Go to Grade 3 Everyday Mathematics Sample Lesson

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1 McGraw-Hill makes no representations or warranties as to the accuracy of any information contained in this McGraw-Hill Material, including any warranties of merchantability or fitness for a particular purpose. In no event shall McGraw-Hill have any liability to any party for special, incidental, tort, or consequential damages arising out of or in connection with the McGraw-Hill Material, even if McGraw-Hill has been advised of the possibility of such damages. Go to Grade Everyday Mathematics Sample Lesson

2 Objective To demonstrate naming quantities greater than with fractions and mixed numbers. Teaching the Lesson materials Key Activities Children model fractions greater than and equivalent mixed numbers by pasting fractional parts of a unit circle onto unit circles. They practice naming numbers of fractional parts as fractions and mixed numbers. Key Concepts and Skills Shade fractional parts of regions to represent fractions greater than. [Number and Numeration Goal ] Model and name mixed numbers and fractions. [Number and Numeration Goal ] Identify equivalent fractions. [Number and Numeration Goal ] Use lines of symmetry to divide figures into equal parts. [Geometry Goal ] Math Journal, pp. 97 and 9 Home Link 6 Teaching Aid Master (Math Masters, p. 6; one copy per children) scissors glue or paste slates crayons See Advance Preparation Key Vocabulary mixed number Ongoing Assessment: Informing Instruction See page 6. Ongoing Learning & Practice materials Children play the Equivalent Fractions Game. Children practice and maintain skills through Math Boxes and Home Link activities. Ongoing Assessment: Recognizing Student Achievement Use the Record Sheet. [Number and Numeration Goal ] Differentiation Options Math Journal, p. 99 Student Reference Book, pp. and Home Link Masters (Math Masters, pp. and 9) Fraction Cards; half-sheets of paper materials READINESS Children use pattern blocks to compare fractions of regions to one whole. ENRICHMENT Children write fractions on a number line. EXTRA PRACTICE Children play Fraction Top-It. ELL SUPPORT Children add the term mixed number to their Math Word Banks. Student Reference Book, pp. 7 and Teaching Masters (Math Masters, pp. 60 and 6) Differentiation Handbook pattern blocks; half-sheets of paper; Pattern-Block Template Fraction Cards Additional Information Advance Preparation Make enough copies of Math Masters, page 6 so each child can have one strip of circles. Cut the strips apart and place them next to the Math Message. Technology Assessment Management System Game Record Sheet See the itlg. 6 Unit Fractions Grade Everyday Mathematics Teacher's Lesson Guide 007 Wright Group/McGraw-Hill

3 Getting Started Mental Math and Reflexes Dictate pairs of decimals. Children write them on their slates and circle the larger number. Suggestions: twenty-seven hundredths; sixty-seven hundredths 0.7; 0.67 five-tenths; five-hundredths 0.; 0.0 three and six-tenths; three and sixteen-hundredths.6;.6 seventy-two hundredths; nine-tenths 0.7; 0.9 forty and eighty-three hundredths; forty-eight and three tenths 0.;. Math Message. Take a strip and cut out the circles.. How would you answer the following problems? Emily had apples. She cut one in half and ate one of the halves. How many apples were left? Then she cut each of the other whole apples in half. She gave all the halfapples to her friends. How many half-apples did she give away? Home Link 6 Follow-Up Have partners share their answers for Problems. Ask a few volunteers to share their solution strategies with the class. Teaching the Lesson Math Message Follow-Up (Math Masters, p. 6) WHOLE-CLASS ACTIVITY Illustrate the number story in the Math Message on the board. Emily had apples. She cut one in half and ate one of the halves. How many apples were left? Teaching Aid Master Name Date Time apples Fractions Greater than One Then she cut each of the other whole apples in half. She gave all of the half-apples to her friends. How many half-apples did she give away? Five halves of apples Write and on the board. Ask: Do these numbers and name equivalent amounts of apples? Yes Math Masters, p. 6 Grade Everyday Mathematics Teacher's Lesson Guide 007 Wright Group/McGraw-Hill Lesson 6

