Guided Lessons

# The Rhyme and Reason for Rounding

This lesson focuses on facilitating a rich classroom discussion around the purpose and methods of rounding numbers up to the thousands place. It can be taught on its own or as support to the lesson Rounding with Number Lines.
This lesson can be used as a pre-lesson for theRounding with Number LinesLesson plan.

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This lesson can be used as a pre-lesson for theRounding with Number LinesLesson plan.

Students will be able to round whole numbers to the nearest thousand.

##### Language

Students will be able to discuss the purpose and method of rounding numbers using strategic questioning and sentence starters.

(3 minutes)
• Lead students in a word association exploration on the term "rounding." Write "rounding" in the centre of a piece of chart paper. Ask students to think of any words or numbers that relate to rounding and discuss them with a partner. Invite a few students to share their ideas with the whole class, and record their word associations in the space surrounding the word "rounding."
• Tell students that today they will take a closer look at the meaning and purpose of rounding numbers.
• Give each student a copy of the Review Your Thinking worksheet. Read aloud the directions and have students complete the "Beginning" section of the worksheet by drawing and writing their ideas or knowledge on the concept of rounding. Encourage students to use the word association chart paper you co-created with their input as a reference. Have students put the paper away and tell them they will fill out the rest later in the lesson.
(10 minutes)
• Distribute a set of the vocabulary cards to each student. Invite students to volunteer to read each vocabulary word and its definition aloud to the class. Model how to draw a symbol, picture, and/or words that help make more meaning of the term in the space provided for an image on each vocabulary card (e.g., write "30 is an ApproximationOf 32.").
• Assign students into partnerships and have them work on adding more details to each vocabulary card. They are encouraged to include the synonym in their home language, pictures, maths expressions, examples, or pictures in the empty space.
• Have a few students use the document camera to share their additions to a vocabulary card with the whole group.
• Place two sets of partners together to create a group of four students. Give each group a piece of chart paper and markers.
• Have all groups write "Purpose of Rounding" on the top of their chart paper.
• Display the following questions as a guide and have students discuss the purpose of rounding in their groups:
• Why do we need to know how to round numbers? ("We need to know how to round numbers because...")
• In what situations or scenarios might we round numbers? ("We might round numbers when...")
• How is rounding numbers useful to us? ("Rounding numbers is useful because...")
• Visit with each group to ensure that all students are participating in the discussion and that their ideas are being documented. Ask probing questions to help students clarify their point, such as, "What makes you say that? Could you say a little more about that?"
• Gather the class as a whole and have each group present their chart paper. As the groups are sharing, jot down the main points that were mentioned by most groups onto a new piece of chart paper, using the key vocabulary learned earlier in this section. Help students see the similarities in their ideas and thoughts about the reasons we use rounding.
(10 minutes)
• Explain to students that when we round, we either round up or round down. Have students share what they think that means. Draw a T-chart with two columns, one titled "Digits" and the other titled "Friendly Number (0 or 10)." Write the digits 0–9 in the first column and have students think-pair-share with a partner about which friendly number goes with each digit.
• Discuss with students the matter of the number 5 and how it technically could have the friendly number of 0 And10 because it is exactly halfway between the two numbers. Explain that a long time ago, mathematicians agreed that if the digit being rounded is 5, it will fall into the category of being rounded up (i.e., 10).
• Tell students that there are a couple different strategies for rounding numbers. The traditional method involves underlining the digit that is in the place value you need to round to, looking at the digit to the right of this digit, and rounding up if that digit is 5–9 or rounding down (leaving the original digit as is) if the digit to the right is 0–4. Show a few examples of this method:
• Round 57 to the nearest tens place. (Answer = 60)
• Round 421 to the nearest hundred. (Answer = 400)
• Tell students that another way to round numbers is to use a number line. Explain that this strategy is helpful because it gives us a visual of whether we should round up or down. Show students how to round these same numbers (57 and 421) using a number line. Emphasize the importance of choosing the two correct numbers for each example and noticing where the main number falls. For example, say, "57 falls between 50 and 60 so I will draw a number line with 50 on the left and 60 on the right. Then, I will draw 9 marks between 50 and 60 to represent 51, 52, 53, etc. I'll try to make the marks as even as possible. I will circle 57 and I immediately notice that it is closer to 60. This shows me that 57 rounded to the nearest 10 places is 60 because it is nearer to 60 than to 50."
• Give students a piece of scratch paper and have them fold it in half. Tell them to work with a partner to round a number. Give students the number 82 and have them round to the nearest tens place using both methods you demonstrated. Students should use one method in one half of the piece of paper.
• Repeat this process with the number 683 and have them round to the nearest hundred on the back of their folded paper using both strategies.
(10 minutes)
• Have students pull out the Review Your Thinking worksheet and instruct them to complete the Middle section. Tell students to use their Vocabulary Cards as a reference as they reconsider and refine their thinking about the purpose and process of rounding numbers. Students are encouraged to draw pictures and write examples to show how their knowledge has shifted at this point in the lesson.
• Distribute a sticky note to each student. Have them write down a two- or three-digit number on the sticky note. Collect the sticky notes and redistribute them to students, making sure they didn't get their own number. Hand out more scratch paper or copy paper to students.
• Instruct students to round the number on the sticky note to the nearest ten (if it's a two-digit number) and to the nearest hundred (if it's a three-digit number). Remind students to show their work on the scratch paper. Tell them that they may choose the strategy that they prefer for this rounding exercise.
• Form new groups of four students and have them share their rounding work with the group. Provide these prompting questions and sentence stems/frames to guide the discussion:
• What number did you round? ("I rounded the number ____To the nearest ____Place and got the answer ____.")
• What strategy did you use to round the number and why? ("I chose the ____Strategy to round the number because...")
• How do you know your answer is correct? ("I know my answer is correct because I...")
• Gather students together as a whole class and have them share some interesting points or processes that arose from their discussions. Record students' responses on a new piece of chart paper and label each idea or experience with the student's name that did the work.
• Encourage students to pause to reflect on how their preferences for the various rounding strategies are similar or different.

Beginning

• Pair students with more advanced students or other ELs who speak the same home language (L1) for partner activities.
• Create and display a word/phrase bank with helpful terms from the lesson for students to refer to, with images if applicable.
• Provide students access to home language resources, such as bilingual glossaries or online dictionaries to help them understand more about the terms used in the class.
• Have students restate the main learning points of the lesson before doing the Independent Work.

• Have students describe their maths processes without relying on the sentence stems/frames.
• Encourage students to rephrase the directions throughout the lesson.
(4 minutes)
• Have students look at the Review Your Thinking worksheet again. Tell them to complete the bottom or last section of the table, to show how their thinking has changed. Remind students to look at the chart paper they created in groups earlier as a reference.
• Have them complete the following sentence stems at the bottom of the table on the worksheet: "Rounding means... Rounding is helpful for..."
• Remind students to add pictures or examples to demonstrate their maths thinking.
(3 minutes)
• Have students share their sentences with a partner before a few students share with the whole group. Acknowledge their ideas or correct any misconceptions.
• Have students review the entire worksheet and discuss as a whole class how their maths thinking changed throughout the beginning, middle, and end of the lesson. Provide sentence stems to use as they observe the shifts in their understanding:
• "In the beginning, I thought..."
• "In the middle of the lesson, I discovered that..."
• "At the end, I learned that..."
• "My understanding of rounding changed from the beginning to the end because I..."
• Collect the worksheet to use as a formative assessment of this lesson.