Filing cabinet of Warm Up Activities

There are so many great class opener activities that I decided I need a place to document them all so that I can make sure I’m am choosing the best tasks for my students.

I wrote an article on ways to use Warm Up Routines in the Winter of 2017

Here is an (editable) copy of my warm up sheet.

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• Sadie Estrella’s Counting Circle because it develops number sense, mental math, and community
• Mary Bourassa’s Which one Doesn’t Belong? thought-provoking puzzles. There are no answers provided as there are many different, correct ways of choosing which one doesn’t belong.
• Elizabeth (@cheesemonkeysf) Talking Points because students practicing listening to each other will seep into every lesson, every day. It can be used as a tool to develop their growth mindset and, bring out and clarify misconceptions.
• Andrew Stadel’s estimation Builds number sense & measurement
• Fawn Nguyen’s Visual patterns Develop algebraic reasoning skills
• Find the Flub through the week I photograph good student errors, then choose 1 for students to correct and analyze each week. Similar to my favorite no. I sometimes use errors from Michael Pershan’s mathmistakes.org
• Balance puzzles Help students to solve & understand algebraic equations
• Agree or disagree math & Would you Rather? for sparking a debate
• Daily SET puzzle and how Michael Fenton implements it here
• Mental Math basic math skills review. No calculators.
• ACT question of the day
• Dan Meyer’s Graphing Stories Helps students create graphical representation of real events, described here.
• Number Talks Build computational fluency using number relationships and the structure of numbers. Fawn set up a site which gives an idea of how these are supposed to go. This article by Sherry Parrish describes it well. I’ve found this worthwhile even with high school students.
  • Also, this! Number Talk Images. I am overwhelmed at the information and content found on this site!
• Fraction Talks are a new, fun tool for fraction number talks.
• Dan Meyer’s 101 Questions website is an amazing Notice & Wonder resource. I do it where every student has to come up with a mathematical question for the image or video that randomly comes up that day
• Robert Kaplinsky’s Open Middle Problems
• Chris Luzniak’s Table Debate More info from his TMC15 presentation here
• Dylan Kane’s Match my Graph
• I can’t wait to try Clothesline Math next semester!

“The Clothesline is the master number sense maker.”

• Marisa W @viemath does Mindset Moments occasionally. Her Words:
  

  After watching the video, all I would ask every time is, “What did you think is the message in this Mindset Moment video? What is your one big takeaway?”

• Area Mazes These would be great for supporting number sense, equations, factors

Do you have a warm up routine or activity that is beneficial to students, but is not on this list? Recommend it here:

Squares, Area & The Pythagorean theorem

After a few days working on surface area, I wanted to challenge my students and address the standard listed below by with a task that applied area in a different context. I debated about using this task because I couldn’t envision how I would engage students and encourage them to persist in proving that a square of certain areas on a coordinate grid is not possible.

HSG-GPE.B.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

Here is the task from Illustrative math (click on the image below to go to their site)

I started class by providing each student with a grid whiteboard and marker and I asked them if they could draw a square whose area is 1 square unit. They did this with no problem and sat looking at me like I was crazy.

Next, I asked if it was possible to draw a square whose area was 2 square units, with the corners on the grid. Common student responses below:

• “It’s impossible!”
• student draws a 1 x 2 rectangle
• student grabs calculator and computes the square root of 2, then attempts to draw a square with sides measuring exactly 1.41421356 units long.
• student divides 2 by 4 draws a square with sides 1/2 a square long, then realized its area is 1/4.
• student divides 2 by 2 and draws a 1 x 1 square, realizes this is their square with an area of 1.

So THIS is what Robert Kaplinsky means when he talks about Depth of Knowledge! It was very insightful to show student understanding of squares, length, area, and what a square unit means.

Eventually a few students said they figured it out, and were so excited to explain to me how they knew it was a square and how they know its area was 2 square units.

I asked students to try drawing a square with integer each area from 1-10 & students were engaged all period. We kept track of the areas that students thought were not possible.

The next class period I gave students whiteboards and a sheet of graph paper. I asked them to draw the squares that they could, and also determine the length of each side, and then double check the area using the formula for the area of a square to ensure that their graphic solution matched their calculated area.

