Math Empowers 4

Middletown Township Public Schools

Grade 4 - Third Trimester 2017-2018

Which One Doesn't Belong?

The Which One Doesn't Belong? activities effectively promote mathematical discourse among students. Students enjoy the images and are motivated to share their mathematical reasoning to support which one doesn't belong. Check out this amazing resource to engage your students today! Or see all of the resources here. Remember there are no answers provided as there are many different, correct ways of choosing which one doesn't belong. Enjoy!

Estimation 180

The Estimation180 website by Andrew Stadel has estimation activities for each day of the school year. These activities help students improve both their number sense and problem solving skills. Check out this amazing resource to engage your students today! Or see all of the resources here to help build number sense one day at a time.

Depth of Knowledge

Webb's Depth of Knowledge (DoK) categorizes tasks according to the complexity of thinking required to successfully complete them. DoK is a way to think about content complexity, not content difficulty. Complexity is different from difficulty. The DoK levels describe the kind of thinking required by a task, not whether or not the task is “difficult”. For all subject areas, there are four DoK levels. A summary of the mathematics DoK definitions is below:


Level 1: Recall

This level involves basic tasks that require recall of facts or rote reproduction of simple procedures. These kinds of tasks do not require any cognitive effort beyond remembering the right response or formula.

Level 2: Skills and Concepts

This level requires a student to make some decisions about problem solving and procedures. DoK 2 tasks may involve applying a skill in a new context or explaining thinking in terms of concepts.

Level 3: Strategic Thinking

This level gets more complex and abstract. Students must use reasoning, planning, and evidence to explain their thought processes. Often, Level 3 tasks have more than one valid response, and students must justify their choices..

Level 4: Extended Thinking

Level 4 tasks are at least as complex as level 3 tasks but require an extended time period—several weeks, perhaps, or even longer—to complete.


Robert Kaplinsky has developed his own user-friendly Elementary Depth of Knowledge Matrix. Check out the matrix below to see some ideas to develop content complexity for students. Click here if you would like to read more about Depth of Knowledge from Robert Kaplinsky.

Angling for Students’ Mathematical Agency

In the recent "Teaching Children Mathematics" article entitled Angling for Students’ Mathematical Agency, researcher José Manuel Martínez and teacher Laura Ramírez worked with a group of fourth graders on measuring angles with protractors. The students went from overreliance on protractors to relying on their own reasoning and understanding of how to measure angles. Instead of focusing on correcting students’ use of the protractor, the researchers focused on what the interaction said about student mathematical agency. Students expressed mathematical agency by (1) challenging the protractor’s effectiveness in helping them measure angles and (2) by imagining an alternative tool. The researchers found that student mathematical agency shifts the locus of knowledge authority from the teacher or the textbook to the students. A “productive struggle” was embraced, helping students grapple with ideas and relationships among angles, measurement, and the protractor.

The Final Countdown

There are so many options for math class beyond the book! Here are some end of year ideas to consider working into your math class. Ignite mathematical thinking in the last weeks of school!

  • “Getting Ready for Grade 5” (Planning Guide)
  • Critical Area Projects (Think Central)
  • INVESTIGATIONS games and activities
  • Problem of the Month or MARS tasks (Cybrary)
  • Revisit the BEST of the BEST online interactives from the resource document.

Summer DreamBox Challenge - 2018

This summer's DreamBox Challenge is all about growth! Persevere through the tough lessons and grow your brain this summer! The school with the greatest growth percentage wins the Summer DreamBox belt! The competition runs July 8th through September 1st.

Growth Mindset

Incorporate Growth Mindset into your summer reading list!


Changing the way we talk to our kids is one step towards helping to reinforce the message of a growth mindset. Another is to read books to kids with stories that convey a similar message.

Click here for a list of fourteen books that let kids know it’s OK to not at first succeed, that failure and challenges can be viewed as opportunities rather than dead ends, and that determination often results in a far better outcome than being perfect.

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Danielle Seibert

Elementary Math Specialist