Sunday, December 30, 2012

Math Task

I used this math task with my advanced third graders. This task can easily be adapted for other grades simply by changing the number of quarters. To begin the lesson, I asked students to identify the patterns posted on index cards that were handed to them as they walked into class. The patterns on the cards were similar to the following ~ Pattern #1: 3, 5, 7, 9... Pattern #2:  A, A, B, B, C, ... Pattern #3: 11, 22, 33, ... Depending on the readiness levels of your students, you can adjust the patterns you use to launch the task. Students were asked to discuss the patterns and identify some of the similarities and differences amongst the patterns. This was used to activate thinking and set the stage for the task. Then we discussed the meaning of the word pattern.

Once this common foundation was established, we reviewed the "I can..." statements for the task. Setting clear targets of learning can help to set a purpose for student engagement. Click the image below to see what we focused on during this task.

Before actually working on the task in collaborative groups, we spent time deconstructing the math task as a whole group much like we deconstruct text in reading. I posted the math task on chart paper for all to see. As a class, we discussed the meaning line by line. The goal was to remove barriers and create a clear picture of what was intended so once the students got started, they would be ready to tackle the task. A few minutes upfront saved minutes of work time and fewer hands went up.

This task not only ties into the CCSS, it also allows for students to practice Mathematical Practice #1: Make Sense of Problems and Persevere in Solving Them. My hope was once students began this task after we deconstructed its meaning, they would be able to dig deep and continue working even when faced with a challenge and most importantly be able to justify their answer by using more than one strategy. Click the image below to grab a copy of the math task.

Graphics by
With a few minutes left of class, students briefly shared their procedures with each other and then completed a Lesson Recap. This was used to help me better understand the level of understanding of my students and where I would need to take them the next class period. A quick formative assessment can help to synthesize learning for the students and provide valuable information to guide further instruction. Click on the image below to download a copy. 


Sunday, December 9, 2012

Bloom's Taxonomy Question Stems

Questioning at a higher level can encourage students to explore deeper understandings of the concepts being taught. As a visual reminder of higher level questions, I use question stem cards and put them on a ring. The question stems come from Bloom's Taxonomy. Questions are leveled. Each level of Bloom's Taxonomy then is put on a different colored index card. This helps to quickly identify question stems that I want to use during a lesson.

When I am doing whole group instruction or small group instruction, I can pick up my ring of cards and differentiate the type of questions I am asking my students to foster deeper conversations. Click on the image and get your own copy of some question stems from the lowest level of understanding which is remembering to the highest level of understanding which is creating.

Saturday, December 8, 2012

Another Look at Math Vocab & Graphic Organizers

Use graphic organizers to deepen understanding of key math vocabulary words in the math classroom. Here are a few graphic organizers that you can download by clicking on the images. The Frayer Model helps students to develop a deeper understanding of complex concepts and can be modified and differentiated to address the readiness levels of your students. Depending on the focus of learning,  the descriptors in the Frayer Model can be changed. Once students have used this graphic organizer with various different descriptors, give students a blank organizer. Then have students fill in the descriptors that they feel will help them best learn the essential vocabulary.

A concept definition map can help students conceptually understand a word by looking at it through different lenses. 

Connect Two is a strategy that can help students see associations and connections between different words. Take two words from the math word wall and see if students can look beyond the literal definitions of these words. Why not try connecting three words sometimes? This strategy can help students to develop associations and see the interconnectedness of math vocabulary.

Along with graphic organizers, using a math word wall can help to foster vocabulary development. If you are looking for a resource that has cards to use for a math word wall, click here: Math Vocabulary Cards.

Monday, December 3, 2012

Text Complexity Bookmark

Text complexity. Taking a new look at the text we use with our students in the classroom. This bookmark tool may be helpful when trying to determine the level of complexity of any given text. By looking at the different layers of a text, we can determine if a particular piece of text is appropriate for a given grade level. The type of text we ask students to read needs to meet the requirements outlined by the CCSS if we are to adequately prepare our students for anchor standard R.CCR.10. This anchor standard states that students should be able to read and comprehend complex literary and informational texts independently and proficiently. Click on the image to get your copy of the bookmark.