4 Date More Than ONE Time Use the circles that you cut out for the Math Message.. Glue halves into the two whole circles. halves or or one and half. Glue 6 fourths into the two whole circles. Fill in the missing digits in the question, the fraction, and the mixed number. How many fourths? 6 Write the fraction: 6 Student Page fourths Math Journal, p. 97 Write the mixed number: Naming Fractional Parts Greater Than ONE (Math Journal, p. 97; Math Masters, p. 6) WHOLE-CLASS ACTIVITY First, ask children to take two of the circles they cut out and fold them in half. Write on each half, and then cut each circle along the fold line. Have the class count halves while you write the fractions on the board: one half two halves three halves, STOP. Ask: How would you write a fraction that names three halves? How is this fraction different from the fractions you have used so far? The numerator is greater than the denominator. Draw two pairs of circles on the board. In one pair, divide both circles in half and shade three of the halves. Label the picture. In the second pair, divide only one circle in half. Shade one of the halves and the complete circle. Label the picture. Ask children to compare the two pictures. The same amount of space is shaded. Continue counting: four halves. Ask: What fraction names four halves? Next, have children paste three of the halves inside the two circles in Problem on journal page 97. Point out that because each circle is ONE, or whole, is more than, and can be written as. Emphasize that and are equivalent names and represent the same amount. Write on the board and explain that the number is called a mixed number because it is made up of a whole number and a fraction. Ask children to fold the other two circles into four equal parts: Write in each part and cut each circle along the fold lines. Have children glue six of the fourth pieces inside the two remaining circles (in Problem ) on the journal page. Then they write a fraction that names the six pieces 6 or and a mixed number that names the six pieces or. If no one wrote or, ask the class to compare the two pairs of circles for halves and 6 fourths. Ask: Why is 6 equivalent to? Why is equivalent to? Both name the same amount of circles. Adjusting the Activity Ask children whether they can think of ways to name all four circles with a fraction. They can probably come up with equivalent halves ( ) and fourths ( 6 ). Encourage them to try other denominators, 0, and so on. If no one suggests it, ask about. Remind them that the number on the bottom of the fraction tells into how many parts the whole has been divided. If the circles are not divided, the denominator is. Since there are undivided circles, is the number in the numerator. Also ask whether they can think of an equivalent mixed number, such as or. A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L 6 Unit Fractions Grade Everyday Mathematics Teacher's Lesson Guide 007 Wright Group/McGraw-Hill

5 Date Student Page Time Ongoing Assessment: Informing Instruction Watch for children who have difficulty writing mixed numbers. Write them on the board as you say them to provide a visual reference for children. Links to the Future The activities in this lesson expose children to the concept of naming fractional parts greater than one as fractions and mixed numbers. Converting between fractions and mixed numbers is a Grade Goal.... More Than ONE continued How many fourths? fourths Color fourths. Write the fraction: Write the mixed number: How many thirds? thirds Color thirds. Write the fraction: Write the mixed number: Naming Parts with Fractions and Mixed Numbers (Math Journal, p. 9) PARTNER ACTIVITY 6. How many fifths? fifths Color fifths. Write the fraction: Write the mixed number: How many thirds? thirds Color thirds. Write the fraction: Write the mixed number: You may want to do Problem with the class to make sure children know what is expected. They color a given number of fractional parts of circles and use the resulting diagrams to name them with a fraction and a mixed number. Note that the answer to Problem 6 is a mixed number greater than. Math Journal, p. 9 Ongoing Learning & Practice Playing the Equivalent Fractions Game (Student Reference Book, pp. and ) PARTNER ACTIVITY The game was introduced in Lesson -. If necessary, children can read the rules for the Equivalent Fractions Game in the Student Reference Book on pages and. Have children record equivalent fraction pairs they make on a Record Sheet made from a half-sheet of paper. Remind them to write an symbol between equivalent fractions. Ongoing Assessment: Recognizing Student Achievement Record Sheet Use the Record Sheet to assess children s progress toward using Fraction Cards to find equivalent fractions. Children are making adequate progress if they record at least pairs. Some children may be able to identify equivalent fractions without using the shaded sides of the cards. [Number and Numeration Goal ] Grade Everyday Mathematics Teacher's Lesson Guide 007 Wright Group/McGraw-Hill Lesson 6

