Cats Are More Loyal Than Men

I'm dying! 😂

My teacher is married to a cat.  Cats are more loyal then [sic] men.

Approximating Square Roots Question Stack

Lately I've been using a lot of question stacks with my students.  I like that this practice structure is self-checking and helps students gain confidence.

My students have learned to approximate irrational square roots to the nearest whole number.  In past years, my students have always done well with determining the closest whole number; however when I asked them to plot an approximate point on a number line, many students put a point right on the whole number.  For example, my students would tell me that the square root of 46 is between 6 and 7 (closer to 7), but when they plotted a point on the number line, the point was right on the number 7 instead of somewhere between 6 and 7.

This year I wanted to give my students more practice with recognizing and plotting these irrational square roots on a number line.  I created two question stacks with different levels of difficulty.  Instead of writing the approximate answers in words (between 6 and 7), all of the answers were shown on a number line.

When it came time for a quiz, I found that my students this year did a much better job with approximating square roots on a number line.

Level 1

Level 2

View/Download: Approximating Square Roots Question Stacks

Making Group Work WORK - #SundayFunday

It's weird to me to think about how we are such social creatures, and yet, adults and children alike have such a hard time working with other people in a group.  I've had many a classes where "group work" meant sitting with other people, but ignoring them while you do your own work.  Often the task is split between the group members, and each person does an unequal share of the work.  If the task can be divided and completed independently, I might argue that it is not a group-worthy task.

Although we live in communities and most of us have probably never gone a full day without interacting with someone, working with other people does not come naturally to most.  In the classroom, that means students need to be taught to work in groups.

Here are just a couple of links to activities designed to teach students how to work in groups.

Sara VanDerWerf's 1-100 Activity

• The Task: Students work together to circle the numbers from 1-100 in order.  
• Your Job: Take pictures of students working in their groups and use these photos to facilitate a discussion about what good group work looks like.
• My Experience: Because taking photos of my students is kind of iffy, I do weird things as I walk around the room to see how many students notice.  For example, I might do some walking lunges or pat my head.  During the discussion, I ask how many students noticed that I was doing these strange things.  Usually not many students do, which leads to the questions, "Why do you think you didn't notice your teacher acting like a weirdo?  What were you doing that made you ignore some of the distractions around you?"

Sarah Carter's Broken Circles Activity

•  The Task: Students work silently to use the pieces in each of their envelopes to create a full circle.  Students must give away and accept others' pieces to do so. 
• Your Job: You don't have to do much during the task, but use Sarah's Broken Circles Reflection sheet to facilitate a discussion afterwards.
• My Experience: Some groups will figure this out in less than 5 minutes.  Others will take closer to 10 minutes.  Bigger groups definitely make the task more difficult. 

Rating Group Work Norms

Sarah identifies the Group Work Norms that Broken Circles is designed to practice.  I used her Group Work Norms posters to create another short activity for my students.

 

First I asked students to rate the importance of each of these norms independently.  I explained that they could have as many 1's, 2's, or 3's as it took to rate all of the norms.  Next I had my students partner with someone else.  I asked them to compare their ratings and then focus on two norms: one whose importance both partners agreed upon (same rating) and one whose importance they disagreed on (different ratings).  Afterwards, partners shared with the class.

List of Perfect Squares Foldable

It's simple, but I love this perfect squares foldable I created for students' notebooks this year.  In the past, I've just had students write a list of perfect squares up through 25^2, but then I'm left with the dilemma of deciding if I should have students write that a whole number squared is equal to a perfect square number or have them write that a whole number is equal to the square root of a perfect square.  I like that students are able to see the relationship both ways with this foldable.

 

    

They print two per page.  Print double-sided (flip on long edge) and cut down the length of the paper.  To fold, first fold in half lengthwise with the picture on the outside.  Then fold in half the other direction with the picture still facing out.

View/Download: Perfect Squares Foldable

Repeating Decimals Exploration

My students have been working on rational number conversions.  We started with fraction to decimal conversions.  I blogged about the notes I used and question stack my students practiced with here.  Next we reviewed how to convert terminating decimals to fractions.  Students put this review sheet in their notebooks.

After a brief review of terminating decimals, I had my students complete a repeating decimals exploration.  I asked them to convert special fractions to decimals using long division or a calculator, and then look for patterns.

 

Students noticed that all of the decimals were repeating.  They noticed that the denominators were all 9s.  They noticed that the numerators showed the digits that repeat when written as a decimal.  They noticed that the number of digits in the numerator matched the number of 9s in the denominator.

Then I asked students to predict what the fraction would be if I gave them the repeating decimal.  After making their predictions, students checked their answers with a calculator.

Things I Like About This Investigation

• Students get practice with converting fractions to decimals - whether that is by long division or entering it correctly in a calculator.
• Students do some notice/wonder while looking for patterns and making predictions.
• Students discover the 9s trick for repeating decimals themselves. 

Limitations and Room for Improvement

• Students didn't learn why the 9s trick works.
• Students only discovered how to convert repeating decimals to fractions if all the digits after the decimal repeat. 
• There was not a big emphasis on simplifying fractions, so students may not realize that simplified fractions with denominators other than 9 can still repeat (e.g., students may not recognize that 7/11 repeats and that it is the same as 63/99).

We summarized the 9s trick in their notebooks with this notes sheet.

View/Download: Converting Decimals to Fractions Notes and Repeating Decimals Exploration 

 

New Kindness Dares

My students are really into completing the Kindness Dares I have in my classroom.  Several students think they have completed every challenge in the bag because they keep getting repeats now, so they have asked me to write some new ones.  I realized that when I first blogged about the dares here, I never shared the files for the dares I used.  Now that I'm writing some new ones, I figured it was time to share them all!

 

Kindness Dares Set #1

 

Kindness Dares Set #2

View/Download: Kindness Dares