Reader Task Considerations: Text Complexity Bookmark

When considering text complexity, it is more than just difficult text.  Qualitative measures, quantitative measures, and reader and task considerations are interwoven elements that can create a complex reading experience for students. By taking a close look at the complexity of the task assigned when students are given a text to read can raise the rigor. Creating bookmarks targeted at a specific focus is one way to create a complex task. Check out the samples by clicking on the image below.

Wednesday, November 28, 2012

Differentiate in the Math Classroom & Have Students Think Deeply

Welcome Chicago! Here is the PowerPoint for this morning's session. Hope you find an idea that you can take back to your classroom and use with your students.

Exploring Subtraction of Fractions

With CCSS students will need to explore mathematical principles, look for patterns and routines, and demonstrate conceptual understandings. In a fifth grade classroom, our students were subtracting fractions and mixed numbers. I wanted our students to grapple with the process and not just be given the steps. Students were given the following task.

In groups, students were asked to look at the subtraction problems and identify rules and patterns that they noticed. Engagement and critical thinking were clearly evident during the small group discussions. The subtraction problems were purposefully arranged to build on each other. After verifying the rules and patterns, students completed the Try It Out! problems to demonstrate understanding. Then came the big challenge. How could our students then apply these learnings to the ultimate subtraction problem...a problem with uncommon denominators and renaming? Click on the image for your copy if you would like to try this with your students.

Tuesday, November 27, 2012

Number Talks to Get Students Thinking Number Sense

I recently read Number Talks by Sherry Parrish. I thought I would give Number Talks a try to ramp up my fourth graders thinking with multiplication. Like many students, once they learn the algorithm, boom, it becomes a rote, automatic process. But my question my students really understand the conceptual meaning of what it means to multiply and what the process really represents?

A Number Talk should take no more than 15 minutes. The ultimate goal is not the answer, it is the processes used. Yes, I said processes, multiple representations. Students are asked to solve the problem using mental paper pencil. Put those pencils down and get those thinking caps on! Once students are able to determine the answer, they give a silent "thumbs up." It does not stop there. Students are encouraged to come up with other ways to solve the problem. When they determine another process, they put up another finger. Are you beginning to see how process is the focus. The silent "thumbs up" gives all students a fair chance to solve the problem while challenging those fast finishers to keep thinking.

The first problem we worked on was 25 x 7. I showed students the problem written horizontally. Remember no paper pencil is allowed. It was silent in the room, and then thumbs started to pop up. After a few minutes, everyone at least had their thumbs up. I asked students to share their answers. At this point, all answers are recorded and respected. Through discussion answers are confirmed, defended, or rejected. Students then went on to share the processes they used to solve the problem. One student explained that  20 x 7 = 140 and 5 x 7 = 35. Then the student went on to add 140 and 35 to get the answer of 175. Another process showed that 4 x 25 = 100. When doubled, it would be 200, but then 25 had to be subtracted because there were only 7 25s and not 8.

We then went on to 12 x 15 written horizontally. Now remember students are encouraged to think and solve using mental math. I will keep the examples short here. One student said he took (12 x 5) + (12 x 5) + (12 x 5) = 180. WOW! When I asked the other students why he did this, they chimed in, "Well, he broke down 15 into three 5s." Why 5s? "It is easier to multiply by. It is like a benchmark," they added. This was the first time my students engaged in a Number Talk. Conceptual understanding of number sense was definitely shown here. Give a Number Talk a try and see the different strategies students can use to a solve problem. Model and guide students to new ways of approaching problems to build their understanding of number sense and various processes. Manipulate and play with numbers to solidify understanding.

