Rich Task- Dunkin’ Donuts

Rich Math Task

Rich Math Task

I recently gave this picture to a my students. No matter how many times I ask my students “What math questions can you ask?” they always start with the basics.

  • How much does a small iced coffee cost?
  • How much does a muffin and medium coffee cost?
  • If I buy 25 Munchkins and pay with a $20 bill, how much change can do I get?

There are many more possible questions similar to these. Depending on your grade level, these could be your go to. For my 7th graders, these are lower level questions. After a few students suggest questions like these, I use my famous quote “Step it up!” Now students know they have to dive deeper into the picture.

Looking deeper reveled to one student the different rate of price increase between coffee sizes.

“This isn’t a question yet but I noticed from small to medium it goes up 30 cents and from medium to large it goes up 20 cents.”

“Ok, somebody turn that into a question.”

  • How big are the drink sizes? (The menu doesn’t tell this info. This is a great part for the students to research. For your information the sizes go 10 oz, 14 oz, 20 oz, 24 oz.)
  • Which drink gives you the best deal (most coffee per money)?
  • Is this a linear relationship?
  • Why is iced coffee more?
  • Are we paying for the ice?
  • Shouldn’t ice be free? Water is free. (Let them go with these curious questions.)

“Ok look at the rest of the menu. What else can we ask?”

  • How much is a dozen?
  • How much do I save from buying 6 donuts? A dozen donuts? What percent savings?
  • How much do I save from buying 6 muffins? A dozen muffins? What percent savings?

These range of questions go from decimal operations to unit rates and percentages. There are so many more possibilities within this menu. Plus you can bring in two follow up tasks with Starbucks and Tim Hortons menus to compare coffee places.


10 Components of Math Success

What makes a math class successful? I have developed 10 components of a successful math classroom that are the basis of the Minds on Math model for learning and teaching.

The first five of ten components that maximize math learning and understanding can be classified as Environment. Learning is emotional. Classrooms must have a feeling of acceptance and belonging for students to thrive. The environment itself can motivate or de-motivate students. We – teachers – have the power to create this feeling for students.

Forbes describes 4 factors that affect motivation for students:

1. Students feeling competent enough to complete classroom tasks

2. Students seeing a link between their actions and outcomes in the classroom

3. Students have an interest or see value in the tasks

4. Students feel a sense of belonging through participation in tasks

These conditions are embedded in the first five components of the Minds On Math model for learning and teaching as described below.

Component #1: Culture

What is the culture of my classroom?

Does the culture allow for students to take risks and feel supported?

Is it ok for students to be wrong? How do they know it is ok?

Is there an emphasis on everyone working as a team and operating as a community?

Does the classroom culture make kids thirsty for learning?

Is there a culture that promotes student success and confidence?

Do students know what to do when they don’t know what to do?

*Positive culture should be created throughout the year and not just during the first week of school. Building a strong culture takes time, reflection and feedback from students and teachers. Individuals should feel important and be encouraged. Without a strong culture and environment, student learning can be compromised.

Component #2: Theme

What is the theme of my classroom?

What do we believe in?

What is our motto?

Why are we here (at school or in math class)?

*Classroom themes that encourage learning emphasize thinking, doing, working hard, and being nice. These four actions are simple, yet complicated. These practices need to be taught, repeated and practice in order for students to begin to live them.

Component #3: Structure

What is the typical classroom routine?

Are all students successful in following classroom routine and procedures?

Are the norms and expectations clear, simple and related to the theme?

Does the classroom structure encourage student independence?

Does the structure develop student habits of mind?

Does the classroom structure support small group and individual instruction?

Does the structure define student and teacher roles?

Does the structure allow for student choice?

*Classroom structure combines routine, procedures and norms that build student independence and habits of mind. Students are more engaged in learning when there are also opportunities for them to choose what they will be working on. While students are engaged in learning, the structure should allow for teachers to work with students in small groups to individualize instruction. Tutoring centers and services have an impact on student learning not just because of the strategies and content they teach, but because of the low ratio of student to teacher interaction. Classroom structure should provide for the same opportunities as these successful tutoring centers.

