A mathematics resource for parents, teachers, and students

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1 Help your child search the newspaper (or go to for daily temperatures and create a graph showing weekly trends. Look at the temperatures for morning, noon, and night. Ask your child to fi nd the difference between the highest and lowest temperature for the day. Copy a license plate number as you are traveling or watching cars go by. Ask your child to read the license plate as a number (excluding the letters). For example, if the license were 62ab315, the number would be sixty-two thousand three hundred fi fteen. Find other license plates and let your child read their numbers. Is the new number less than, greater than, or equal to your fi rst license plate? Ask your child to estimate the difference between your fi rst number and another license plate. Is it about 10, 100, 1,000, or 10,000 more or less? Find the license plate with the greatest and smallest number on it. Play the game What s the Difference? The object is to make the smallest difference (answer in a subtraction problem). You will need at least two players and playing cards (Ace =1) through 10 (10=0). Place the deck face down. A player draws a card from the deck and places it face up. Each player selects a space on his game board and writes the number of the card on that space. Game boards can be drawn on paper as shown below: Players draw fi ve more cards to fi ll in their game cards. As shown below: Player 1 Player Players complete the subtraction. The player with the smallest difference is the winner for the round and scores 1 point. In the event of a tie, each player receives 1 point. Any negative difference causes that player to strike out for that round. The winner of the game is the player with the most points after a set number of rounds or a set time limit. Addition and Subtraction of Whole Numbers Third Grade 1 of 6 Use mental math to add and subtract Use estimation to determine reasonableness of sums and differences Read, interpret, solve, and compose simple word problems dealing with addition and subtraction Use inverses to verify accuracy of computation Write and simplify expressions using symbols in place of numbers Represent, read, and name numbers from tenths to ten-thousands place 1. Kim, Bud, and Sam each have a herd of cows. Kim has two black cows, four brown cows, and three red cows. Bud has three black cows, one brown cow, and four red cows. Sam has five black cows, three brown cows, and two red cows. How many cows does each person have? How many cows in all? Are the herds equal in size? How can we make them? Explain your thinking using words, numbers, or pictures. Kim has 9 cows, Bud has 8 cows, and Sam has 10 cows; there are 27 cows in all. The herds are not equal in size. If Sam would give Bud a cow, the herds would be equal. 2. Suppose you found an old roll of 15 cent stamps and a roll of 33 cent stamps. Can you use a combination of 15 cent stamps and 33 cent stamps to mail a package for exactly $1.77? If you use (4) 33 cent stamps and (3) 15-cent stamps, you can mail the package for exactly $1.77 because $ =$1.77. Addend: a number being added. In = 14, 5 and 9 are addends and 14 is the sum. Associative Property of Addition: when there are three addends, the sum does not change regardless of which two numbers you group together first. As in: = (3 + 5) + 2 = 3 + (5 + 2) = 10; = = 10 Commutative Property of Addition: the order in which two numbers are added does not change the sum. As in: = 16 and = 16 Difference: the answer obtained when you subtract two numbers Doubling: adding the same amount twice; or two times a number Identity Property of Addition: when zero is added to any number, the sum is the original amount. Or, adding zero to any number does not change the number. Inverses: operations that undo each other, such as addition and subtraction as well as multiplication and division. Minuend: the number you subtract from. As in: = 155; 522 is the minuend. Operations: addition, subtraction, multiplication, and division Subtrahend: The number being subtracted. As in: = 155; 367 is the subtrahend. Sum: the answer obtained when you add two numbers; total number of elements in the sets that were combined 12 Ways to Get to 11 by Eve Merriam Domino Addition by Lynnette Long Ten Sly Piranhas by William Wise Mission Addition by Loreen Leedy Elevator Magic by Stuart J. Murphy

