Cologne Academy. Mathematics Department Grade 3 Math. (Aligned Text: Math in Focus Singapore Math Common Core Ed.)

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1 Cologne Academy Mathematics Department Grade 3 Math (Aligned Text: Math in Focus Singapore Math Common Core Ed.) Curriculum 100% Aligned Adopted: 08/2014 Board Approved: 07/24/2014 Updated: 08/26/2016 Page 0

2 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, Essential Vocabulary... 5 Pacing Chart... 6 Unit 2 Overview: Multiplication & Division & Real World Problems... 7 Essential Vocabulary... 9 Pacing Chart Unit 3 Overview: Input-Output, Number Sentences & Fractions Essential Vocabulary Pacing Chart Unit 4 Overview: Time, Temperature, Data Analysis & Geometry Essential Vocabulary Pacing Chart Highlighted items indicate overlap of MN State Standards and the Sequence. Boxed items indicate content to be introduced post-mcas. Page 1

3 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 or on the Cologne Academy intranet. Further research/exploration may be required to locate additional resources. Page 2

4 Overview Strand(s): Numbers & Operations, Geometry & Measurement Unit 1: Ordering & Comparing, Rounding, and Adding & Subtracting Numbers to 100,000 Approximate Duration of Study: 7 FULL Weeks of Instruction MNSS Knowledge Skills Fluency Core Knowledge Number to 100, 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. 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. Place Value Rounding, Estimating and Comparing 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, = 4,327 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) 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. 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. Unit 1 Page 3

5 Place Value: Add & Subtract 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.). Add and subtract multi-digit numbers using place value as a guide. Add and subtract with and without regrouping up to 10, Addition and subtraction are inverse (opposite) operations. Use addition to check subtraction and vice versa. Addition & Subtract in the Real World Multiplication Addition and subtraction of whole numbers can be applied to real-world situations. Multiple strategies can be applied to assess the reasonableness of results. 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 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 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. Mentally multiply by 10, 100, and 1,000. Estimate a product. 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. Page 4 Unit 1

6 Properties of Multiplication 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 = x 2 = 80 5 x 2 = 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.) Multiplication in the Real World Multiplication can be applied to real-world situations. 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? Essential Vocabulary: Value, Dozen, Half-Dozen, Pair, Digit, Place Value, Ten Thousands, Thousands, Hundreds, Tens, Ones, Expanded Form, Estimate, Rounding, About, Sum, Difference, Number Line, Greater Than (>), Less Than (<), Equal To (=), Inverse Operations, Product, Multiple, Array, Skip Counting, Even, Odd, Commutative, Associative, Distributive, Partial Products, Regrouping, Fact Family. Interim 1 Unit 1 Page 5

7 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 Number 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 Week 8 Week 8 Multiplication Properties of Multiplication Multiplication in the Real World 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 Text sections: 9.1 to 9.4 Week 9 Review Week 10 Interim 1 Unit 1 Page 6

8 Overview Strand(s): Numbers & Operations, Geometry & Measurement Unit 2: Multiplication & Division & Real World Problems Approximate Duration of Study: 8 FULL 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. Division 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. Division in the Real World Division can be applied to real-world situations. 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? Unit 2 Page 7

9 Input & Output Rules Variables Unknown Values A repeated rule can be used to produce a set of numbers that follow a pattern. o Rule: times 3 x y 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. Fractions: Numerator and Denominator Fractions: Representation & Measurement 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). A mixed number consists of a whole part and fractional part. An improper fraction is a fraction whose numerator is greater than the denominator. A mixed number can be converted to an improper fraction and vice versa. 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 Unit 2 Recognize, read and write fractions up to 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 = Know and write decimal equivalents to 1, 1, Measure distances to the nearest half-unit. Page 8

10 Fractions: Relativity Fractions: Ordering & Comparing Decimals Money: Making Change Data Analysis 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. Decimals represent parts of whole numbers. A value less than 1 is represented by using a decimal. 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. Data can be represented by: o Frequency table o Bar Graph o Picture Graph o Number Line Plot Scale measures quantity. o The scale is marked on the x- or y-axis. 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. 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 =. Read and write decimals to the hundredths. o Make change, up to one dollar, using as few coins as possible and in more than one way. o Write amounts of money using $ and signs, and the decimal point. o Add and subtract amounts of money. o Multiply and divide amounts of money by small whole numbers. Collect data. Display and interpret data Create and interpret bar graphs. Measuring Time 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. 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). Unit 2 Page 9

11 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. Essential Vocabulary: Divide, Dividend, Divisor, Quotient, Fact Family, Rule, Input, Output, Input-Output Table, Table of Values, Pattern, Variables, Number Sentence, Equation, Part, Whole, Numerator, Denominator, Fraction, Unit Fractions, Mixed Number, Improper Fraction, Equivalent, Set, Point, Distance, Unit, Decimal, Hundredth, Coin, Change (in relation to money), Data, Frequency Table, Bar Graph, Picture Graph, Number Line Plot, Vertical Axis, Horizontal Axis, Scale, Digital, Analog, Hours, Minutes, Seconds, Linearly, Duration, Calendar, Elapsed Time, A.M., P.M., Date, Day, Week, Month, Year. Interim 2 Unit 2 Page 10