 Component #4: Know students

Do I know my students personally and academically?

Do I have a variety of strategies to analyze student understanding?

Are my assessments informal, ongoing and frequent?

Is assessment a part of daily classroom ritual?

What is my observation documentation system?

How does formal and informal data drive my instruction?

Am I teaching lessons or teaching students?

*Assessment is the act of gaining knowledge of student understanding or misunderstanding. Assessment can be formal and summative, but most often should be subtle and formative. Teacher learning is more important than student learning. Without a clear knowledge of what students know and don’t know, teachers cannot maximize student achievement.

 Component #5: Face time

How often am I able to instruct and interact with students in small groups and individually?

What is the rest of the class doing while I work with a small group?

*Ultimately students are more accountable for their learning when the teacher to student ratio is as close to 1-to-1 as possible. Student learning and achievement continues to grow when the classroom culture and structure allows for opportunities for small group instruction targeted to individual student needs. When class sizes are 25 – 35 students, it seems nearly impossible to reduce this ratio. With a culture and structure in place that has elements of choice, teachers can lower the ratio at times and increase accountability and achievement.

The next three components can be classified as Experience.

What are the mathematical experiences we provide our students each day?

Do these experiences teach students how to learn and how to think?

Do the experiences develop student habits of mind?

What kind of experiences allow for differentiation and individualized instruction?

How do mathematical experiences create a balance of exploring concepts while becoming fluent with skills?

What experiences provide a depth of content and a focused engagement on learning?

The 3 criteria answer these questions:

Component #6: Big Ideas

What are the overarching concepts of the year?

What is the most important content of my course?

Does each lesson and unit during the year relate to at least one of the major ideas?

What math ideas are not appropriate for “units” but need to thread through the year and taken to a deeper level during each quarter of the year?

*A continuous focus on the top 3 to 4 big ideas of a grade level or course can create a “snowball” effect of learning. Lea, a teacher from Ohio, uses the phrase and idea of “snowballing” content which means adding to and creating bigger, rather than “spiraling” which can be random and disconnected. Lessons focusing on Big Ideas more often than on skills provide more entry points for all levels of students allowing ease for differentiation. Mathematics learning and teaching is enhanced by balancing a “birds eye view” of the content through themes and concepts, with a “microscopic view” of the course content by drilling down to skills. This zoom-in-and-out approach creates different perspectives and embraces mathematical connections.

**Below are Big Idea lists for each grade band. There is a flow and connection from one set of ideas to the next level. The High School focuses (#2-4) are recommended by the College Board.


1. Number** (this is the major focus of k-5)

2. Algebraic Thinking

3. Shape and Area

Middle School

1. Number and Operation

2. Rate and Function

3. Space and Dimension

High School

1. Number* (needs to continue in high school in connection with course topics)

2. Rate

3. Function

4. Accumulation

Component #7: Embedded Intervention

What are the key concepts struggling students lack?

How do I fill below grade level gaps in understanding while teaching the content of my course?

*There are 3 targeted areas that fill gaps in student math understanding. These targets can be embedded into regular classroom instruction at all levels and connected to any concept. The goal is to be deliberate ad intentional about number selection and problem situation when designing lessons and choosing sample problems. Frequent formal and informal assessment on these three target areas, and intervening during structured small group time, fills gaps in student understanding while connecting ideas to course content.

Three target areas of focus:

1. Understanding representation of number by focusing on tens and parts.

a. Knowing how adding, subtracting, multiplying and dividing by 10 affects numbers.

b. Being able to break apart and put together numbers in different forms to ease computations.

2. Understanding the concepts of subtraction and division.

a. Relating subtraction to take away as well as distance and range.

b. Being able to “see” division in two ways: number of groups and number in each group.

c. Knowing that subtraction and division are less flexible than addition and multiplication because they are not commutative.

d. Seeing fraction as division.

3. Applying tens, parts and operation of number to 3 abstract concepts: Time, Money, Measurement

Component #8: Rich Tasks and Problems

What tasks am I providing that give students experience with the Mathematical Practices?

How do I teach students to embrace their own habits of mind through open ended tasks and problems?

