one operation. o Such as: (43-32) (5+3) = Read and write expressions that use parentheses to indicate order of multiple operations. Essential Vocabulary: Array, Skip Counting, Perfect Square, Square Root, Square Root Sign ( ), Multiply, Factor, Product, Divide, Dividend, Divisor, Quotient, Even, Odd, Regroup, Order of Operations, PEMDAS, Multiple, Fact Family, Associative, Commutative, Distributive, Partial Products. Interim 2 Unit 2 Page 9
Pacing Chart Unit 2: Multiplication & Division & Real World Problems Time Frame Topic Suggested Activities/Assessments Resources & Text Alignment Week 11 Week 12 Week 11 Week 12 Week 13 Week 14 Week 15 Week 15 Multiplication & Division Properties of Multiplication Projects, websites, etc. Text sections: 6.2 to 6.5, 7.1 to 7.3, 6.6 to 6.7, 8.1 to 8.5 Teacher created, websites, etc. Text section: 6.1 Multiplication & Division in the Real World Text sections: 9.1 to 9.4 Square & Square Roots Expanded Form Week 16 PEMDAS Week 17 Winter Break 2015-2016 Week 18 Review Week 19 Interim 2 Unit 2 Page 10
Overview Strand(s): Algebra, Numbers & Operations Unit 3: Input-Output, Number Sentences & Fractions Approximate Duration of Study: 8 Weeks of Instruction MNSS Knowledge Skills Fluency Addition increases a value, subtraction decreases a value There is a relationship between addition and subtraction facts. Demonstrate fluency with basic addition facts and related subtraction facts. Multiplication is repeated addition. Demonstrate fluency with basic multiplication facts. Division is repeated subtraction. Demonstrate fluency with basic division facts. Input & Output Rules 3.2.1.1 Variables 3.2.2.1 Unknown Values 3.2.2.2 A repeated rule can be used to produce a set of numbers that follow a pattern. o Rule: times 3 x y 2 6 3 9 Letters (variables) can represent unknown values in a number sentence. Basic multiplication and division facts can be used to solve for the unknown. Identify and apply the rule in an input-output table to continue the pattern or solve for missing values. Create an input-output table using a given rule. Use a variable to represent the unknown value in a number sentence based on real world situation. o The number sentence 8 m = 24 could be represented by the question How much did each ticket to a play cost if 8 tickets totaled $24? Find unknown values in multiplication or division equations. o In the form of x 9 = 63; 81 = 9. Unit 3 Page 11
Fractions: Numerator and Denominator 3.1.3.1 Fractions: Representation & Measurement 3.1.3.2 Fractions: Relativity 3.1.3.3 Fractions: Ordering & Comparing 3.3.2.1 Data Analysis 3.4.1.1 Fractions can be represented by words and symbols. Fractions represent a part of a whole. The numerator represents the part (top of fraction) and the denominator represents the whole (bottom of fraction). Fractions are used to represent: o Parts of a whole o Parts of a set o Points on a number line o Distances on a number line The size of a fractional part is relative to the size of a whole. In unit fractions, the larger the denominator, the smaller the value. In fractions with like denominators, the larger the numerator, the larger the value. Data can be represented by: o Frequency table o Bar Graph o Picture Graph o Number Line Plot o Line Graph Scale measures quantity. o The scale is marked on the x- or y-axis. Unit 3 Recognize, read and write fractions up to 1 10. o Parts of a shape ( 3 of a pie) 4 o Parts of a set ( 3 out of 4 people) o Measurements ( 3 of an inch) 4 Recognize fractions whose denominators is 100. Recognize equivalent fractions. 1 o 2 = 3 6 Create equivalent fractions Simplify fractions.. Know and write decimal equivalents to 1, 1, 3. 4 2 4 Measure distances to the nearest half-unit. Explain that the size of a fraction depends on the size of the whole. (Choose which fraction represents the smaller/larger amount even though the fractions may be the same.) o One-half of a small pizza is smaller than one-half of a large pizza, but both represent one-half. Order and compare unit fractions and fractions with like denominators using the signs <, > and =. Collect data. Display and interpret data Create and interpret bar graphs and line graphs. Page 12
Lines 3.3.1.1 Angles The scale of a graph determines how it is read. o On a bar graph, each line or space may represent more than one unit. Appropriate title, labels and units must be used. Lines are used to describe and create geometric shapes. An angle is a shape, formed by two lines or rays. : angle symbol. Identify horizontal, vertical, parallel and perpendicular lines. Name lines and line segments. o Line AB, segment CD. Identify angles by letter names. o ABC. Identify a right angle. Identify acute, obtuse, and straight angles. Essential Vocabulary: Input, Output, Rule, Input-Output Table, Variable, Number Sentence, Equation, Part, Whole, Fraction, Numerator, Denominator, Equivalent, Set, Point, Distance, Unit, Unit Fraction, Data, Frequency Table, Bar Graph, Vertical Axis, Horizontal Axis, Picture Graph, Number Line Plot, Line Graph, Scale, Lines, Horizontal, Vertical, Parallel, Perpendicular, Intersect, Line Segments, Angle Symbol, Right Angle, Acute, Obtuse, Straight. Interim 3 Unit 3 Page 13