12 Pacing Chart Unit 2: Multiplication & Division & Real World Problems Time Frame Topic Suggested Activities/Assessments Resources & Text Alignment Week 11 Week 13 Week 11 Week 13 Division Division in the Real World 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 sections: 9.1 to 9.4 Week 14 Week 14 Input & Output Rules Variables Projects, websites, etc. NEED RESOURCES Teacher created, websites, etc. NEED RESOURCES Week 14 Finding Unknown Values Unknown values millionaire: NEED RESOURCES Week 15 Fractions: Numerator and Denominator Text Section: 14.1 Week 15 Fractions: Representation & Measurement Text Section: 14.4, 14.6, 15.1 Week 16 Week 16 Fractions: Relativity Fractions: Ordering & Comparing NEED RESOURCES Text Section: Text Section: 14.4 Week 17 Decimals Week 18 Winter Break Page 11

13 Week 19 Week 17 Week 21 Money: Making Change Data Analysis Need resource Text Sections: 13.1 to 13.3 Week 22 Interim 2 Unit 2 Page 12

14 Overview Strand(s): Algebra, Numbers & Operations Unit 3: Input-Output, Number Sentences & Fractions Approximate Duration of Study: 7 FULL 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. Converting Time 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 Temperature can be measured in Fahrenheit and Celsius. O : degree sign. 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. Lines Angles Polygons Lines are used to describe and create geometric shapes. An angle is a shape, formed by two lines or rays. : angle symbol. 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. Unit 3 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. Create geometric shapes. Recognize vertex (plural: vertices). Identify sides as line segments. o Side CD. Identify pentagon, hexagon, and octagon (regular). Page 13

15 Perimeter Squares and Square Roots The distance around an object is the perimeter. Find the perimeter of different objects by adding the given values for the sides or measuring. Identify perfect squares and square roots to 100. The product of a number multiplied by itself is called a perfect square. Recognize the square root sign: Calculating the square root of a number results in the original number used to find a perfect square. Essential Vocabulary: Temperature, Fahrenheit, Celsius, O Degree Symbol, Thermometer, Freezing Point, Line, Vertical, Horizontal, Diagonal, Parallel, Perpendicular, Intersect, Line Segments, Ray, Angle Symbol, Right Angle, Polygon, Regular Polygon, Quadrilateral, Rectangle, Right Triangle, Parallelogram, Trapezoid, Square, Rhombus, Heptagon, Nonagon, Decagon, Vertex, Pentagon, Hexagon, Octagon, Perimeter, Perfect Square, Square Root, Square Root Sign ( ). Interim 3 Unit 3 Page 14

16 Pacing Chart Unit 3: Input-Output, Number Sentences & Fractions Time Frame Topic Suggested Activities/Assessments Resources & Text Alignment Text Sections: 16.1, 16.3 to 16.5 Week 23 Week 24 Measuring Time Converting Time Week 23 Week 24 Text Section: 16.2 Week 23 Week 24 Temperature Text Sections: 16.6, 16.7 Week 25 Lines & Angles Text Sections: 17.3, 17.4 Week 26 Week 27 Week 28 Week 28 Week 29 Polygons Perimeter Square & Square Roots Review Weeks 30 Interim 3 Text Section: 18.1 Text Sections: 19.4, 19.5 Unit 3 Page 15

17 Overview Strand(s): Geometry & Measurement, Data Analysis Unit 4: Time, Temperature, Data Analysis & Geometry Approximate Duration of Study: 5 FULL 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. Linear Measurement Weight 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. 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. 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. 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. Unit 4 Page 16

18 Capacity Probability 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. A simple event has a single outcome (result). 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. Record outcomes for a simple event. Display results graphically. Congruency and Symmetry Solid Figures Congruent shapes are exactly (identical) the same in shape and size. Lines of symmetry divide a shape into congruent parts. 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. Recognize and draw congruent figures. Identify a line of symmetry. Create symmetric figures. Identify solid figures. o Sphere, cube, rectangular solid (prism), pyramid, cone, and cylinder. Number Line & Ordinal Position There is a name for numerical positions. o Identify ordinal positions, 1 st to 100 th. Locate positive and negative whole numbers on a number line. Roman Numerals 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 Identify Roman numerals from 1 to 20 (I - XX). Unit 4 Page 17

19 Division Division is repeated subtraction. Divide two- and three-digit dividends by one-digit divisors. Solve division problems with remainders. Check division by multiplying (and adding remainder). Order of Operations There is an order of operations for solving problems with more than one operation. The order of operations follows GEMDAS 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: Face, Three-Dimension, Vertex, Edge, Sphere, Cube, Rectangular Solid (Prism) Pyramid, Cone, Cylinder, Congruent, Symmetric, Line of Symmetry, Three-Dimensional, Solid, Ordinal Position, Positive, Negative, 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, Positive, Negative, Roman Numerals: I, V, X, L, C, D, M, Decimals, Hundredths, Order of Operations, GEMDAS. Interim 4 Unit 4 Page 18

20 Pacing Chart Unit 4: Time, Temperature, Data Analysis & Geometry Time Frame Topic Suggested Activities/Assessments Resources & Text Alignment Linear Measurement Capacity Weight Week 33 Spring Break Week 34 Mathematics MCAs Number Line & Ordinal Position Roman Numerals Congruency and Symmetry Solid Figures Probability Ordinal Numbers Activities: See Grade 2 Mathematics Resources (s:drive) See Grade 4 curriculum appendix for Roman Numeral conversions. Unit 4 Page 19

21 Division GEMDAS Week 38 Interim 4 Unit 4 Page 20

Cologne Academy. Mathematics Department Grade 3H Math. (Aligned Text: Math in Focus Singapore Math Common Core Ed.)

Cologne Academy. Mathematics Department Grade 3H Math. (Aligned Text: Math in Focus Singapore Math Common Core Ed.) 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