2 Break My Eggs. This game can be played with two or more players. Write numbers (0-10) in the holes on the bottom of an empty egg carton. Label one hole BONUS for 10 extra points. Put two manipulatives (marbles, dried beans, etc.) in the egg carton. Close the lid and let your child shake the carton. Using the numbers on which the manipulatives landed, the player multiplies. The answer is the points earned for that turn. If one or both of the manipulatives land on the hole labeled BONUS, add 10 points to the score and shake again. Keep a total of points. Players may play as teams or keep score individually. A Fair Share. Give your child the responsibility of sharing a box of markers, a bag of candy, or a package of baseball cards equally among two, three, or four family members or friends. Remember that it won t always work out equally and it is okay to have remainders. Factors: Two or more whole numbers multiplied together to get a given number called the product. Product: The result of multiplication. Array: The arrangement of objects in equal rows. Example: 2 6 Quotient: The result of division. Dividend: Number being divided; total amount being divided into groups. Ex. 24 8=3; 24 is the dividend, 8 is the divisor, and 3 is the quotient. Divisor: Number dividing into the total; may be the number of groups or the number of items in a specifi c number of groups. Remainder: Amount left over after dividing a number. Equal: Having the same value. Commutative Properties: In addition and multiplication, numbers may be added or multiplied together in any order. Associative Properties: In addition and multiplication, no matter how the numbers are grouped, the answers will always be the same. Identity Properties: When a number is added to zero, the result is the number itself, and when a number is multiplied by one, the result is the number itself. Multiplication and Division of Whole Numbers Third Grade 2 of 6 Use mental math to multiply and divide Demonstrate fl uency with the multiplication facts up to 10 X 10 Use estimation to determine reasonableness of products and quotients Read, interpret, solve, and compose simple word problems dealing with multiplication and division Use inverses to verify accuracy of computation Write and solve expressions using symbols in place of numbers Represent numbers from tenths to ten-thousands place and accurately read and express in written and oral forms Demonstrate understanding of the relative sizes of digits in a number 1. Tyler and Hailey are playing a game called Chance. They get three points every time they draw a blue card and five points every time they draw a red card. Whoever gets 75 points first wins the game. Tyler has 41 points now, and he has 9 cards. How many cards does he have of each color? Explain your thinking using words, numbers, or pictures. I thought of multiples of 3 and multiples of 5 and added them together to try to get 41. 3: 3, 6, 9, 12, 15, 18, 21 5: 5, 10, 15, 20, 25, 30, 35, 40, 45 Tyler could have two blue cards and seven red cards because 2 3=6, 7 5=35, and 6+35 =41 points, and 2+7= 9 cards. 2. There are 24 slices of pizza. How many slices would each person get if there were: Three people? Four people? Six people? Eight people? Twelve people? Three people would each get 8 slices; four people would each get 6 slices; six people would each get 4 slices; eight people would each get 3 slices; twelve people would each get 2 slices. 3. There are 18 people coming for dinner. How can we set up tables to seat everyone? No one will sit at the head or the foot of the tables. Draw rectangles to represent the tables and mark to show where someone will sit. Multiplication is repeated addition. For example, if three book bags contains two books each, then we know that = 6 is the same as 3 x 2 = 6. Division is counting things out and then putting them into equal groups. For example, if we have eight books and two book bags, how many books can we put into each bag equally? (8 divided by 2 = 4) The Hershey s Milk Chocolate Multiplication Book by Jerry Pallotta The Doorbell Rang by Pat Hutchins Amanda Bean s Amazing Dream by Cindy Neuschwander One Hundred Hungry Ants by Elinor Pinczes 2X2=Boo! A Set of Spooky Multiplication Stories by Loreen Leedy Best of Times by Greg Tang

3 Encourage your child to estimate and measure distances and objects at home. Ask questions such as, How far is it across the kitchen table? Involve your child in your own measuring activities and hobbies like sewing or carpentry are natural for this. Create a chart of activities that you do at night (such as dinner, homework time, and TV time. Discuss the length of time each activity takes). Cut apart cereal and other boxes to see the different shapes that make up the solid fi gures. Centimeter: A metric unit of length; 1 meter = 100 centimeters. Equilateral triangle: A triangle with three equal sides and three equal angles. Foot: A customary unit of length 1 foot = 12 inches Hexagon: A polygon with six sides. Isosceles triangle: A triangle with two equal sides and two equal angles. Kilometer: