By: Katrina Maccalous

As an adult, I assumed rounding and estimation were a simple concept…I mean…we use it all the time with finances! However, it became quite clear to me once I began teaching, that this concept would actually be one of the more difficult concepts for children to understand. While many can memorize the old rule of “5 or more, raise the score (round up)…4 or less, let it rest,” do they actually understand what they’re doing and more importantly WHY that rule exists?

The idea of why, and the meaningfulness behind the idea of rounding/estimation/approximation, has become a focus with my own students during our early days back at school (and spiraling throughout during morning routines). If they can see why it works and why we do it, then we’ve not only established a purpose, but worked on the idea of number sense. (So, so important!- I will definitely post about this all too crucial skill many times in the future.)

So, this week, my students began tackling this concept! My plan of attack is to always begin with inquiry. What do they know about rounding, and provide a real world example to grapple with.

This year, I used a future camping trip that I am planning as my example, but any examples such as grocery shopping or planning how many treats to bring for a party will work too. Without any instruction on HOW to determine how much I should bring, I told them the cost was $101.97, and asked them what would be an easier amount to bring. Without much hesitation, they all agreed that $102 would be easier to bring, because 0.97 cents is almost one dollar. They were rounding, even though they may not have realized it.

Then I gave them another example. This time 17, and asked them what number it was closest to. As I walked around the room, questioning students, I was pushing them to prove their thinking (justify). Below are some examples that they produced without any guidance other than to prove to me and others that 17 was closer to 20. During a quick share, I had those students explain how they knew that 17 rounded to 20. I made sure to also call on a student who brought up the idea of 5.

(This is the perfect opportunity to model WHY the 5 or more/4 or less rule works by showing how 5 is the halfway point of 10, so 15 is halfway between 10 and 20…50 is half of 100, and so on. I also show this on “rounding mountain,” with 5 at the peak.)

Based on this formative assessment and discussion, I determined that we were ready to challenge ourselves with a number in the thousands period (family). I followed the same process with a new number, and released my students to try and make connections to what we had just discussed. (How students react in these situations is really helpful in determining what level of modeling/direct instruction must take place.)

I had anticipated that I would need to model the steps with these larger problems, and I was correct. We regrouped, and I guided them through the process while modeling the thinking process of noticing what place value I was being asked to round to, what two multiples it was between (1,000; 2,000; etc.), placing those on the number line, finding the midpoint, and placing the number on a number line to determine which multiple it was closest to.

Then student had an opportunity to explain what they saw me do in their own words with a partner.

Since we are working on a blended learning model, we logged onto Canvas to watch another explanation and a “Rules for Rounding” fill-in-the-blank activity. Students took notes during these in their math journals for future referencing.

After some more exploration and guided practice (dependent on the pacing of the lesson thus far), I like to have students take on the role of teacher and create their own “anchor charts.” This provides them the opportunity to practice “talk read talk write” and engage in a gallery walk to observe each others’ rules, ending with a closing discussion of ideas and any misconceptions seen.

Note: This lesson could easily be broken into multiple days, and it definitely needs to be revisited throughout the year.

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Later in the week, we will move to applying this idea with compatible numbers and estimation. Many conversations and respectful debates will occur to analyze rounding examples and non examples! My goal here is to get kids thinking about why it works and also when it doesn’t.

Below I’ve included two virtual lessons I recorded for my students online, as well as some helpful tips, basic rules, and examples/resources. I will update this post as I, yet again, make adjustments based on observations from implementation!

Happy teaching!

Rules for Rounding:

1. Identify (find) the number in the place value you are rounding to.
2. Determine what two multiples the number is between.
3. Which one is it closest to?
4. If it’s halfway or more…think 5 or more…move up! (“5 or more, raise the score”)
5. If it’s less than that…4 or less… make it go back (“4 or less, give it a rest”)
6. Everything larger stays the same, everything after drops to zero.

Student Poster from Last Year:

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Video Lessons:

Activities:

Roll and Round

Directions:

1. Players take turns rolling a set amount of dice (tip: differentiate by place value size). They then arrange the dice to make a number (EXAMPLE: 5, 8, 1, 2, 2 might become 12,582)
2. One player flips over a place value card to determine how they will round their number (nearest…10, 100, 1,000…)-again, another way to easily differentiate the task. Get it free here for a limited time!
3. All players then round their number to the place value drawn. You can provide students with an open number line to support them if needed.
4. The player with the highest value wins that round.

Compatible Number Match

Directions:

1. Students lay all the cards face up.
2. Players take turns finding two numbers that are compatible with each other.
3. If they make a match and explain why the two numbers match, they keep the cards.
4. Players continue taking turns until no matches/cards are left. The player with the most cards wins. (freebie here!)