Pacing Chart Unit 3: Input-Output, Number Sentences & Fractions Time Frame Topic Suggested Activities/Assessments Resources & Text Alignment Week 20 Input & Output Rules Projects, websites, etc. Input & Output Rules Week 21 Variables Variables Week 21 Finding Unknown Values Unknown values millionaire: http://www.math4children.com/grade3/games/classroomgames/bravo-games/equations%20and%20variables/ Finding Unknown Values Week 22 Week 24 Fractions: Numerator and Denominator Fractions: Numerator and Denominator Week 22 Week 24 Fractions: Representation & Measurement Fractions: Representation & Measurement Week 22 Week 24 Fractions: Relativity Fractions: Relativity Week 22 Week 24 Fractions: Ordering & Comparing Fractions: Ordering & Comparing Week 25 Data Analysis Data Analysis Week 26 Lines & Angles Lines & Angles Week 27 Review Weeks 28 Interim 3 Unit 3 Page 14
Overview Strand(s): Geometry & Measurement, Data Analysis Unit 4: Time, Temperature, Data Analysis & Geometry Approximate Duration of Study: 8 Weeks of Instruction MNSS Knowledge Skills Fluency Addition increases a value, subtraction decreases a value Demonstrate fluency with basic addition facts and related subtraction There is a relationship between addition and subtraction facts. facts. Use mental computation strategies to add and subtract. Multiplication is repeated addition. Demonstrate fluency with basic multiplication facts. Division is repeated addition. Demonstrate fluency with basic division facts. Polygons 3.3.1.2 Perimeter 3.3.2.2 3.3.2.3 Linear Measurement Probability Polygons are closed shapes using straight lines. Polygon is classified by number of sides and vertices. There are four right angles in a square or rectangle. The distance around an object is the perimeter. There is a relationship between length and the numbers on a ruler. Know that one foot = 12 inches; one yard = 36 inches; 3 feet = 1 yard; 1 meter = 100 centimeters, 1 meter is a little more than one yard. A simple event has a single outcome (result). Unit 4 Create geometric shapes. Recognize vertex (plural: vertices). Identify sides as line segments. o Side CD. Identify pentagon, hexagon, and octagon (regular). Find the perimeter of different objects by adding the given values for the sides or measuring. Make linear measurements in yards, feet, and inches; and, in centimeters and meters. Measure and draw line segments in inches (to 1 inch), and in 4 centimeters. Write mixed numbers. Estimate linear measurements, then measure to check estimates. Record outcomes for a simple event. Display results graphically. Page 15
Weight Capacity Solid Figures Weight indicates how heavy an object is. Weight is measured using a scale. Weight can be measured in pounds and ounces; grams and kilograms. There are abbreviations for the units of weight. o Pound: lb.; Ounce: oz. o Gram: g.; Kilogram: kg. Capacity (volume) indicates how much a container can hold. Liquid capacity is measured in cups, pints, quarts, gallons, and liters. Liters is a metric unit; cups, pints, quarts, and gallons are U.S. units. There are relationships between gallons, quarts, pints, and cups. o 1 quart = 2 pints; 1 gallon = 4 quarts. o 1 liter is a little more than 1 quart. Lines and faces are used to describe and create threedimensional geometric shapes. Three-dimensional figures can be classified by the number of sides, vertices, faces and edges. Compare weights of objects using a balance scale. Estimate and measure weight in pounds and ounces; grams and kilograms. Use abbreviations: lb., oz., g, kg. Estimate and measure capacity in cups, pints, quarts, gallons, and liters. Compare U.S. and metric liquid volumes: quart and liter. Convert between equivalent measures that have different units. o 4 quarts = 1 gallon; 1 quart = 2 pints. Identify solid figures. o Sphere, cube, rectangular solid (prism), pyramid, cone, and cylinder. Congruency and Symmetry Congruent shapes are exactly (identical) the same in shape and size. Lines of symmetry divide a shape into congruent parts. Recognize and draw congruent figures. Identify a line of symmetry. Create symmetric figures. Essential Vocabulary: Polygon, Quadrilateral, Vertex, Regular, Rectangle, Right Triangle, Parallelogram, Trapezoid, Square, Rhombus, Pentagon, Heptagon, Hexagon, Octagon, Nonagon, Decagon, Perimeter, Face, Three-Dimension, Vertex, Edge, Sphere, Cube, Rectangular Solid (Prism) Pyramid, Cone, Cylinder, Congruent, Symmetric, Line of Symmetry, Length, Ruler, Foot, Inch, Yard, Meter, Centimeter, Mixed Number, Simple Event, Outcome (Result), Weight, Pound, Ounce, Gram, Kilogram, Capacity (Volume), Cup, Pint, Quart, Gallon, Liter, Metric Unit, U.S. Unit. Interim 4 Unit 4 Page 16
Pacing Chart Unit 4: Time, Temperature, Data Analysis & Geometry Time Frame Topic Suggested Activities/Assessments Resources & Text Alignment Week 29 Polygons 3.3.1.2 Text Section: 18.1 Perimeter Week 29 3.3.2.2 3.3.2.3 Text Sections: 19.4, 19.5 Week 30 Linear Measurement Week 31 Probability Week 32 Week 33 Weight Capacity Week 34 Solid Figures Week 35 Congruency and Symmetry Ordinal Numbers Activities: http://busyteacher.org/classroom_activitiesgrammar/numerals_and_dates/ordinal_numbersworksheets/ See Grade 2 Mathematics Resources (s:drive) Week 36 Review Week 37 Interim 4 Unit 4 Page 17