A unit of measurement for length in the metric system; 1 km = 1000 meters Meter: The standard unit of length in the metric system. Millimeter: A metric unit of length; 1 meter = 1000 millimeters Parallelogram: A quadrilateral with opposite sides that are parallel and of equal length and with opposite angles that are of equal measure. Plane figure: A two-dimensional shape such as a rectangle or a square. Polygon: A closed plane figure made with three or more sides and angles. Quadrilateral: A four-sided polygon. Rectangle: A quadrilateral with four right angles and two pairs of opposite, equal parallel sides. Rhombus: A parallelogram with four equal sides and equal opposite angles. Scalene triangle: A triangle with all 3 sides having different lengths. Solid figure: A three-dimensional object such as a cube or a cylinder. Square: A quadrilateral with four equal sides, four right angles, and opposite sides parallel. Triangle: A polygon with three sides. Trapezoid: A quadrilateral with one pair of parallel sides. Yard: A unit of measurement in the U.S.A. (Customary) system; 3 feet = 1 yard Geometry and Measurement Third Grade 3 of 6 Identify and describe plane fi gures and solid fi gures based on geometric properties Develop an understanding of the inner-relatedness of solid and plane fi gures Investigate the outcomes when geometric fi gures are combined and cut apart Expand the ability to see geometry in the real world Further develop their understanding of the concept of time by determining elapsed time (to an hour, half, and quarter-hour) Continue to develop their abilities to recognize the appropriate unit of length needed to measure a specifi ed item Compare the relationship of one unit to another within a single system of measurement Check by measuring to determine if estimates are accurate for length and temperature Determine a tool that is appropriate for measuring length Recognize benchmarks for commonly-used units of measure 1. Sort shapes into groups by attributes. Identify the shape and describe it. C A B D E A, B, and D are all quadrilaterals. A is a trapezoid, B is a square or rhombus, and D is a parallelogram. C and E are both triangles. E is a scalene triangle with one right angle and C is an equilateral triangle because all the sides are the same length. Measuring seems simple, but for elementary students it can pose a real challenge. Even though students can do measurement worksheets and manipulate measurement data on paper, they may not have had much experience using rulers and other measuring tools. Sometimes students need help: To line up the ruler so that the end of the object is at zero. To measure from the zero end of a ruler. To use appropriate units and not combine metric and U.S.A. customary units. To use tools appropriate for the task: yardstick, meter sticks, rulers, and tape measures. A vital part of your child s learning is the opportunity to discuss reasonableness of measurements, to measure several times, and to correct measuring mistakes. Encourage your child to use pictures to represent measurement conversion. For example, 3 feet =? inches 1 foot 1 foot 1 foot 12 inches 12 inches 12 inches 12 in in in. = 36 inches Three Pigs, One Wolf and Seven Magic Shapes by Grace Maccarone Grandfather Tang s Story by Anne Tompert The Fattest, Tallest, Biggest Snowman Ever by Bettina Ling The Measuring Penny by Loreen Leedy The Greedy Triangle by Marilyn Burns

4 When your family is sharing food, talk about fair shares and help your child name fractions. If you want to split a pizza among fi ve people, how can you split it fairly? How much does each person get? Cooking is a great way to learn about fractions. How can we measure ¾ cup? Show your child how the fractions appear on a measuring cup. Ask your child to help you double recipes, or cut recipes in half. Try to notice ads and articles with headlines like three out of four doctors prefer Brand X pain reliever or 1/2 of all Americans don t get enough sleep. Talk to your child about these ads. What does three out of four mean? Look for decimal fractions in the news. Dimes represent 1/10 or 0.1 of a dollar. Common fraction: A number used to name a part of a group or a whole containing a fraction bar, a numerator, and a denominator. Decimal fraction: A fraction written as a decimal. Denominator:The bottom number of a fraction that represents the number of equal parts a whole or set has been divided into. Equivalent sets: Collections containing the same number of objects. Fractions and Decimals Third Grade 4 of 6 Recognize that the numerator is the top number of a fraction and that it represents the number of a set or whole Recognize that the denominator is the bottom number of a fraction and that it represents the total objects of the set or the total parts of the whole Explain the concept that the larger the denominator, the smaller the size of the piece Compare simple fractions and tell why one is greater than, less than, or equal to the other Represent halves, thirds, fourths, sixths, eighths, and tenths using various fraction models 1. Use drawings to represent 2/6 + 1/6. 