Greater Than, Less Than, Equal To

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1 Game 15 Greater Than, Less Than, Equal To Recommended Grades K 4 Time Instruction: minutes Independent Play: minutes TEACHING TIPS Manipulatives For modeling this game, yellow wooden hexagons from pattern blocks sets work well. They are readily seen because of their size and have a weight that will be recognized and measured more easily using the scale. For playing the game, use small counters, interlocking cubes, or even pennies. Enlarged Numeral Cards A set of enlarged numeral cards is recommended to model this game. Use a photocopier to enlarge the cards provided in REPRODUCIBLE B or, alternatively, use ten sheets of white copy paper or construction paper and write one of the 0 10 numerals on each (use a thick black marker so the numbers can be seen easily). A Deck of Cards For the purposes of this game, a deck of cards is four of each number If using a deck of playing cards, the 0 will not be available. Aces represent the value of 1. Consider preparing decks of playing cards ahead of time, removing all the face cards. See the Connections to the Common Core State Standards for Mathematics, page xv. Overview Introduce this game after lessons on both basic addition and the concept development of equalities and inequalities. To play, pairs of students take turns drawing numeral cards and completing number sentences. Together, they determine which symbol (>, <, or =) goes with each sentence. The player with the greater sum keeps all four cards in that round. The player with the most cards at the end (ten rounds) is the winner. It s important to have balance scales accessible for supporting students understanding of inequalities and equalities. Additional versions of recording sheets are also included to allow for differentiated instruction. Materials balance scale, 1 per pair of students sticky notes labeled >, <, and =, 3 per pair of students manipulatives (see Teaching Tips) Numeral Cards 0 10 (REPRODUCIBLE B), 1 set enlarged for classroom use Numeral Cards 0 10 (REPRODUCIBLE B), 1 deck per pair of students or playing cards (face cards and Jokers removed; Aces remain to represent the value of 1), 1 deck per pair of students Greater Than, Less Than, Equal To Recording Sheet, Version 1 (Two Addends) (REPRODUCIBLE 22), 1 enlarged for class use continued 78

2 Greater Than, Less Than, Equal To Recording Sheet, Version 1 (Two Addends) (REPRODUCIBLE 22), 1 per pair of students Greater Than, Less Than, Equal To Game Directions (REPRODUCIBLE G-15), 1 per pair of students Related Games Game 8: Compare (Shake and Spill) Game 21: More! Key Questions Can you explain how is greater than? How many more would you need for the two sums to be equal? Teaching Directions Part I: The Connection Relate the game to students ongoing work. Equalities and Inequalities: Making Comparisons 1. Review the idea of equalities and inequalities through comparisons. To do so, use items in the classroom. For example, ask students to find one unsharpened and one sharpened pencil in their desk. Ask students to compare the two pencils. What do they notice? Students observations might be the following: One is new and the other is used. One is longer and the other is shorter. One has a fresh eraser and the other eraser is worn. 2. Explain to students that during the game Greater Than, Less Than, Equal To, they will be comparing sums. Because sums have a numeric value, students will be able to tell which one is greater or less. 79

3 Math Games for Independent Practice TEACHING TIPS Arranging Students For the demonstration area, have students make two concentric circles. In the first circle, students kneel or sit; in the second, students stand. This ensures that everyone can view the demonstration area. A Balance Scale Using a balance scale gives students a concrete visual for seeing the equalities and inequalities of the numbers being compared. If a balance scale is not available, create drawings on a board or space where all students can see them. Using Manipulatives for Comparison Using nonnumeric items for comparison, such as counters or interlocking cubes, may provide students more practice in counting the items when combining, whereas using pennies (which have a value of one) might allow them to rely more on their basic addition facts. Equalities and Inequalities: Reviewing Concepts, Symbols, and Names 1. Review and introduce equalities and inequalities concepts, symbols, and names of signs. Do this through observation-style learning. Designate a table or desk as the demonstration area. Place a balance scale in the middle of the area. 2. Begin by showing students the balance scale. Point out that nothing, or zero, equals zero. Affix a sticky note with an equal sign to the middle of the scale so students can see the equality. 3. Next, place a counter on one side of the scale. Students should now see that one side of the scale has more than the other. Explain, One side has more than the other. This is called an inequality. 4. Write the word inequality where all students can see it. Ask students to identify the root word. Most students will be able to see and hear the root word equal in inequality. 5. Discuss what inequality means. Record some of the students words where everyone can see them. Typically, students will offer phrases and words such as the following: Not the same Not equal Unalike 80

