Comparing Numbers Unit of Study 2: Place Value Concepts to 1,000 Global Concept Guide: 4 of 4

Content Development  Comparison relationships should be understood with WORDS first (greater than, less than and equal to).  134 is LESS THAN 212  234 is GREATER THAN 123  312 is EQUAL TO or THE SAME AS 312  Comparison symbols (>, <, =) should be used only after students have a good understanding of the comparison words. Avoid using the “alligator mouth” to teach the meaning of symbols. Instead, utilize number line understanding to help students place meaning with the symbols.  As you move to the left on the number line, the values are decreasing ( greater than).

Day 1  Essential Question: How can base ten models help you compare numbers?  The goal of Day 1 is for students to compare numbers using words. Students should not use symbols (, =) on Day 1.  23 is LESS THAN 34  189 is GREATER THAN 124  19 is THE SAME AS or EQUAL TO 19  Avoid using words such as BIGGER or SMALLER when comparing numbers. Instead, focus on the value of numbers (greater than, more than, less than, fewer than).  Students should use base-ten blocks, place-value charts, pictorial representations and secret code cards to solve real world comparison problems.  Organizational strategies are key in helping students to compare numbers efficiently with precision. (e.g. grid paper to separate digits, place value mats, quick pictures that are organized and spaced, etc.)  Lesson 2.11 is a good resource to use on Day 1, however, encourage students to justify their responses by writing a sentence proving their answer. For example, #3 on p.99, students should say or write, “Jake’s puzzle has more pieces because I know 180 is GREATER THAN 164.”

Day 2  Essential Question: How can you compare 3-digit numbers?  Symbols may be introduced on Day 2 but if students are not ready, wait to introduce until Day 3.  Refrain from using the phrase “the alligator’s mouth is going to eat the bigger number” because this creates misconceptions and not a true understanding. This language does not attend to precision which is Standard Mathematical Practice (SMP) 6.  Comparing Numbers game and Max’s Mumm task would be good to use on Day 2 to provide opportunities for students to compare numbers using pictures and words. Comparing Numbers Max’s Mumm  Sample journal question: How is comparing 157 and 153 different from comparing 218 and 118?  By the end of Day 2, students should be able to correctly compare numbers using words, and if ready, develop an understanding of the comparison symbols.

Comparing numbers using a number line ? Using a string and post it notes, have students order numbers. Students can then determine what numbers could be where a question mark is placed. Students should explain how they know their number could fall there on the number line.

Day 3  Essential Question: How do the comparison symbols help you compare numbers efficiently?  Students should focus on comparing numbers from real world word problems using the comparison symbols (>, <, =). Avoid using the alligator mouth to teach the symbols, instead, rely on the number line to develop understanding of the symbols.  Students should continue to use the words (greater than, less than and equal to) to accompany the symbols.  Lesson 2.12 provides opportunities for students to practice using the comparison symbols. However, encourage students to justify their responses using words, pictures etc.  What’s your Size can also be used to provide opportunities for students to use symbols when comparing. What’s your Size  By the end of Day 3, student should correctly use the comparison symbols to compare numbers.

Enrich/Reteach/Intervention Reteach:  Reteach lessons ideas from lessons (p. 97B; 101B; R20-21) would be appropriate. If students need more practice, use the questions in these lessons to develop additional questions.  Students that are struggling may not be ready for the symbols. They may need to build or draw a picture to help them truly understand number comparison.  Animated Math Model: Comparing Numbers Animated Math Model: Comparing Numbers Enrich  Enrich lessons ideas from lessons (p. 97B; 101B; E20-21) may be used to help stretch student thinking.