6 Date Math Boxes. In the number 6.7: the 7 means the 6 means the means the means the means. Circle the fractions that are equivalent to Student Page 7 tenths 6 ones thousandths tens hundredth 9 Time. On which color is the spinner most likely to land? Least likely to land? red green yellow blue red green 9 9. Use a straightedge. Draw the other half of the symmetric shape. Math Boxes (Math Journal, p. 99) INDEPENDENT ACTIVITY Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson -. The skill in Problem 6 previews Unit 9 content. Writing/Reasoning Have children write an answer to the following: In Problem, what does share equally mean? Sample answer: Share equally means to divide an amount or a group of things into equal parts. In Problem, each person gets an equal amount. 0. Share $.7 equally among people. Each person gets $.. Share $0.00 equally among people. Each person gets $.0. Math Journal, p Solve Home Link (Math Masters, pp. and 9) INDEPENDENT ACTIVITY Home Connection Children color figures according to directions and then write fractions and mixed numbers to describe those pictures. Name Date Time HOME LINK Family Note Home Link Master Fractions and Mixed Numbers Today the class began looking at fractions greater than and mixed numbers. We have been working with region or area models (shaded areas) for these numbers. Problem asks about fractions of a set. The whole is a dozen eggs, so each egg is of the whole. Have your child explain how he or she figured out what the fraction and mixed number should be for the egg-carton drawings. Please return this Home Link to school tomorrow. Name Date Time HOME LINK. Try This Home Link Master Fractions and Mixed Numbers cont.. How many fourths? 6 fourths Color 6 fourths. 6 Write the fraction: Write the mixed number: or What fraction of the WHOLE carton is each egg?.. 9 How many fifths? fifths Color 9 fifths. Write the fraction: 9 Write the mixed number:. How many thirds? 7 thirds Color 7 thirds. Write the fraction: 7 Write the mixed number: Write the fraction: Write the fraction as a mixed number: or Practice Math Masters, p. Write these problems on the back of this page. Solve and show your work Math Masters, p Unit Fractions Grade Everyday Mathematics Teacher's Lesson Guide 007 Wright Group/McGraw-Hill