How do I plan and develop questions to extend problems and tasks for a greater depth of content?

Am I balancing the types of questions such that there are many that promote thinking?

How do my tasks and problems stimulate curiousity and make kids thirsty for learning?

What tasks, problems and questions promote student engagement?

Do I allow for a variety of ways for students to show understanding?

*Rich tasks can be found at a variety of websites, some listed below. To make any problem or task “rich,” the first step is to give students the situation and remove the questions. Second, allow students to create the math questions themselves. Finally, create variations to each task or problem (“what ifs”) to provide more depth of content. Try not to move away from tasks and problems too quickly as to force student (and teacher!) persistence and perseverance. After introducing a problem or task, give students plenty of time to just make sense of the information. Solving is not the first step and it’s not the last step.

See Rich Task Ideas Here

The next two components can be classified as Extension.

How do we get the extension and depth of content and move away from the “mile wide, inch deep” trap?

There are 2 answers for this:

 Component #9: Questions

How do I design questions that meet individual student needs?

How do my questions promote student curiosity, engagement and thinking?

How do my questions target the Big Ideas?

How can I “stop planning lessons” and “start planning questions”?

How do my questions “make kids thirsty” for learning?

What opportunities do I provide for students to create math questions for tasks and problems?

*The idea of “teaching with questions” connects back to the theme of the newsletters earlier this year. Questions have the power to engage and motivate students as well as scaffold and extend the content. Questions allow for differentiation. Questions can extend tasks and problems allowing for the depth of content. Planning daily questions can be the new way of lesson planning!

Component #10: Connections

What connections are made between units of study throughout the year?

How do I connect content from previous grades to the content in my course?

How do I connect abstract/algebraic content to a concrete and visual representation?

Does each unit of study connect to each of the 3 Big Ideas: Number, Rate and Function, Space and Dimension?

*Students do not naturally make the connections between each concept and skill that is taught. They need to see how each lesson, topic and skill connects to previous learning. Choosing tasks and problems that can be extended and varied allows for opportunities to bring in multiple concepts at the same time. By teaching multiple concepts at the same time, students begin to see how different area of mathematics are related. To make math accessible to all students we must make math visual and make math connect!





Learning is a Journey- 3 Day Common Core Event

Transformational Instruction and Minds on Math presents an Educational Event!

3 days featuring four national presenters

Learning is a Journey

Inspire students along the way!

This 3-day professional development provides answers to questions about how to implement the Common Core State Standards. Look no further for the current Best Practices in education from assessment and instruction to classroom structure and intervention. Don’t miss this unique “one stop shop” PD opportunity to hear from four leading experts in math and reading in the content! Register today!!

Monday, June 16 – Wednesday, June 18, 2014

Daily 9am – 3pm – – Light breakfast and sign in at 8:30 AM each day

At the beautiful!! – – Cherry Valley Lodge, 2299 Cherry Valley Road, Newark, Ohio 43055, 740-788-1200

$199 per day – – Please call 740-964-9652 for multiple day and group discounts!

Reading Made Easy: Content Area Reading (Monday, June 16 – – Grades 5-12)

  • Featuring Erica Holton & Joe Soss, Concept Core Consulting, LLC,
  • Learn how to integrate vital reading and writing skills into any content area curriculum to help students unlock content knowledge as well as improve literacy skills. Integrating the Common Core is truly made easy by using question stems to facilitate higher-level thinking. With Reading Made Easy: Keep your curriculum. Add the skills. Ensure student success.

Using Rich Math Tasks to Bring Common Core Alive! (Tuesday, June 17 – – Grades k-12)

  • Featuring Jonily Zupancic, Minds On Math, LLC
  • Engage and motivate students with rich tasks, problems and questions that teach deep mathematical concepts in less time. Individualize instruction for maximum student achievement by promoting a “minds-on” instructional model. Increase student independence and accountability by providing a culture of thinking with a focus on learning.

Balanced Guided Math (Wednesday, June 18 – – Grades k-8)

  • Featuring Angela Bauer, Bauer Educational Enterprises LLC,
  • Learn how to implement a guided math framework, incorporating large group mini-lessons, teacher-led guided groups, and engaged math stations. Leave with several schedule options, math station ideas, guided group planning details, assessment tips/recording sheets, and spiral review expertise. Guided math fits with your district’s curriculum and standards.