Sunday, November 25, 2012

Using a Word Bank to Foster Vocab Usage

The language of mathematics is important. With CCSS students are going to be expected to communicate precisely and accurately (Mathematical Practice 6: Attend to Precision). In addition, students are going to be expected to explore math concepts and use math vocabulary to explain  math processes (Mathematical Practice 3: Construct Viable Arguments and Critique the Reasoning of Others). Try adding a word bank to mathematical tasks to encourage the usage of specific math vocabulary. It is important that students have been explicitly taught the meanings and conceptual understandings behind the words before they are asked to use them. Repeated exposure and authentic usage can help math vocabulary to be meaningful, specific, and precise. See how the following activity was adapted using a word bank. Students are asked to use specific math vocabulary to defend their thinking. Click on the image to grab your copy.

Friday, August 10, 2012

Math Vocabulary: Graphic Organizers and Movement

Vocabulary in the math classroom can sometimes be challenging for students. Look at the chart below to see how math vocabulary can be looked at through different lenses.
Math vocabulary can have multiple meanings. Think about the word gross. A math gross (noun) is very different than a gross (adjective) mess. Some vocabulary words are specific to math so repeated exposure outside the math classroom might not often happen. Outside of the context of math, where have you seen the word algebra used? Whether through explicit or implicit instruction, students can benefit from vocabulary instruction that takes on multiple modalities.

When introducing math vocabulary, try using a graphic organizer. The Frayer model lends itself to differentiated math instruction. It also helps to represent words in more than one way. Click on the image to grab a copy. There are differentiated versions for the different learners in your classroom.

Memory for learning can be enhanced by utilizing movement for instructional purposes. The movement increases sensory input to the brain. (Wolfe 2001) Try adding movement activities to teach and review math vocabulary. If you click on the image below, you can find four different ways you can incorporate movement into the math classroom while teaching/reviewing vocabulary. These activities can be used as a "brain break" to get students up and moving while still learning! Use words that are part of your Math Word Wall to review. If you have other ideas of movement activities that can be used with vocabulary, please share! 

Monday, August 6, 2012

Math Differentiation in a Nutshell Template

Elementary Example
With the school year just around the corner, we will be facing a whole new class of students with different readiness levels. How do we reach each student? Are there multiple entry points of learning so we can hook all our students? Do we have a list of resources/ideas to address those students who are below target, on target, and above target?

Middle School Example
This is a template I have used in the past to help brainstorm and create a resource for differentiation in the math classroom. You can see a few different examples and the variety of resources listed. Two of the templates were compiled by teachers in my district during some differentiation training I facilitated. One was completed at the elementary buildings. Currently, our math program is Trailblazers. Another one was completed at the middle school. Currently, our math program for grades 6-8 is Connected Mathematics 2 (CMP2). Once this template is filled out, it becomes a friendly reminder of "go to" resources when trying to address the various readiness levels of our students. This template certainly does not have to be completed by buildings. The benefit of this, however, is there are many teachers contributing ideas. Collaboration is a powerful tool!

Classroom Example
For personal classroom use, the template can be filled out for a particular concept. See my 3rd grade example using Common Core standard 3.MD.1. You can see how the Common Core standard is included. Specific activities/resources to address different readiness levels are listed as well. The key to any learning opportunity is closure/synthesis. Notice how I included "I can..." statements at the bottom of my 3rd grade template.

Some of the ideas/math tools listed on my 3rd grade differentiation template on time can be found pinned on my Pinterest. Click here and preview some of my boards. At this time, I have devoted Pinterest entirely to math! Need some ideas, find a board that relates to your topic of study and find resources you can use with your students to address their various readiness levels! It is amazing the resources that are out there that teachers are willing to share.

Grab a copy of any of these templates by clicking on the image or images of choice!
Blank Template

Sunday, July 29, 2012

Math Vocabulary Cards

Looking for a resource for math vocab cards. Check out the following link. Vocab cards are categorized by grades K-5. Visually appealing cards that can become part of a Math Word Wall.