1/6 1/6 1/6 2/6 + 1/6 = 3/6 2. You toss 10 balls in a game at the fair and you only get 3 in the bucket. Draw a representation of your score and write your score as a fraction and a decimal fraction. Fraction: 3/10 Decimal: If you cut a pie into different size pieces with the denominator increasing (such as halves, fourths, eighths, and tenths), what happens to the pieces of pie? Draw pictures to represent your answer. Numerator: The top number in a common fraction representing the number of equal parts of a whole or group under consideration. Unit fraction: Any common fraction with a numerator of one. Eating Fractions by Bruce McMillian The Doorbell Rang by Pat Hutchins The Half Birthday Party by Charlotte Pomerantz A decimal fraction is just another name for a decimal number. Your child needs to understand the relationship between fractions and division. She should be exposed to the different notations for the same problem (for example, 6 2 = ½ of 6 = 6/2). Students get confused when asked if one half always equals a half. Show different ways that a half can be represented, such as half of a large pizza and half of a small pizza. The whole determines what the half represents.

5 As you are reading the newspaper or a magazine, point out various graphs and charts to your child and talk about how you make sense of them, what they mean, and why you re interested in them. This is an opportunity for you to show your child how graphs communicate important information to you and your family. You will find that there are many opportunities to collect data around your home. Which color or make of car is the most common on your street? Do more households in your neighborhood have a dog or a cat? After a while, collecting and thinking about data may become a habit that you and your child share. Collect the data and present in a table and then a bar graph. M&M Math: Open a small bag of M&M s. Create a table of M&M colors. Write the number of each color next to the word. Create a bar graph that shows the number of M&Ms of each color. Create a scale based on different intervals such as 2, 5, or 10. Ask your child questions that can be answered from the bar graph. Bar graph: a way of displaying data using horizontal or vertical bars so that the height or length of the bar indicates its value Scale: the numbers along the axes on a graph. The numbers are arranged in equal intervals. Interval: a regular distance or space between values Lemonade for Sale by Stuart J. Murphy Graph It! by Lisa Trumbauer Tiger Math by Ann Whitehead Nagda Graphs by Sara Pistoia Graphing Activities by Joy Evans Graphs by Bonnie Bader Students have worked with pictographs, Venn Diagrams, and bar graphs in previous grade levels. The scale increments on the bar graphs for third grade are 1, 2, 5, and 10. Using different increments is a new idea for third grade. Data Analysis Third Grade 5 of 6 Collect, organize, and display data in tables and bar graphs Construct bar graphs using a variety of scales (increments of 1,2,5, and 10) Interpret data in bar graphs Solve problems by organizing and displaying data 1. Find out what kind of shoes students have in the class. The choices are tennis shoes, boots, sandals, other. Make a table and bar graph to display this information Tennis Boots Sandals Other Shoes Number of Students time in seconds pear banana peach apple Type of Fruit Abby Blanca Chris Dana Evan Cousins Types of Shoes Other Sandals Boots Tennis shoes Students' Shoes Number of Students 2. Answer the following questions using the bar graph below. a. How many more students like apples than pears? b. Which fruit should be served more often in the school cafeteria and why? Favorite Fruit a = 35 students b. Apples they are the most popular fruit. 3. Uncle Bob asked his nephews and nieces who could Cousin Prediction Measurement whistle the longest on one breath. Each cousin predicted his time, Abby 15 sec 12 sec and then Uncle Bob actually Blanca 10 sec 12 sec measured their whistle times. The results are in the table. Make a Chris 20 sec 16 sec double bar graph and use it to Dana 5 sec 10 sec answer the questions: Who had the longest Evan 15 sec 12 sec whistle? Who was closest to his own prediction? Prediction Whistle Times Measurement 25 Chris has the longest 20 whistle time; his bar is the tallest. 15 Blanca made the 10 closest prediction; her bars are the closest in 5 height.

