ARMY OF ANTS
SUBTRACTION STRATEGY: ROUND THE SUBTRAHEND AND ADJUST
Explore efficient strategies to subtract values within 50
Intentionality
Spark Curiosity
Fuel Sensemaking
During Moves
Student Approaches
Next Moves
Consolidation
Reflect and Consolidation Prompts
Resources & Downloads
Educator Discussion Area
Intentionality & Unit Overview
Length of Unit: 5 Days
Access each lesson from this unit using the navigation links below
Students will explore subtraction in a context encouraging students to use a strategy that allows them to flexibly work with the subtrahend by rounding it to the nearest decade then adjust to subtract numbers within 50
Intentionality…
In this task, students will engage in a subtraction context and lead towards the “round the subtrahend and adjust” strategy.
Some of the big ideas that may emerge through this task include:
- Subtraction names the missing part in terms of the whole
- Different subtraction situations will elicit different strategies
- Number relationships provide the foundation for strategies to help students remember basic facts
- Efficient operational sense strategies should be number oriented
- Subtraction can be used in either take away, comparison, or missing addend situations. Take away is explored in this task.
- Subtraction represents the difference or space between two numbers
- Models can be used to connect concrete to abstract
Spark Curiosity
What Do You Notice? What Do You Wonder?
Show students the following video:
Then, ask students:
What do you notice?
What do you wonder?
Give students about 30-60 seconds to do a rapid write on a piece of paper or silent individual think time.
Replaying the video can be helpful here if appropriate. Ensure that students do not long enough to 1:1 count each fish. This will encourage some subitizing to occur and for students to visual what they saw.
Then, ask students to pair share with their neighbours for another 60 seconds.
Finally, allow students to individually share with the entire group. Be sure to write down these noticings and wonderings on the blackboard/whiteboard, chart paper, or some other way that is visible to all. This helps students to see the thinking of their classmates and ensures each student that their voice is acknowledged and appreciated. Adding student names or initials next to their notice/wonder is one way to acknowledge their participation and can motivate others to join in.
Some of the noticing and wondering may include:
- I notice that there are a lot of ants.
- I notice there are ants in the hills.
- I wonder what kind of ants they are.
- I wonder how big the colony is.
- I wonder where the queen ant is.
Estimation: Prompt
After we have heard students and demonstrated that we value their voice, we can ask the estimation question. The students may have already made some guesses of the amount of ants in the previous section. The students will feel valued as you now ask them to make a true estimation.
How many ants are in this part of the colony?
Follow up that question with:
How could you convince someone that your estimation is correct?
We can now ask students to make an estimate (not a guess) as we want them to be as strategic as they can possibly be. Before collecting student estimates, students can share their estimates with neighbouring students along with the reasoning.
Consider asking students to think about a number that would be “too low” and a number that would be “too high” before asking for their best estimate in order to help them come up with a more reasonable estimate.
While Students are Estimating:
Monitor student thinking by circulating around the room and listening to the mathematical discourse. You may identify some students whose thinking would be valuable to share when the group’s estimates are collected.
Encourage students to make estimations rather than 1:1 counting each ant. The video may be paused for longer before it goes blank but we want students to make estimations based on their mathematical understanding and spatial sense.
Similar to collecting their noticings and wonderings, collect students’ range of estimates and/or best estimates along with initials or names. Having some students share justifications is an opportunity for rich, mathematical discourse.
Estimation: Reveal
Fuel Sense-making
Crafting A Productive Struggle: Prompt
Since you have already taken some time to set the context for this problem and student curiosity is already sparked, we have them in a perfect spot to help push their thinking further and fuel sense making.
Share the following video with the prompt.
Each day the ants work together to support their colony. One day 28 ants left the colony to gather food, 9 of them found food right away so they went back to the colony. How many of the ant group are still searching for food?
During Moves
While Students Are Productively Struggling…
Monitor student thinking by circulating around the room and listening to the mathematical discourse. Educators are looking for students that are making their thinking visible so it can be displayed during consolidation. Select and sequence some of the student solution strategies and ask a student from the selected groups to share with the class from:
- most accessible to least accessible solution strategies and representations;
- most common misconceptions;
- most common/frequent to least common/frequent representations; or,
- choose another approach to selecting and sequencing student work.
The strategies you might see students use include:
- Direct model and counting all
- Counting back
- Round the subtrahend and adjust
Assessment:
This checklist can be used for tracking formative assessment as students are working. The information collected can be used to form whole group, small group or one-to-one support models.