Register by Friday, May 30 by calling 740-964-9652 or email

Pay by check or credit card after registering by phone or email.

Reserve hotel by Friday, May 16 by calling 740-788-1200

Mention “Transformational Instruction” to get a special room rate!

Learning is a Journey Flyer

Rich Task- Choir Problem

The Choir Problem:

Rich Task- Math

Rich Task- Choir Problem

The school choir must have concert programs printed and they have contacted 2 companies for prices. Company A charges an initial fee of $10.00 plus 4 cents for each program printed. Company B charges 2 cents per program with an initial set up fee of $30.00.

What math questions have students created for this situation?

What is a “typical” question for a situation like this?
(Which company is the better deal? At how many programs will the cost at each company be the same?) These typical questions aren’t always as important as the questions that lead us to this point or the questions that extend beyond.

Below are some examples of student and teacher created questions…

-What does “per” mean?
(Great question! Can have lots of discussion about this little 3 letter word.)
– How is 4 cents written as a decimal?
– How is 4 cents written as dollars?
– How many programs are needed?
– How many people will attend?
– If 300 people are to attend, which company costs less?

– Which company is cheaper for 5 programs?
– How much do 5 programs cost at each company?
(The same question can be asked in different ways to allow for more students to make sense of the problem and have access to finding a solution.)
– How many programs can be purchased at Company A for $20?
(This question can be answered by all levels of students. Some students may use a table, others may guess and check, some may solve with an equation.)

– Write and expression for the function for Company A.
– Define the variables for this situation.
– Suppose this is a large concert at a concert hall and 3000 programs need printed. Which company is cheaper?

– How many programs can be purchased at Company B for $40?
– How many sets of 4 cents are in ten dollars?
– How many sets of 2 cents are in ten dollars?
– How many cents are in ten dollars?
-How many pennies are in a dollar?
-How many quarters are in a dollar?
-How many nickels are in a dollar? (this stumps many middle school students)
– What percent of $10.00 is 2 cents?

– What fraction of a dollar is 2 cents?

…I have gone off in left field with the last few questions, but these include one of the 3 concepts that students in secondary grades struggle with. The 3 concepts are: Money, Time and Measurement. It is valuable to digress to these concepts as often as possible to continue to build number and fill gaps with these ideas.

– How much are 500 programs at Company A?
– If I have $60 to spend, how many programs can I purchase at each company?
– What is the “rate” for each company?
– How are “rate” and “per” related?

– If Company C charges $20 and 4 cents per program, how does the cost of this company compare to companies A and B?

– If the cost of programs is graphed for each of the 3 companies, how can the graph be described?

– At how many programs do company A and B cost the same?
– At how many programs do company A and C cost the same?
-Describe the graph of the number of programs and costs for company A and C.

– Use the Rule of Four to present solutions to the questions above.

> The Rule of Four is a way to represent situations in 4 ways:
1. Numeric (numbers and tables)
2. Graphic (graphs or pictures)
3. Situational (words or patterns)
4. Algebraic (expressions and equations)

This situation and questions explore concepts from money to fraction to solving equations with no solution. The opportunities for differentiation are presented by the number of questions and the variety of questions. By spending time one problem, students have time to think and process. The result is depth of content and learning.

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7 Signs That Your Students Are Not Thinking

Are your math students thinking? Are they actually thinking? Or are they mimicking your thinking? [Click to Tweet]

How can you tell if your students are not thinking? What can you do about it?

1. You are doing all/most of the math.

During a 45 minute class period, the teacher should not be doing math for more that 15 minutes. Your students should be doing the math the majority of the time. You should not be at the board working through problem by problem, step by step. By doing this you are the one thinking in the classroom. Even if you ask your students the next steps in the problem, not all of the students are putting thought into the problem.

They should be the ones doing the math. Asking each other what the next step in a problem should be. Presenting their ideas and solutions.

2. Your students are not struggling.

Achievement without struggle can be meaningless and forgettable. Students should have to struggle to complete math problems. If your students are not struggling the reason can fall into two categories.