6 Provide your child with opportunities to count by 10s, 20s, 50s, and 100s. Look for patterns in nature and your environment, such as, If one chair has 4 legs, how many legs do 5 similar chairs have? Discuss how symbols are used to represent relationships among quantities. For example, discuss the relationships in the number sentences below to determine the missing numbers. 2+3= 3 Answer: =15 + = 16 Answer: = 8 Invite your child to play number of the day. Choose a number that you will call the number of the day. The fi rst time you do this activity, choose a number under 15. Ask your child to think up different ways to make the number of the day using equations. Example: Let s come up with different ways to make 11. Here s one way: = 11. Can you fi nd a different way? Sum: the total or whole amount as a result of adding; the answer in an addition problem Addends: the numbers being added together to get the sum Difference: the number that is the result of subtracting one number from another; the answer to a subtraction problem Product: a number that is the result of multiplying two or more numbers together; the answer to a multiplication problem ALGEBRA: The Study of Patterns Third Grade 6 of 6 Apply patterns and rules to describe relationships and solve patterns Represent unknowns using symbols such as and Write and evaluate mathematical expressions using symbols and different values 1. Look at the pattern. 100, 97, 94,,, Continue the pattern. Use words and numbers to explain the rule. 91, 88, 85 Rule: Subtract 3 to get the next number in the pattern. 2. Find the missing numbers in the function. Explain how you know. Input Output ?? 56 Input Output I noticed that 7 x 7 =49 and 7 x 3 = 21 and 7 x 10 =70. So I decided that 7 x input = output. Then I multiplied 7 x 5 to get 35 and worked backwards to get 8 by dividing: How many oranges (on right side) equal one melon? If we put one more melon on the left side, the scales will be balanced. Use words and numbers to explain. Multiple: the product of a given whole number and an integer or the result of repeated addition. For example, multiples of 3 are: 3,6,9,12,15, etc. Factors: a whole number that divides exactly into another number, or whole numbers that can be multiplied together to make a third number. To factor means to write the number as a product of its factors. For example: 4 and 5 are factors of 20. Pattern: a set of numbers or objects that are generated by following a specifi c rule. Patterns can be numerical or geometric. 2 oranges = 1 melon because if I have 3 melons and 6 oranges, then it would take 2 oranges to equal one melon (3 x 2 = 6). The word algebra is often associated with content in middle and high school and can cause a feeling of anxiety. When children are exposed to algebraic thinking in elementary school, they can learn the foundations for algebraic thinking and enjoy success in later grades. Algebraic thinking includes understanding patterns and relationships, analyzing situations and change, and using models to represent relationships. Students in grades pre-k 5 enjoy studying patterns and fi guring out how they work, whether the patterns are geometric or numeric, repeating or growing. So have fun with patterns which are everywhere! One Hundred Hungry Ants by Elinor Pinczes The Doorbell Rang by Pat Hutchins Anno s Magic Seeds by Mitsumasa Anno The Rajah s Rice by David Barry The King s Chessboard by David Birch