7 Differentiation Options READINESS Modeling Fractions of Regions Larger than One Whole (Math Masters, p. 60) INDEPENDENT ACTIVITY Min Teaching Master Name Date Time Comparing Figures Use only triangles, rhombuses, trapezoids, and hexagons from your pattern blocks to solve the problems below.. One hexagon is the WHOLE. Cover the WHOLE with triangles. How many triangles fit in the whole hexagon? Use your pattern blocks to build a figure that is greater than one WHOLE. Use your Pattern-Block Template to draw your figure below. 6 To provide experience with comparing fractions of regions to the WHOLE, have children build the shapes on Math Masters, page 60 with pattern blocks. Cover your new drawing with triangles. How many triangles fit in your figure? Answers vary.. One trapezoid is the WHOLE. Cover the WHOLE with triangles. How many triangles fit in the whole trapezoid? Use your pattern blocks to build a figure that is greater than one WHOLE. Use your Pattern-Block Template to draw your figure below. ENRICHMENT Placing Fractions on a Number Line (Math Masters, p. 6) INDEPENDENT ACTIVITY Min Cover your new drawing with triangles. How many triangles is your figure worth? Answers vary. Math Masters, p. 60 To apply children s understanding of mixed numbers, have them identify and locate numbers between consecutive whole numbers on a number line. Have children discuss how they decided where to place their fractions on the number lines. EXTRA PRACTICE Playing Fraction Top-It (Student Reference Book, pp. 7 and ) PARTNER ACTIVITY Min To provide practice with comparing fractions, have children play Fraction Top-It, which was introduced in Lesson -6. Children may play the advanced version of the game. If necessary, they can read the rules for both versions of Fraction Top-It in the Student Reference Book on pages 7 and. Teaching Master Name Date Time Fractions on a Number Line ELL SUPPORT Building a Math Word Bank (Differentiation Handbook) SMALL-GROUP ACTIVITY Min To provide language support for fractions, have children use the Word Bank template found in the Differentiation Handbook. Ask children to write the term mixed number, draw a picture representing the term, and write other related words. See the Differentiation Handbook for more information.. Identify at least fractions that are between 0 and. On a half-sheet of paper, record your fractions as mixed numbers and as fractions. Then place them on the number line below. Answers vary. 0. Identify at least fractions that are between and. On a half-sheet of paper, record your fractions as mixed numbers and as fractions. Then place them on the number line below. Answers vary. Math Masters, p. 6 Grade Everyday Mathematics Teacher's Lesson Guide 007 Wright Group/McGraw-Hill Lesson 67

8 Date Time More Than ONE back to lesson Use the circles that you cut out for the Math Message.. Glue halves into the two whole circles. or one and half halves or. Glue 6 fourths into the two whole circles. Fill in the missing digits in the question, the fraction, and the mixed number. How many fourths? fourths Write the fraction: Write the mixed number: Grade Everyday Mathematics Student Math Journal 007 Wright Group/McGraw-Hill one hundred ninety-seven 97

9 Date Time More Than ONE continued back to lesson. How many fourths? fourths Color fourths. Write the fraction: Write the mixed number:. How many thirds? thirds Color thirds. Write the fraction: Write the mixed number:. How many fifths? fifths Color fifths. Write the fraction: Write the mixed number: 6. How many thirds? thirds Color thirds. Write the fraction: Write the mixed number: 9 one hundred ninety-eight Grade Everyday Mathematics Student Math Journal 007 Wright Group/McGraw-Hill

10 Date Time Math Boxes back to lesson. In the number 6.7: the 7 means the 6 means 7 tenths. On which color is the spinner most likely to land? Least likely to land? the means the means the means green yellow blue red 9 9. Circle the fractions that are equivalent to.. Use a straightedge. Draw the other half of the symmetric shape Share $.7 equally among people. Each person gets $. Share $0.00 equally among people. 6. Solve Each person gets $. 9 Grade Everyday Mathematics Student Math Journal 007 Wright Group/McGraw-Hill one hundred ninety-nine 99

11 Name Date Time back to lesson HOME LINK Fractions and Mixed Numbers Family Note Today the class began looking at fractions greater than and mixed numbers. We have been working with region or area models (shaded areas) for these numbers. Problem asks about fractions of a set. The whole is a dozen eggs, so each egg is of the whole. Have your child explain how he or she figured out what the fraction and mixed number should be for the egg-carton drawings. Please return this Home Link to school tomorrow.. How many fourths? fourths Color 6 fourths. Write the fraction: Write the mixed number:. How many fifths? fifths Color 9 fifths. Write the fraction: Write the mixed number:. How many thirds? thirds Color 7 thirds. Write the fraction: Write the mixed number: Copyright Wright Group/McGraw-Hill Grade Everyday Mathematics Math Masters 007 Wright Group/McGraw-Hill

12 Name Date Time back to lesson HOME LINK Fractions and Mixed Numbers cont. Try This. What fraction of the WHOLE carton is each egg?. Copyright Wright Group/McGraw-Hill Write the fraction: Write the fraction as a mixed number: Practice Write these problems on the back of this page. Solve and show your work Grade Everyday Mathematics Math Masters 007 Wright Group/McGraw-Hill 9