Saturday, July 28, 2012

Math "Scrunchie" (aka Cootie Catcher) for Adding and Subtracting Time

Use this math "scrunchie" as a way to reinforce adding and subtracting time. I use the term "scrunchie" because we really aren't telling fortunes nor catching cooties when we use these in the math classroom :)! "Scrunchie" actually comes from the UK and that's what my students do when they use this foldable...they scrunch it together. Creative Teaching Press has published books using math cootie catchers to reinforce skills/concepts by grade level. The authors are Sharon L. Apichella and Mary D. Sutton. Using the one on time from the book and designing my own allowed me to address the different readiness levels of my students. I designed this "scrunchie" with a Common Core standard in mind for 3rd grade. When differentiating in the classroom, it is important that students have instruction and tools at their readiness levels. This kinesthetic and novel approach to reviewing skills can help to solidify understanding! Its self-checking nature provides students with immediate feedback. Click on the image below to grab a copy!

Friday, July 27, 2012

Literature in the Math Classroom

Literature can create a meaningful context for math concepts being taught (Price, Lennon 2009). Here is a brief list of math books that can be used to introduce, reinforce, or enrich a math concept. Click on the image below to get a copy of the list.

Questioning in the Math Classroom

What do students do when they do not know how to get started? What do students do when they get stuck? I have created questions that students can ask themselves in these situations. As 21st century learners, students need to be independent problem solvers. Modeling how to use these questions with students can help them become more responsible for their own learning. Modeling can be done during a whole group think aloud or during small group instruction.

The questions are color-coded. If students do not know how to get started on a problem or task after instruction and directions are given, the green cards can be used. Green means go. If students get stuck while doing a problem, the yellow cards can be used. Yellow means slow down and use caution. When students are done, are they really done? The red cards can be used to encourage students to stop and think about the reasonableness of their answers. Red means stop. In all these instances, students are self-regulating their own learning and asking themselves questions. By having these questions available to students on a ring or to put in their math notebooks, students can become better questioners. What's even better, students can learn to ask questions that they themselves have to answer in order to move their learning along. Encourage students to ask themselves THREE questions before they raise their hand to ask for help..."Ask yourself three before you ask me."

Want students to think deeper? Encourage students to ask themselves questions similar to those found on the purple cards. For those early finishers, ask students to answer one of the purple questions. These questions are designed to extend thinking and encourage higher level thinking. Ultimately in math, we want students to think beyond the answer!

How can you encourage student participation during small group instruction? Have the black cards available for students to use during small group. The black cards were cut out and hot glued to a Popsicle stick. I chose to put all these questions on black so students would not associate a particular question with a certain color. While discussion is occurring in small group, students can pull a stick and be asked to share their ideas to the question they find on their stick. To differentiate, look at the questions and hand out the question that you think best fits the readiness level of each student. While doing a math think aloud have these questions available. After modeling, ask students to share their thinking to one of these questions.

These questions are just a start! Once students become comfortable with self-questioning or questioning to dig for deeper meaning, they, too, can generate new questions that you can add to the collection. Click the image below to grab your own copy!

Thursday, July 26, 2012

Small Group Instruction ~ Record Keeping

Small group instruction in the math classroom provides differentiated learning opportunities for students. Keeping track of student performance and progress sometimes can present a challenge. Here are two different versions of recording sheets you might find helpful to use with your students. One recording sheet can be used for all students in a given group on a given day. Recording key observations for students in a small group can help to plan future instruction for each student. One key to successful differentiation is flexible grouping. Keeping track of whether students are below target, on target, or above target for a given standard/objective can help in planning the next stages of instruction. The second recording sheet can be used to track student performance for given standards for a given unit. The follow up information that can be recorded includes the different learning experiences whether it involves remediation, additional small group instruction, enrichment, extension, etc. Grab a copy by clicking the image below.