4 Game 15: Greater Than, Less Than, Equal To 6. Remove the sticky note with the equal symbol from the scale. Replace it with the sticky note showing the greater than (>) symbol. 7. Ask students, How can we get the scale back to a neutral or equal position? Students will likely suggest removing the counter or adding a counter to the side with none. 8. Act on the suggestion of adding a counter. Place a counter on the side with nothing. 9. After the scale steadies, ask students, What should the symbol in the middle read? Replace the sticky note on the scale with a sticky note showing the equal symbol. 10. Now place a second counter on the same side of the scale. This action presents an opportunity to introduce the less than symbol. Remove the sticky note with the equal sign and place the sticky note with the less than symbol on the scale. A CHILD S MIND Understanding the Symbols > and < Precision of language when introducing the equality and inequality symbols is extremely important. Depending on the age and experiences of students, do not be surprised if they use words such as alligator or arrow to describe the symbols. Encourage students to use the correct names for the symbols. 11. Continue the demonstration, having students help place counters on the scale, change the symbols, and read the symbols. 81

5 Math Games for Independent Practice Equalities and Inequalities: Recording Equations 1. The purpose of this part of the lesson is to take students from a more concrete model of equalities and inequalities (the balance scale) to an abstract representation (equations). Have students return to their seats and focus on the front of the classroom. 2. Recreate what you did previously with the balance scale, only this time, record the corresponding equations where everyone can see them, rather than using the sticky notes. Start by removing all counters from both sides of the balance scale and recording: `0`=`0` 3. Then, place a single counter on one side of the scale, just as before. Tell students while writing, When we add one counter, the mathematics that shows what we did is, zero plus one is greater than zero. Write: 0`+`1`>`0 4. Next, add one counter to balance out the scale. Tell students while writing, Zero plus one is equivalent to zero plus one. Write: 0`+`1`=`0`+`1 5. Last, add one more counter to one side of the scale. Tell students while writing, Zero plus one is less than one plus one. Write: 0`+`1`<`1`+`1 Students should be able to see the scale s imbalance and, hopefully, link it to the equation that represents the inequality. 6. At this point in the lesson, your recording should look like this: 0`=`0 0`+`1`>`0 0`+`1`=`0`+`1 0`+`1`<`1`+`1 82

6 Game 15: Greater Than, Less Than, Equal To Ask students if they have questions and clarify any confusion. Part II: The Teaching Introduce and model the game to students. 1. Tell students they will be playing the game Greater Than, Less Than, Equal To. Place a set of enlarged numeral cards 0 10 near the scale and ask students to reassemble around the scale. 2. Display the first part of an enlarged version of the Greater Than, Less Than, Equal To Recording Sheet (REPRODUCIBLE 22) where everyone can see it. Player 1 Player 2 3. Ask a student to draw two numeral cards from the stack of cards. Tell the student to turn over the cards, show them to everyone else, and read the numbers. 4. Record the numbers in the blanks under Player 1 on the recording sheet. 5. Ask another student to draw two more numeral cards from the deck. Tell the student to turn over the cards, show them to everyone else, and read the numbers. 6. Record the numbers in the blanks under Player 2 on the recording sheet. 7. Ask students, Which symbol will make the number sentence true? If your number sentence reads: Player 1 Player Students will likely know that seven (5 + 2) is less than nine (8 + 1). Place the less than symbol into the square on the recording sheet. 8. Repeat Steps 3 7 so students experience one more round with a different number sentence. TEACHING TIP Arranging Students For the demonstration area, have students make two concentric circles. In the first circle, students kneel or sit; in the second, students stand. This ensures that everyone can view the demonstration area. TEACHING TIP Linking to the Concrete When asking students to determine which symbol goes into the number sentence, it may be helpful to have student volunteers place counters on the balance scale. In the example provided, the inequality could be shown by placing five counters plus two more on one side of the scale, then eight counters plus one more on the other side. 83

