- How are mathematical representations of relationships made?
- How can the study of mathematics aid in clear communication?
- How can identifying regularity or repetition help with problem-solving efficiency?
- How do we represent, compare, quantify, and model numbers using mathematics?
- What does it mean to analyze or estimate a numerical quantity?
- What qualifies a tool or approach as suitable for a particular task?
- Greater Than: Bigger.
- Less Than: Smaller.
- Equal To: The same value as.
- number tiles 1–9 (3–6 sets)
- jar (one jar for each set of number tiles)
- whiteboard
- whiteboard marker
- whiteboard eraser
- Comparing Numbers Group Activity (M-1-1-3_Comparing Numbers Group Activity)
- Comparing Numbers Worksheet (M-1-1-3_Comparing Numbers Worksheet and KEY)
- Order Up game (M-1-1-3_Ordering Numbers Game Board)
- place-value number cubes (tens and ones) for each partnership
- pencil
- base-ten blocks
- blank hundreds chart (allows for teacher or student to write in the number range being worked in) (M-1-1-3_Blank 100 Grid)
- blank number line (allows for teacher or student to write in the number range being worked in) (M-1-1-3_Number Line)
- As students finish the M-1-1-3_Comparing Numbers Worksheet and KEY, you should watch them to make sure they are ordering and comparing numbers correctly.
- Watch your students play the Order Up game (M-1-1-3_Ordering Numbers Game Board).
- During the section on instructional procedures, keep an eye on the responses from the students.
Explicit instruction, modeling, scaffolding, and active engagement
W: Explain to the class that they will be sorting and comparing two-digit numbers in this lesson.
H: Students will engage in Order Up and Number Tile activities.
E: To produce the largest and smallest number, students will manipulate tiles and choose where to place them.
R: Students will be able to evaluate their comprehension of ordering and comparing numbers through the pre-, during-, and post-lesson questions.
E: To assess students' comprehension of ordering and comparing numbers, use their responses throughout the lesson and the Comparing Numbers worksheet.
T: You can modify the lesson by implementing the ideas mentioned in the Extension section.
O: The purpose of the lesson is to reinforce and broaden the understanding of sorting and comparing numerical values. Students are required to manipulate several two-digit numbers using number tiles. Students will make two numbers: the largest and the smallest. They will go over and practice using the <, >, and = symbols.
"We're going to study how to create and compare numbers today. We will need to understand place values to accomplish this. Remember our previous days' work and draw this number in base-ten blocks," you can say after writing the number 53 on the board. Give students some time, and then keep an eye on their development. Invite a student to present what they drew. Draw the student's drawing on the board so that everyone can see it while they describe it. "What do we call these?" (cubes), you ask, pointing to the cubes. "What value do they stand for?" (ones) "What location do we call these?" (longs), you ask, pointing to the longs. “What place value do they represent?” (tens)
Write the following on the board.
________ ________
tens ones
"Let's make a new two-digit number now." Select a tile with a number from the jar and write it on the ones line. Select a different number tile from the jar and record the value on the line marked "tens."
Give the students a whiteboard to cut in half, and instruct them to write the number on the left side and illustrate it with base-ten blocks. Observe the work that students are doing.
"Can we create another two-digit number with these two digits?" Give students time to reflect before calling on them again until someone signals for them to switch places or to reorder.
Make two fresh horizontal lines (do not remove the initial set) and inscribe the numbers in the opposite sequence. Give students the task of writing the new number on the right side of their whiteboards and drawing it in base-ten blocks. Keep an eye on the work that students do.
________ ________ ________ ________
tens ones tens ones
Say, "Which number is bigger or greater than the other?" Invite a couple of students to come in. How do they know which is better? Ask the students. If necessary, guide them. (There are more tens in the larger number.)
Say, "There are signs we can use to show which number is bigger and which is smaller," while drawing a large circle in between each set of lines. "This sign is like a crocodile's mouth," you can say after placing the relevant sign in the circle. The largest number is what the crocodile seeks to devour at all times. Read the statement that the numbers are trying to convey. "____ is bigger or smaller than ____."
________ ________ 
_______ ________
tens ones tens ones
Give the students instructions to wipe their boards while you remove the numbers from the board's lines. Write the number on the ones line of one number tile, then the number on the tens line of another number tile that you have chosen. Give students instructions to write the number on the left side of their whiteboards and to illustrate it using base-ten blocks. On the right side of their whiteboards, repeat the procedure for the rearranged tiles in the second set of lines.
Ask students, "Which number is bigger? " after they have both written and drawn two-digit numbers. "How are you aware?" (The larger figure contains more tens.) "What symbol appears between your digits?" Remember that the open portion gets to the higher number.
Read the statement that the numbers are trying to convey. ("____ is either greater or less than ____.")
Divide the class into three or four groups. Each student should receive a copy of the Comparing Numbers Group Activity (M-1-1-3_Comparing Numbers Group Activity). Watch the students as they work on the task and offer assistance when required. Invite groups to assemble and present their numerical assertions. Distribute copies of the Comparing Numbers WWorksheet and KEY (M-1-1-3_Comparing Numbers Worksheet and KEY) to every student. As you move around the classroom, watch the students and probe further to find out which ones understand ordering and comparing numbers and which ones require more explanation.
Extension:
Routine: Partners play Order Up (M-1-1-3_Ordering Numbers Game Board). One game board and one set of place-value number cubes are required for each player.
In the initial box, each player writes 1, and in the final box, 99. Player 1 generates a two-digit number by rolling two place-value number cubes. Somewhere between 1 and 99 is the number that he or she writes on the game board. The second player follows suit. Players keep switching off, rolling the number cubes to generate a two-digit number, and writing it down on their game boards in the right sequence. The player whose boxes are filled in the most at the end of the allotted time wins.
More activities are listed under Related Resources.
Small Group: Let students construct each number they are ordering or comparing using base-ten blocks. For ordering and comparing numbers, let them use the hundreds chart (M-1-1-3_Blank 100 Grid) and/or the number line (M-1-1-3_Number Line).
Students who have trouble understanding greater than or less than can play War, a card game. Divide the number of cards equally among two or more players after shuffling the deck. The top card is removed from the deck by the players and placed face-up on the table. In that round, all of the cards are awarded to the player who places the most of them. Continue until the player runs out of cards or the timer expires. After the game, the player with the most cards wins. (This game can also be played backward, with the cards going to the player who places the smallest number.)
Expansion: Learners can sketch three number tiles and list the six possible combinations for each number tile, going from greatest to least. (1, 2, 3 would become 321, 312, 231, 213, 132, 123, for instance). Students will compare their work with that of other students who have finished the expansion after repeating the procedure twice more.
