Transitioning to the Standard Algorithm


When should the standard algorithm be introduced?

When should the standard algorithm be introduced?


Many of my second grade classrooms are in the middle of their addition units. The classes often teach place value and addition strategies during the months of September and October. When introducing addition strategies, teachers rarely start using the standard addition algorithm (see # 4). Manipulatives and visual representations are heavily used during the first month of school.  The process below differs per school, but I’m finding that this is often the case in many of the second grade classes that I’ve observed. Keep in mind that I’m missing other approaches, so perceive the following as a few highlighted strategies that are used during the first few months of school.


Finding the sum of objects

Students are introduced to some from of unifix cubes or counters. Students are asked to compile the groups of counters to find the sum. For the most part students find this task quickly and are ready to move onto the next portion.  This is also a first grade skill that’s reviewed at the beginning of second grade.


Identifying numbers on the number line

The number line usually follows the counters. Sometimes the number line makes an appearance before the counters, but it’s usually afterwards. The number line is used extensively. Students are asked to find numbers on the number line. This builds number sense and an understanding of the reasonableness of an answer. Eventually students are asked to add numbers with hops showing the addition involved.

Find the sum of 25 and 15.

Find the sum of 25 and 20.

Base-ten blocks are then introduced to emphasize place value. Students are asked to combine base-ten blocks to find the sum. They are asked to find the sum of the base ten blocks and place them on the number line.


What is the sum?

The four processes above aren’t necessarily mandates, but it’s found in the sequence of the textbook.  I should mention that the same process is used with subtraction later in the year. What I’m finding is that there’s rarely a mention of using the standard addition algorithm to find the sum. I don’t necessarily think that’s a problem, but it raises the question of when should the algorithm be introduced? In what cases should the algorithm be introduced and is it only used in certain circumstances.

Think of 200 + 198. Would your students use the standard algorithm for this?  Some might, other might prefer to use another method. Regardless of when the standard algorithm is introduced, there will still be students that would prefer to use the algorithm.  Is that the most efficient method?

The topic of this post was tackled during last Thursday’s #ElemMathChat. Most of the questions revolved around when the standard algorithm should be introduced and mistakes that occur when students focus on the steps.  There were many useful answers, but I’m not positive if one right answer climbed its way to the top.  There are many factors at play here. Some teachers feel pressured to move through the curriculum at a high pace because of testing.  They might teach the algorithm sooner, while others might not mention it and scroll through the prescribed lesson sequence.  Most teachers would like students to have a conceptual understanding of numbers and systems before moving towards a standard algorithm. How much time is spent developing that truly depends on the teacher and student. I’m not judging any teacher is these situations as we are all in this together, but I believe having this discussion is important.  I think this also plays a role in how other algorithms are introduced.


Exploring Rules and Patterns


This past week my upper elementary classes started their equations, patterns, and rules units.  The units are composed of patterns, special cases, student-created rules, and solving equations.  To be honest this is one of my favorite units and involves a good amount of pattern exploration.  Through exploration, students construct their own understanding of how mathematical rules can be developed by analyzing patterns.   Many of these activities involve manipulatives or visual representations of various patterns.  I’m going to highlight three specific activities that seemed to work well this past week.

Analyzing the Perimeter

What's the Rule?

What’s the Rule?

Students were given a handful of square geometry blocks.  They were asked to find the perimeter of one block.  This was quick as students just needed to count the sides of the block.  Four!  Students then put together two blocks and found that the perimeter didn’t double, instead it was six. Students continued the patterns and discussed with their group what the rule could possible be.  Some groups used the whiteboards to write possible solutions.  Throughout this activity students struggled at first and then came to an understanding that the rule just didn’t include one operation. After the rule was discovered the students found the perimeter of 100, 200, and even 1,000 squares put together in a horizontal row.  I believe this activity also helped establish the reason for having mathematical rules.