Student MI Chart

Using Multiple Intelligences to differentiate process is one way to tap into students' learning styles. Have students complete this MI chart, filling in the bars to represent their learning preferences. Use these charts to help plan different learning opportunities that address the learning styles of your students. Students can be grouped according to their preferences. Students also can be encouraged to tap into some of the other intelligences that are not their preferences. Display your students' MI charts prior to the beginning of the year parent meeting and see if parents can pick out their child's MI chart. Parents, and students, can visually see the diversity of the students in your class this year. Click on the image below to grab your copy.

Midwest Diff Conf ~ Chicago

Thank you to all those who attended the session on Differentiate Your Math Instruction to Maximize Learning at the conference Tuesday morning. What a fantastic group of teachers! Keep checking back. I will be uploading the resources from the presentation in the coming days.

Tuesday, July 17, 2012

Fraction Learner Menu Using Thinker Keys

Thinking is essential in math. I am always looking for ways to push the level of thinking of my math students beyond just calculating an answer. With Common Core, students are asked to show multiple representations and dig deeper into mathematical understandings. Using Tony Ryan's Thinker Keys, I designed this Learner Menu for students to use to push the level of conceptual understanding of fractions with some higher level thinking. The Learner Menu could be used after instruction has taken place on the key concepts. Notice how the criteria at the top of the menu asks students to demonstrate their mathematical thinking and understanding when completing the tasks. Also notice how there is not one right answer, and sometimes that answer is not "right there.

Thinker Keys are a tool teachers can use to embed thinking into any lesson. They can be used as part of a Learner Menu as seen here. Thinker Keys can start a lesson. To encourage Math Talk, Thinker Keys can be used as part of small group work. In 2005, Tony Ryan, a Learning Consultant from Australia, updated the Thinker Keys. The earlier version, which is used on this menu, helps to foster creative thinking while focusing on deeper understanding of the standards. If you would like to learn more about the Thinker Keys, click on the links below.

Friday, July 13, 2012

Need a Hand? Try This!

What can students do when they recognize they do not understand what to do in math? That is besides asking the teacher for help or saying "I don't get it." Students need strategies in math, just like in reading, to help them overcome the hurdles when understanding breaks down. I created these "Need a Hand? Try This" cards to provide students with strategies that they can try independently. You know that saying, "Ask three, then me." Well, using these strategies, the mantra can be, "Try three, then ask me."

I used die-cut handprints, labels, and a metal ring to make this resource for students to use. My goal is to have students persevere and be independent learners even when things do not come easy. These strategies can be modeled during think alouds so students understand what each strategy "looks like" and "sounds like." These strategies can empower students.

You can grab a copy of the strategies by clicking on the image below. Just use 1" x 2 5/8" labels when printing a copy. These strategies also can become part of students' math notebooks or used as part of a bulletin board display.

Need a Hand? Try This!

What can students do when they recognize they do not understand what to do in math? That is besides asking the teacher for help or saying "I don't get it." Students need strategies in math, just like in reading, to help them overcome the hurdles when understanding breaks down. I created these "Need a Hand? Try This" cards to provide students with strategies that they can try independently. You know that saying, "Ask three, then me." Well, using these strategies, the mantra can be, "Try three, then ask me."
I used die-cut handprints, labels, and a metal ring to make this resource for students to use. My goal is to have students persevere and be independent learners even when things do not come easy. These strategies can be modeled during think alouds so students understand what each strategy "looks like" and "sounds like." These strategies can empower students.

You can grab a copy of the strategies by clicking on the image below. Just use 1" x 2 5/8" labels when printing a copy. These strategies also can become part of students' math notebooks or used as part of a bulletin board display.

Wednesday, July 4, 2012

Guess My Favorite

Here is a quick activity to hook students into a lesson or use as a bell ringer to start class. Tie in Common Core with logical reasoning. You can create the activity with a specific target of learning or have students create the template and share with classmates. Click here for your freebie.
Guess My Favorite

Common Core

The convenience of having Common Core at your fingertips can be done using this widget. Visit the link below to see how to embed this handy resource onto your blog. If you look to the right of this blog post, you can see how you, too, can have Common Core at your fingertips.

Try it out!
Thanks Lori at for sharing this!