1) You are asking questions that are too easy. Questions should be doable for students but should require effort. Students should not have mastered all of the skills necessary to complete a problem. They should be learning as they work through a problem.

2) You jump in to save the day too quickly. As a teacher we want to help our students. Sometimes helping too early and too often can harm our students. You need to allow students time to think, process and persevere. Students can also develop a learned helplessness. If they know that you will jump in and walk them through a problem, why would they work through it on their own?

3. Students are not given rich problems/tasks.

Students should be solving problems in context. They should be surrounded by a scenario, picture or video. Problems should be connected to a meaning. Students should have to spend time figuring out   what the question is asking and what the steps to solve are. Giving students a worksheet full of problems out of context simplifies this process and doesn’t allow students to make connections.

4. Your students are only answering questions you are asking.

Students should be involved in creating the question they answer. Present your students with a scenario/picture/video without any question. Have them create the questions. Coming up with questions to ask instead of answering questions allows students to think of problems in a different way.

5. They look bored and you have the same group of students always participating.

This is a well known sign that your students are not thinking. If day after day students are not engaged take a look at the structure of your classroom. What can you change to get more students active and involved?

6. They have difficulty applying knowledge to a different type of problem.

If students cannot apply knowledge from one problem to the next, they have not mastered the knowledge to begin with. This connects with giving the students problems to solve in context. Working through problems in context provides more opportunities to connect to different problems allowing students to transfer their knowledge.

7. They do not have choice in any assignments they complete.

Choice can be a powerful thing for students. If students are given a choice in certain assignments, they put thought into which assignment they want to complete. They can analyze their strengths and weaknesses to decide which assignment they want to work on. This allows them to become more in-tune with themselves as math students.

Rich Task- Muggsy Bogues 2

In the previous post I introduced you to this rich picture.

Rich tasks using basketball players

Rich tasks using basketball players

And we completed steps 1-3 of using rich tasks in the classroom. On to step 4.

4. Provide differentiated questions.

Here is a list of questions that you can add to your student generated questions.

  • Who are these two players?
  • How tall are each of them? In inches and centimeters?
  • What is the difference in the player’s height?
  • Who is the tallest player in NBA history? How tall is he?
  • Who is the shortest player in NBA history? How tall is he?
  • What are the Mean, Median, Mode and Range of the heights of players currently in the NBA? Or a certain team?
  • How does this compare to players in college? Or a certain college team?
  • How does the mean height in the NBA compare to the mean height of men in the United States?
  • What is the sock length for each player?
  • What is the total volume for all three basketballs?
  • What is the total surface area for all three basketballs?
  • What are the player’s shoe size?
  • Graph the relationship between a player’s height and their shoe size. (From a certain NBA team or a set of NBA players).
  • Find the line of best fit for this graph.
  • What is the equation?
  • Based on your equation, what size shoe should blank, blank, and blank wear?
  • Graph the relationship between a player’s height and the amount of points they scored.
  • Is their a correlation.

As you can see you can ask a range of questions sparked from one picture or situation. Not all of these questions are specifically from this picture. That is fine. Those were questions brought up based on the curiosity sparked from the picture. A lot of the questions involve the students doing research to find the answers. They will become active in the classroom. This list also covers many different topics. Rich tasks allow you to cover more content than isolated problems.

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Rich Task- Muggsy Bogues

In my previous post I talked about the 6 steps to implement rich tasks into you classroom. I will be posting pictures, videos, scenarios that you can use in your classroom. Some of these I have used before and have a set of questions that you can add to your student generated questions. Some of them are brand new and I hope that we can create the set of questions.

1. Find a situation/scenario/problem/picture/video

Rich tasks using basketball players

Rich tasks using basketball players

Here is a picture of two basketball players. (I know their names but I am not going to tell you.) Don’t give your students too much information. Make them curious.

2. Remove all questions

This was easy. There were no questions attached to this picture.

3. Gather student generated question

This is where you come in. Send me math questions that can be asked from this picture. Add a comment or Tweet me. Once I get a good set of questions I will post them.

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