Rule Tables

Students used four dice, a whiteboard, iPad, and dry erase marker to complete this activity. Two of the dice were operation and they had + and – on the sides.  The other two were typical six-sided 1-6 dice.   Students rolled all four dice and created a rule.  For example, if a student rolled a 6, 2, +, and – then he/she could say the rule is + 6 – 2.  Students wrote the rule on top of the whiteboard and used one of the die to roll five numbers that would be included in the in column.  Afterwards, students were asked to find the out column using the rule that was created.  A few examples are below.


The students then took a picture of their product and sent it to Showbie.  Later on that day the class discussed how to combine rules.  So instead of + 6 – 1 this rule could be + 5.  The students were then combining all of their rules.  This activity led to some productive discussions on how to simplify or expand rules.

Visual Patterns


I came across Fawn’s Visualpatterns site a couple years ago.  This is a fantastic resource that I introduced this past week.  I printed out some of the patterns and placed them in manilla file folders.  The picture of that is located near the top of this post.  The six folders were placed around the classroom.  Student groups visited each folder and determined the rule. While in the group students worked together and filled out the sheet below.

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Modified from this site.

Students took whiteboards and started to build possible rules for the pattern. Once they accomplished this they filled out the table and graphed the relationship.   I appreciate that students are asked to graph their findings.  This could lead into so many other math topics. Students only rotated through two folder stations so we’ll continue this activity next week.  By the way, the students were stoked when I showed them the visual patterns site and not because it has the answers.  A few students even said they were going to check out the other patterns on the site.  I’m looking forward to utilizing this resource a bit more next week.

How do you introduce patterns, rules, and equations?


Assessments and Growth Mindset


School has been in session for over month and many of my classes had a unit assessment last week.  The district adopted math program has 10-12 unit checkpoints (depending on the grade level) for the school year and each assessment covers specified math strands.  These assessments are designed to assess understanding and include an open response that emphasizes students’ conceptual understanding and math communication skills.  The entire unit assessment takes about 50+ minutes to complete.

I usually try to administer and grade all the tests on the same day.  This doesn’t always happen.  Before passing the tests back to the students the class generally has a discussion about certain problems that were missed more than others.

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What’s up with problem eight ?

We also have celebrations as a class.  During the class discussion we don’t blame, but reflect on what the numbers might mean.  This idea has taken time to cement and required a bit of modeling.  Based on the results I might even teach a brief mini lesson to help address and reduce misconceptions.  This is also an opportunity for students to analyze their own test and look for correlations.  Afterwards, students are given a sheet to reflect on their own analysis. Students are asked to review their assessment and give feedback on their own performance.

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Click for file

After the students fill out the above sheet they visit the teacher for a brief conference.  These last a quick 2-3 minutes and include a time to check-in with the student. We have a conversation about the student’s reflection and look for opportunities to improve in the future.  This is also a time to set some possible goals.  The sheet is glued into the student’s math journal and can be a document that the student will look back on as the year progresses.

I feel like the process of analyzing, reflecting and setting goals is important.  I believe it reinforces a growth mindset mentality, but it also has me wondering about the role of different assessments in the learning process.  I’d say about 95% of what is used at the elementary level is formative.  I could see how that changes as students progress through middle and high school.  Feedback and the possibility to make positive strides towards improvement can often be utilized with most assessments, regardless if you label it formative or summative.  If a school truly embraces a growth mindset model, what role do summative assessments play? I believe that summative assessments have a role.  I’m just thinking that they may be perceived a bit differently if a school emphasizes a growth mindset model.

image credit: Woodley Wonderworks 

Starting an Elementary Coding Club


Starting a Coding Club

Coding in Elementary School

Last year my classes participated in the Hour of Code.  It was an engaging and unique experience for the students and many of them continued to explore coding throughout the school year.  As the year progressed students started using the app Hopscotch and explored  I thought that an Hour of Code was amazing, but not enough for some students.