13 Name Date Time Comparing Figures back to lesson Use only triangles, rhombuses, trapezoids, and hexagons from your pattern blocks to solve the problems below.. One hexagon is the WHOLE. Cover the WHOLE with triangles. How many triangles fit in the whole hexagon? Use your pattern blocks to build a figure that is greater than one WHOLE. Use your Pattern-Block Template to draw your figure below. Cover your new drawing with triangles. How many triangles fit in your figure?. One trapezoid is the WHOLE. Cover the WHOLE with triangles. How many triangles fit in the whole trapezoid? Use your pattern blocks to build a figure that is greater than one WHOLE. Use your Pattern-Block Template to draw your figure below. Cover your new drawing with triangles. How many triangles is your figure worth? Copyright Wright Group/McGraw-Hill 60 Grade Everyday Mathematics Math Masters 007 Wright Group/McGraw-Hill

14 back to lesson Copyright Wright Group/McGraw-Hill. Identify at least fractions that are between 0 and. On a half-sheet of paper, record your fractions as mixed numbers and as fractions. Then place them on the number line below. 0. Identify at least fractions that are between and. On a half-sheet of paper, record your fractions as mixed numbers and as fractions. Then place them on the number line below. 7 Fractions on a Number Line Name Date Time 6 Grade Everyday Mathematics Math Masters 007 Wright Group/McGraw-Hill

15 Name Date Time Fractions Greater than One back to lesson Copyright Wright Group/McGraw-Hill 6 Grade Everyday Mathematics Math Masters 007 Wright Group/McGraw-Hill

16 Name Date Time Math Word Bank A back to lesson Copyright Wright Group/McGraw-Hill Differentiation Handbook Grade Everyday Mathematics Differentiation Handbook 007 Wright Group/McGraw-Hill All rights reserved, used with permission

17 back to student page Numbers and Counting Place Value for Decimals When we write a money amount like $6., the number is a decimal. The place that each digit has in the number is very important. dollars dimes pennies 6. Decimals were invented by the Dutch scientist Simon Stevin, in. In England,. is written as.. In France,. is written as,. The decimal point separates dollars from cents. The 6 is worth 6 dollars. The is worth 0 cents, or dimes, or 0 of a dollar. The is worth cents, or pennies, or 00 of a dollar. We can use a place-value chart to show how much each digit in a decimal is worth. The place for a digit is its position in the number. The value of a digit is how much it is worth. The number.6 is shown in a place-value chart below. s 0.s 0.0s 0.00s ones place tenths place hundredths place thousandths place. 6 The in the ones place is worth ( ones). The in the tenths place is worth 0. ( tenths). The in the hundredths place is worth 0.0 ( hundredths). The 6 in the thousandths place is worth (6 thousandths)..6 is read and 6 thousandths. The decimal point is read as and. Grade Everyday Mathematics Student Reference Book 007 Wright Group/McGraw-Hill thirty-five

18 back to lesson Games Equivalent Fractions Game Materials deck of Fraction Cards (Math Journal, Activity Sheets ) Players Skill Recognizing fractions that are equivalent Object of the game To collect more Fraction Cards. Directions. Shuffle the Fraction Cards and place the deck picture-side down on the table.. Turn the top card over near the deck of cards.. Players take turns. When it is your turn, turn over the top card from the deck. Try to match this card with a picture-side up card on the table. If you find a match, take the matching cards. Then, if there are no cards left picture-side up, turn the top card over near the deck. If you cannot find a match, place your card pictureside up next to the other cards. Your turn is over.. The game ends when all cards have been matched. The player with more cards wins. The top card is turned over and put on the table. The picture shows 6. Player turns over the card. This card matches 6. Player takes both cards. There are no cards left picture-side up. So Player turns over the top card and puts it near the deck. The picture shows 6. Player turns over the 0 card. There is no match. This card is placed next to 6. It is Player s turn again. 6 0 Grade Everyday Mathematics Student Reference Book 007 Wright Group/McGraw-Hill two hundred eighty-three