7 Math Games for Independent Practice TEACHING TIP The Balance Scale As students play the game independently, have one or two balance scales available for them to check their work. Be mindful that if students are not used to having this kind of learning tool available to them, they will likely need some time to experiment with it. You may want to introduce the balance scale to the class a few days before the lesson so that students can try it out prior to playing this game. TEACHING TIP Number Sentences on Recording Sheet Draw students attention to the three sentences at the bottom of their recording sheets. It is their responsibility to complete these sentences after they ve finished the game. Together we had: inequalities. greater than (>). less than (<). equalities and Part III: Active Engagement Engage students to ensure they understand how to play the game. 9. Now give students an opportunity to explore the game in pairs. Have students come up in pairs, draw numeral cards, and fill in the corresponding blanks on the recording sheet. Engage the rest of the class in determining whether the equation requires a greater than, less than, or equal to sign. Usually, five to six rounds of this is sufficient to ensure students have a sound understanding of the game. 10. Collect the number sentences that have been created. If they were written on the board, do not erase them because you will be using them in the link portion of the lesson. Part IV: The Link Students play the game independently. 11. Set students up for independent practice with the game. Each pair of students should be given a deck of numeral cards 0 10 and a copy of the recording sheet (REPRODUCIBLE 22). Also, distribute the game directions (REPRO- DUCIBLE G-15) as needed. 12. Before students start playing, draw their attention to the three sentences at the bottom of their recording sheets. Write the sentences where everyone can see them, next to the number sentences completed during the modeling of the lesson. Complete the sentences as a class, clarifying meaning if needed. Tell students that it is their responsibility to complete the sentences on their recording sheets after they ve finished their game. 13. Explain that the player who has the greater sum gets to keep the cards for that round. Students play until their recording sheets are full (ten rounds). 84

8 Game 15: Greater Than, Less Than, Equal To MATH WORKSHOP AND SUMMARIZING THE EXPERIENCE Teach this game at the beginning of the week to the whole class, then make it an integral part of your math workshop (for more on math workshops, see Chapter 5 in From Reading to Math by Maggie Siena). Build in time to observe students playing the game. Note their individual skill level and use of the symbols; come together as a class later in the week and hold a discussion. Begin a class chart with two columns: Equalities and Inequalities. Have students record corresponding number sentences under each column, then select one of the equations in the Equalities column and ask key questions. For example, for the equation = you could say, Explain how this is true. A student might reply, If you take one from the five and put it with the three, it s four plus four. Have the student use manipulatives to show her thinking visually. Using an Interactive Whiteboard If an interactive whiteboard is available, cloning pennies, circles, or squares assists in demonstrating how = Students pull from the cloned virtual manipulatives and move the pieces accordingly. DIFFERENTIATING YOUR INSTRUCTION There are several ways to modify the game according to the levels and needs of your students. Increase the Number of Addends Have students play with three addends on each side of the equation. REPRODUCIBLE 23 is provided for this purpose. Change the Operation Have students play the game with subtraction or multiplication instead of addition. The player with the larger difference or product takes all the cards for each round. Just as in the original version, the player with the most cards wins. REPRODUCIBLE 24 and REPRODUCIBLE 25 are provided for this purpose. 85