So I spoke with two other colleagues and one mentioned that we should probably offer a technology/coding club for the 2014-15 school year. We spoke with our administrator and it was approved as a school club.  At the time we were excited yet a bit anxious because we all knew very little about using code in the classroom.  I have a bit of background in using HTML, but that’s about it.

Over the summer another colleague and I were able to visit the DG58 SAMRi conference in Downer’s Grove. I’m always impressed with the teacher workshops that they put together. While there, I was able to attend a session by James on Coding in the Classroom.  The session had around 30 interested teachers with a variety of experience with coding.  The notes for the session can be found here.  After the session I felt like I had gained a better understanding of how to use the Scratch coding language.

After the workshop I checked out Help Your Kids with Computer Coding and Super Scratch Programming Adventure from the local library.  I found both books be valuable in building an understanding of using Scratch. So I decided to open up a Scratch account and started to explore.  I completed a few lessons within the books above and felt a bit more comfortable with using the program. I was also able to connect with other teachers on Twitter to learn more about the topic.  Mary inspired me to start looking at using Scratch to possible create an introduction game for my students. I especially found Havard’s Creative Computing to be helpful with lesson planning.

During the month of August the team created a digital pamphlet that explained the class to parents of the community.  The team limited the roster to the first 20 students in grades 3-5 that registered.  The pamphlet was distributed with the principal’s digital monthly newsletter. Within the first two days we had approximately 40 students that registered.  My colleagues and I started to think that this was a bigger deal than what we originally thought.  We sent out emails to the parents indicating whether their child will be participating or not.  Based on the demand we may offer a spring session.

Last Wednesday was our first coding club class.  Students participated in an introduction activity where they needed to guide each other to different parts of the classroom using commands that are found in Scratch.  They could only use specific verbs found on notecards. This activity also had the participants get acquainted with each other.  Afterwards students logged into their accounts and started to explore the different aspects of Scratch.  Before leaving the class on the first day students were able to start their first program called escape the dragon.

Going forward, I’m interested to see what is created through this class.  Throughout the class the students will develop their own portfolio of creations that they can share with others.

photo credit: the waving cat via photopin cc

Math Genius Hour Research

About two weeks ago my classes started their math genius hour projects. Students started with a  wonderwall, created multiple questions, and then decided on one question that they wanted to emphasize.  The students generated and picked the question.  I signed-off on the question and the students chose what math strand they wanted to highlight. Eventually the math strand will dictate what will be included in the presentation.


If needed, students can refine their questions to show more detail.  Some students may do just that.  Some of the students won’t really know until the research process starts. As you can see, students definitely were wondering how ____ is made. I can’t describe in words the amount of curiosity that this type of project brings to the table. Instead of asking the teacher for their answer (they still do though) I’m asking students to research for themselves.

Most of the students will begin researching their questions using a variety of online resources next week.  What I found out last week was that students weren’t aware of how to search, gather, or cite information. Before the students begin their research I wanted to review how to use online sources correctly.  A few students raised their eyebrows and asked why we’re learning about research skills in math class.  Many of the students have never heard of the term digital literacy before.  I thought this was a great opportunity to discuss the importance of being able to find and use online resources effectively.  The class explored (1) (2) a few different resources on how to search for information online.

We also looked at the following questions:

- Who created the website ?
- How does the site address end ? (.gov .edu .net .org)
-Does the page contain any type of advertisement ?  

So where are we now? Some students have already started to research their topics.  Students are asked to find at least three sources before picking a presentation tool.  They are filling out the sheet below to compile their information.

Math Genius Source Sheet

Click for pdf

Once the research is complete students will pick their presentation tool.  I’m also looking at having students reflect on their math genius project journey in their journals.  Now, I’m looking at what type of presentations tools they can use … that’s my research for the weekend.

Using Genius Hour Ideas in Math Class



One of my goals last year was to incorporate more student content creation in my classroom. The journey was challenging but definitely worthwhile. Students created a variety of projects that helped showcase their math understanding. There were elements of choice in the projects and I felt like student engagement and curiosity bloomed.