19 Games back to lesson Equivalent Fractions Game (Advanced Version) Materials Players Skill deck of Fraction Cards (Math Journal, Activity Sheets ) Recognizing fractions that are equivalent Object of the game To collect more Fraction Cards. Directions. Shuffle the Fraction Cards and place the deck picture-side down on the table.. Turn the top card over near the deck of cards.. Players take turns. When it is your turn, take the top card from the deck, but do not turn it over (keep the picture side down). Try to match the fraction with one of the picture-side up cards on the table. If you find a match, turn the card over to see if you matched the cards correctly. If you did, take both cards. Then, if there are no cards left picture-side up, turn the top card over. If there is no match, place your card next to the other cards, picture-side up. Your turn is over. If there is a match but you did not find it, the other player can take the matching cards.. The game ends when all cards have been matched. The player with more cards wins. two hundred eighty-four Grade Everyday Mathematics Student Reference Book 007 Wright Group/McGraw-Hill

20 back to lesson Games Fraction Top-It Materials deck of Fraction Cards (Math Journal, Activity Sheets ) Players Skill Comparing fractions Object of the game To collect more cards. Directions. Shuffle the Fraction Cards and place the deck picture-side down on the table.. Each player turns over a card from the top of the deck. Players compare the shaded parts of the cards. The player with the larger fraction shaded takes both cards.. If the shaded parts are equal, the fractions are equivalent. Each player then turns over another card. The player with the larger fraction shaded takes all the cards from both plays.. The game is over when all cards have been taken from the deck. The player with more cards wins. Players turn over a card and a 6 card. The the card has a larger shaded area. The player holding card takes both cards. 6 Players turn over a card and a card. The shaded parts are equal. Each player turns over another card. The player with the larger Fraction Card takes all the cards. Grade Everyday Mathematics Student Reference Book 007 Wright Group/McGraw-Hill two hundred eighty-seven 7

21 two hundred eighty-eight Grade Everyday Mathematics Student Reference Book 007 Wright Group/McGraw-Hill Games back to lesson Fraction Top-It (Advanced Version) Materials deck of Fraction Cards (Math Journal, Activity Sheets ) Players Skill Comparing fractions Object of the game To collect more cards. Directions. Shuffle the Fraction Cards and place the deck picture-side down on the table.. Each player takes a card from the top of the deck but does not turn it over. The cards remain picture-side down.. Players take turns. When it is your turn: Say whether you think your fraction is greater than, less than, or equivalent to the other player s fraction. Turn the cards over and compare the shaded parts. If you were correct, take both cards. If you were wrong, the other player takes both cards.. The game is over when all cards have been taken from the deck. The player with more cards wins. Joel draws a card. Sue draws a card. It is Sue s turn, and she says that her fraction is less than Joel s. They turn their cards over and find that the shaded areas are equal. The fractions are equivalent. Sue was wrong, so Joel takes both cards.

22 back to lesson NOTE: Card backs show written fraction only. 6 Fraction Cards Date Time Activity Sheet 6 Grade Everyday Mathematics Student Math Journal 007 Wright Group/McGraw-Hill

23 back to lesson NOTE: Card backs show written fraction only. back to game instructions Fraction Cards Date Time Activity Sheet 6 0 Grade Everyday Mathematics Student Math Journal 007 Wright Group/McGraw-Hill

24 back to lesson NOTE: Card backs show written fraction only. back to game instructions Fraction Cards Date Time Activity Sheet Grade Everyday Mathematics Student Math Journal 007 Wright Group/McGraw-Hill

25 back to lesson NOTE: Card backs show written fraction only Fraction Cards Date Time Activity Sheet 0 0 Grade Everyday Mathematics Student Math Journal 007 Wright Group/McGraw-Hill