Guided Lessons

# Mistakes in Comparing Multi-Digit Numbers

In maths, mistakes are welcome! This lesson helps your students identify and fix errors made while comparing three- to four-digit numbers. Teach the lesson on its own or as support to the lesson Let's Compare Whole Numbers!
This lesson can be used as a pre-lesson for theLet's Compare Whole NumbersLesson plan.

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This lesson can be used as a pre-lesson for theLet's Compare Whole NumbersLesson plan.

Students will be able to compare two multi-digit numbers.

##### Language

Students will be able to correct and explain errors in multi-digit number comparisons, using key grade level vocabulary, with the support of sentence starters.

(3 minutes)
• Ask students to consider the word Compare. State an example of a time you compared two things (e.g., "I wanted to buy a new soccer ball for my son so I compared the two kinds they had in the store. One was bigger than the other. It was red. The smaller one was blue. I decided to get the smaller one because it was a better size for my son. It was also cheaper than the red one.").
• Have them turn to a partner and talk about words, pictures, or sentences they think of when they think of comparing. State the following questions to get students interested in the concept of comparing: What does it mean to compare things? When in your life have you compared? Invite students to share key points from their conversation with their partner and jot down their remarks.
• Explain that comparisons happen all the time. We compare food, toys, books, movies, people, places, and more on a daily basis without even realizing it. Tell students that today they are going to practise comparing whole numbers with up to four digits. Specifically, they will look at errors or mistakes that others have made while comparing numbers, discuss the mistake, and fix it.
(7 minutes)
• Distribute a set of the vocabulary cards to each student. Invite student volunteers to read one of the vocabulary words and its definition. Encourage students to add to the definition in their own words, by stating the synonym in their home language (L1) or using the word in a sentence.
• Repeat this process with all of the words in a whole class discussion setting. Then, tell students to draw a picture or symbol in the empty space on each Vocabulary Card. Remind students that the image they draw should help them undestand the meaning and remember the definition of the word. Ask a few students to share their pictures with their classmates on the document camera. Have students keep their stack of Vocabulary Cards on their desk for future reference.
• Show students the numbers 6,701 and 6,710. Tell students that we learn to compare numbers so that we have good number sense or an idea of what a number really means or represents. Explain that having good number sense means being able to visualize or imagine the value of a number, or how much it is.
• Tell students that when comparing large numbers in the thousands, they must consider place value. Instruct them to look from LeftTo Right, from highest place value to lowest, comparing each digit in both numbers.
• Draw a place value chart with one column for each place value digit: thousands, hundreds, tens, and ones. Write 6,701 and 6,710 in the chart, one number on top of the other. Explain that you would start in the thousands place and see that both numbers have 6 thousands. Then, you would compare the hundreds place and see that they both have 7 hundreds. After that, you look in the tens place and that's where you see a difference! The first number has 0 tens while the second number has 1 ten. This leads you to the realization that the 6,701 is less than 6,710.
• Teach students that there are special symbols or signs in maths that help us compare numbers. Remind them of the meaning of the <, >, and = signs. Explain that for the example you just did, you could also write 6,701 < 6,710 and you would read this expression as six thousand seven hundred one is less than six thousand seven hundred ten.
(8 minutes)
• Place students into effective partnerships. Hand out a whiteboard and marker to each student. Model again how to draw a place value chart and have them draw one on their whiteboards. Tell students they can just write "Th." for thousands, "H." for hundreds, "T." for tens, and "O." for ones.
• Give students one set of numbers to compare using the place value chart on their whiteboards: 8,499 and 8,520. Instruct students to write the numbers in the chart and compare them. Have them write an expression using the symbols they learned earlier (8,499 < 8,520).
• Provide students with transition words to use, such as "First," "Then," "After that," and "Finally." Tell them to compare their maths processes and their answer with their partner. Also instruct students to write out the expression in word form as you did in your example. Remind them to refer to their Vocabulary Cards for support as they describe their work.
• Invite a few students to share their number comparison and any important issues that arose from their discussion with their partner.
• Ask students this question: "How might a person make a mistake when comparing numbers?" Give them the sentence starter, "A person might make a mistake when comparing numbers when they..."
• Lead them in a think-pair-share to answer this question. Record students' answers on chart paper, in a list format. Ideas they might come up with include not placing the right digits in the correct place value, not realizing the meaning of each digit, not following the process (step-by-step digit comparison), etc.
• Explain to students that mistakes are always welcome especially in maths practise because from our own mistakes and the errors of others, we can learn how to be better maths thinkers.
(12 minutes)
• Distribute the Errors in Comparing Numbers worksheet to students and display a teacher copy. Read aloud the directions and demonstrate an example of how to find the error and correct it in the first number comparison.
• Tell students that they are to write the word form of the number so they practise reading large numbers correctly. Then they must find the mistake and describe or explain why it's wrong and what they need to do to fix it. Explain that the sentence stems are there to support them through the process.
• Inform students that they may work with their partner on problems #2–6. Emphasize that it is acceptable for them to have different ways of explaining the error and how to fix it.
• Circulate and offer assistance as needed.
• Invite some students to share their explanations with the whole group.
• Facilitate a class discussion on the work using these sentence stems/frames:
• "I agree with ____That the mistake is..."
• "I would add.... to ____'s explanation."
• "I wonder what would happen if..."
• "I disagree with ____Because..."

Beginning

• Give students access to bilingual glossaries and online dictionaries for them to look up unfamiliar words throughout the lesson.
• Place students with more advanced ELs for partner work.
• Pull aside a small group of students as they work on the group work and guide them through the process.
• Have students repeat the directions in their home language (L1) or in English (L2) before beginning their work.
• Allow students to work on the formative assessment piece with a helpful partner.

• Encourage students to speak and write their answers without using the sentence frames/stems.
• Allow students to be the first to share their ideas or rephrase their classmates' contributions to class discussions.
• Have students create and display a word/phrase bank with helpful terms from the lesson for reference purposes, with images if applicable.
(3 minutes)
• Write a few number comparisons on the board or a piece of chart paper (e.g., 3,405 > 3,310; 2,988 = 2,988; 5,439 < 5,349).
• Point to each number comparison and have them show you a thumbs-up if the expression is correct or a thumbs-down if it is incorrect.
• Tell students to turn to a neighbour and explain the error in the last expression and what they could do to fix it (change the less than symbol to a greater than symbol because five thousand four hundred thirty-nine is greater than five thousand three hundred forty-nine).
(2 minutes)
• Pass out sticky notes to students.
• Have students complete the following sentence stem on the sticky note: "The main idea of today's lesson was to..."
• Tell students to place their note on the board and use their responses to guide future lessons.