This year I’m trying something different. I’ve always been impressed with the idea of using genius hour in the classroom. What intrigued me was the student choice and engagement piece. The idea of students owning their learning and being intrinsically motivated to participant in the learning process is important. Hearing stories from Paul and Joy inspired me to think of ways that I could apply a genius hour philosophy in an elementary math classroom.

I had a few discussions with colleague and kicked around a few ideas on how to get started. I started off with an informal wonder wall. Students started to generate questions that they would like to answer. I soon found out that this was a challenging task for the students. They weren’t used to this type of assignment. When asked to create a question for the wonder wall they had trouble. Many students asked what I wanted and were unsure of what questions to create.  I showed the students the Google and Siri test. If the question that they came up with could immediately be Googleable or Siriable (words?) then they should probably find another question. This actually worked as the class used some horrible and decent examples. After a while and some modeling, students started to compile a few different questions.

I then placed the different math strands on the whiteboard: geometry, measurement & data, number & operations and algebra. The class then started to sort their questions into the different math strands.


Students decided on what math strand to emphasize and documented it on their recording sheet. The class then discussed the math genius project flow chart.

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Click for file

I wanted to give students a bigger picture of what’s going to happen over the next month or so. Since my classes only have about an hour to work on this project a week, it’ll probably take at least a month of sessions to finish. I really have no idea though. It could take a couple of months, but it depends on how the students progress.

After we reviewed the flow chart the class will be moving into the research portion. Students will use a variety of tools/resources to research their topic to find some sort of conclusion. The students will be using the sheet below to document their research.

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Click for file

So far so good. Next week the classes will continue to research their questions and think about what type of presentation tool they’d like to use. This is definitely a journey and I’ll be documenting our progress through this blog.

Additional files:  Source Sheet Check List


Estimating in the Elementary Classroom


Using Estimation180

My school finished its ninth day of school yesterday. It’s been a journey as students are understanding class routines better.  At this point in the year, students and teachers are starting to become more solid in their processes.  Many of my students arrive to class at different times. Some students are at an elective or leave class a bit earlier/later than the rest of their peers. Regardless of the arrival time, when students enter the room they follow a flow chart. Students have their own folder and materials inside that are ready to go. I usually have some type of visual brainteaser for the week and a grade specific Scholastic math magazine. In the past I’ve used different types of math warm-up activities to start class.

This year I adapted my warm-up strategy. I wanted to individualize the type of responses within that warm-up time slot. After researching a few different tools, I decided to try Andrew Stadel’s Estimation180 this year. I think of Estimation180 as an opportunity for students to develop a stronger sense of numbers and practice estimation skills in the process. Initially, I thought that the site would be great for middle or high school students. I then found the below sheet and site that seemed helpful. This is one way in which student can document their thinking.  The template also includes lessons that could link to Fawn’s Visual Patterns site.

Click to download template

This template inspired me to adapt the sheet to fit an elementary classroom. I changed the template a bit to work with a third grade math class.  A few colleagues and I will be using this sheet early next week.

So now, students enter the classroom, pick up their folder and begin to work on their daily estimation challenge warm-up  sheet.  The estimation is displayed on the whiteboard. Students pick a high, low and exact estimate. I ask the students to prepare to tell me about the reasoning that they used to come to the concluding estimate. The class then completes the online portion of the site and submits a response. We then look at other responses and reasoning.

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After a brief discussion the result is revealed. Students write in the correct numbers and find the + / – . The entire activity takes about 5 – 10 minutes.

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I’m planning on using Estimation180 a few days a week and incorporate Visual Patterns for the rest of the days. The template also includes a few different reflection pieces.  I feel like these activities provide students opportunities to produce a product and reflect on the results. At some point I’d like to add a journaling component to encourage more reflection and possible goal setting.