Early strategy | Direct modelling and counting all | Students will count the initial value, count the amount added then count all of the amounts. Example: Count 1: 23 blocks to start Count 2: 8 of the blocks moved to the side Count 3: Count the remaining 15 blocks. |
Pre-cursor skill | Count forwards from various points | Watch for students that need to count forwards starting from 1. You may hear a student that is counting on from 8, whisper their count “1, 2, 3, 4, 5, 6, 7, 8” then start counting on while tracking out loud. |
Count Back strategy | Students are holding one number in their head and continuing to count backwards and track their count | |
Count Up | Students are finding the difference/space between in the numbers by adding up from the lower number to the higher number | |
Subtract 10 off the decade | This skill demonstrates student understanding of place value. By mentally subtracting 10 (or 20, 30, 40, etc) from a number, students will only need to adjust the tens column (or possibly the hundreds column as the numbers get bigger). Can students do this without counting back 10? | |
Strategic and efficient strategy: Round the Subtrahend and adjust | The Round the Subtrahend and adjust strategy demonstrates the understanding of difference. Students round the subtrahend to a decade number first and then subtract that amount. For example, 34 – 19 can be mentally solved by subtracting 20 first (34 – 20 = 14). Now an adjustment needs to be made because too many were subtracted, so 1 more needs to be added. 14 + 1 = 15. Therefore 34 – 19 = 15 | |
Student Approaches
Student Approach 1: Counting All with a Tool
I counted out 28 blocks for the 28 ants that went to look for food.
Then I counted 9 blocks and put them to the side.
I counted 19 blocks left so there are 19 ants still looking for food.
Student Approach 2: Counting All with a Drawing
I drew 28 circles for the 28 ants. I crossed out 9 of the circles and counted the remaining amount of circles. There were 19 circles not crossed so there are 19 ants still looking for food.
Student Approach 3: Count Back with finger trackers
I thought about 28 in my head and then counted back 9 on my fingers. Each time I put down a finger, 27, 26, 25, 24, 23, 22, 21, 20, 19.
Student Approach 4: Round the Subtrahend and adjust
I know that 28 – 10 is 18, but since it is 9 I took away too much so it is 19.
Next Moves
Reveal
Show students the following reveal video:
Facilitator Note:
The open number line (or empty number line) is an incredible tool for students to use to demonstrate their thinking. It allows flexibility from the traditional number line because students do not have to count the “ticks’ or “spaces”, instead they may jot their thinking anywhere on the line.
Consolidation
Consolidation: Making Connections During Classroom Discourse
Consolidate learning by facilitating a student discussion.
The goal of the consolation is to demonstrate the flexible way that we can subtract an easier number by rounding the subtrahend and adjusting. The “Round the Subtrahend and Adjust” strategy demonstrates the understanding of difference. Students round the subtrahend (the number being subtracted) to a decade number first and then subtract that amount. This is an effective strategy when the subtrahend is close to a decade number (e,g., 8, 9, 18, 19, etc). By subtracting 10 in any of these cases, the students are eliminating the need to count back and are instead working with the numbers.
In both of these examples, too much has been taken away so an adjustment needs to be made to compensate for that.
In this question, only 8 was supposed to be subtracted. Since 10 was subtracted instead, that was 2 too many. Therefore, two more needed to be added on to adjust for the “over subtraction”.
Similarly, this question has a subtrahend of 19. By subtracting 20 instead, that means that 1 too many was subtracted. So in this case, one more needed to be added on.
In order for this strategy to be efficient, students need to be able to mentally subtract 10 (or 20, 30, 40, etc) from a number without having to count back. Students who struggle with this may need further place value support. Students that were counting back often “get lost” as they have to travel over a decade. As the numbers get higher or the count back becomes larger, counting is not always as reliable. There are too many pieces for a student to keep track of.
This problem may become more obvious by modelling the thinking on an open number line. It will allow students the opportunity to see that we are trying to figure out the space or the difference between them.
We want students to start feeling more comfortable with subtracting numbers in a way that makes sense to them rather than just counting.
During the discussion, encourage students to start by showing their work without an explanation. Classmates will use this time to understand the visual and make their own assumptions about the work in front of them. It is also an option to ask students “What do you think this group did to solve this question?”. This will engage students in the work. The group can clarify any misunderstandings.
Reflect and Consolidation Prompts
Round the subtrahend and Adjust is an effective way to subtract. It is important for students to understand when to use a strategy rather than just relying on their favourite strategy. In this case, this strategy is most effective when the subtrahend is just under the decade (8, 9, 18, 19, etc). In each, it is easier to mentally subtract the decade number and adjust to get the answer. Support may be needed for students to recognize how they need to adjust after rounding the subtrahend. Sometimes students may continue subtracting. The following picture shows a common mistake. The first number line shows the student subtracting one more after subtracting 10. The bottom number line shows the correct idea that too much was subtracted so the real answer is one higher.
Consider the strategies that the students used. Perhaps a review of subtracting off the decade is necessary (e.g., 23 – 10, 34 – 20, 56 – 20, etc).
Provide students an opportunity to reflect on their learning by offering these consolidation prompts.
Consolidation Prompt #1:
How is subtracting 10 or 20 from a number easier than subtracting 9 or 19?
Consolidation Prompt #2:
45 – 19
Show your thinking on a numberline.
We suggest collecting this reflection as an additional opportunity to engage in the formative assessment process to inform next steps for individual students as well as how the whole class will proceed.
Resources & Downloads
Printable Lesson Plan PDF
Videos, Images & Media Files
Apple Keynote Presentation
Powerpoint Presentation
Printable Consolidation Prompts
Educator Discussion Area
Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.
Explore Our 60+ Problem Based Units
This Make Math Moments Lesson was designed to spark curiosity for a multi-day unit of study with built in purposeful practice, number talks and extensions to elicit and emerge strategies and mathematical models.
Dig into our other units of study and view by concept continuum, grade or topic!