After about 20 minutes I asked the class if they noticed anything about the relationship between the side lengths and the areas of the squares. Many said it appears that if the area is x, then the side length is the square root of x. AHA!

With additional discussion students were able to explain that since there are no pair of integers squared that sum to 3, 6, or 7 it is impossible to draw a square with those areas whose corners were on the grid. I also asked students what would be areas of the next 3 largest squares that would be possible to draw.

They were able to tell me and explain how they knew!

Through this task students learned more than I possibly could have taught them through 2 days of direct instruction and drill like practice. Students developed a more intuitive understanding of:

• perpendicular lines having opposite reciprocal slopes
• the meaning of slope
• the Pythagorean Theorem
• area
• properties of squares
• squaring & square roots
• proof.

Annie was right in saying that teachers who argue that there is no time to implement these tasks with such a jam packed curriculum are missing the point. I have to constantly remind myself, that the hurrier I go the behinder I get!

Surface Area Interactive Notes

I gave this sheet to students and had them cut out the nets and use a ruler to measure and calculate the area of each face.

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Then we folded on the dashed lines and taped only 1 face into our Interactive notes, adding any additional information next to the net.

This is one of my favorite notebook pages because students refer back to it often to help them visualize all of the faces of 3-d solids in later practice.

   

Introducing Surface Area with Pop Box Design

After sharing this activity on last nights Global Math Department meeting (recording here), I thought I should also post it here.

I came across the Pop Box Design task developed by Timon Piccini and knew it would be a good fit for my students.

My students needed to understand surface area, not just be able to use formulas. I’m proud that during this activity I didn’t say surface area once.

I started by playing Timon’s Act 1 of this task and allowing time for students to notice & wonder about the short video. Then students predicted which box uses less cardboard (lower left of board).

We spent the remainder of the period playing with cm cubes and reviewing the meaning of and difference between surface area & volume using the worksheet attached in Timon’s 3 act.

The next class, I provided 12 pack boxes of each shape and put them in students hands, asking again – Which one uses more cardboard?

Students grabbed rulers and got to work finding area. They asked if they should be using inches or centimeters. I responded by asking which one requires more cardboard?

Once students determined the amount of cardboard used for each box, they logged into Google Classroom and wrote a letter to either soda box manufacturer or to me sharing their work, conclusions & recommendations:

The Good

• Using Google Classroom to manage letters & provide feedback. Students are still revising their letters.
• Illustration of surface area, we’ve referred back to this as we dug deeper into more advanced surface area problems.
• Physically touching & measuring the boxes increases buy in, engagement & understanding.

Change for next time

• Work with the class to develop a list of key elements to include in the letter.
• Some facts on cost of cardboard, ink, production & environmental impacts to increase relevancy.
• Improve connection between cubes & cardboard task. Some students did not see how these were related.

This task was a good, efficient way to ensure that students understand what surface area means and not just develop their ability to calculate surface area. As we practiced more advanced surface area problems, students were more understanding of what they were doing and was better able to develop formulas to find surface areas of a variety of  solids.

The Diamond Building

I adapted Jeff De Varona’s Diamond Building lesson into a 3-act task, but instead of having act 3 be a reveal of the actual height, I had students calculate the height a second way to confirm their results. It took 2 short class periods (about 40 mins each) with my struggling students, but it may be able to be completed in 1 class period if you spend less time noticing/wondering/developing questions. I had students work in randomly assigned groups of 2 or 3. They were engaged the entire time and seemed to enjoy the task.

I started by only providing sheets 1 and 2 at first & running it like a typical 3 act. Then I provided “diamond height method” info via projection & allowed students time to work using big whiteboards and share their conclusions. This activity was followed the next day by providing the pages 3 & 4 of the attached file and having students determine the building’s height by the “clinometer method” then discussion of actual height & sources of error.

I used this lesson as a summary to a unit on right triangles, a few days after doing a clinometer activity based on this. My favorite part was listening to students try to determine how to find the height of 1 diamond using only the fact that it is constructed of 2 equilateral triangles with sides length 7 feet. Some students constructed 30-60-90 triangles and used trigonometry, which is exciting because I did not explicitly teach special right triangles in this geometry class. Most students realized they could use the Pythagorean theorem.

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