Micro-Project: Cantilevers!

This semester one of my goals is to give students opportunities to work on mini-projects - mostly one-page explorations of math outside of the typical curriculum.  I wrote about the one we did in February here.  (I wanted to share some of these but I didn't ask students to leave their last names off of the projects ... learning that if I want to post their work, I have to specify first names only).

Today I gave students a "micro" project ... smaller, shorter than even a mini project!


We start Rational Functions on Friday.  We are going to start our unit with a math lab to collect and analyze data.  The lab on Friday uses spaghetti to make a cantilever.  We'll measure the deflection as we increase the number of pieces of spaghetti.

I suspected that students might not know what a cantilever is.  So I asked them to find an interesting example of a cantilever.  I created template slides in Google Presentation.  Each student puts their fascinating find on a slide with the link to the picture and a short blurb about the cantilever.

After a short test today, students had time to begin their work.  Already nearly half of my students have created their slide.  Here are examples (I haven't proofed these) ...





A couple of the students as leaving today "made fun" of how easy this homework is.  I'm OK with that.  Now when we work with our spaghetti on Friday we will have some visual ideas of cantilevers and the variables involved in making them work!

Our next project ... using our seven parent functions to create a work of art in Desmos!

Digital Frames - Exploring Color

I have begun to play around with creating borders.  I see the elementary folks on TpT create so many intricate designs.  I don't print much in color; I don't have a color printer at home or work.  So it is cost prohibitive.  

Here is a set of borders representing typical math manipulatives in the elementary years ... linking cubes, pattern blocks, and cuisenaire rods.  

Do you "decorate" stations?  Do you use color?  Art?  How do you use digital frames?

Blogosphere ... Good Ideas Round 5

In the last week or two, I've run across so many interesting sites!  Here are just a few of them ...

Colleen Young is a mathematics specialist with a strong interest in IT as well.  She has created two amazing websites ... one is her blog, and the other is a collection of mathematics starters and plenaries (ending activities!).  Fair warning ... her sites are chock full of ideas, activities, and links to more ... reserve some time for exploration :)

Vi Hart calls herself a mathemusician!  Her website has numerous pictures and videos of mathematic amusements!  When students are saying math is just boring, they need an opportunity to see math at play.  This website is a good place to explore!

Last, many of us are participating in Jo Boaler's course, How to Learn Math.  I found some helpful information, documents to use in planning, and surveys and such to use with students at these two sites:  InspiringLearners and MindsetWorks.  At InpsiringLearners there is an awesome poster illustrating a fixed vs a growth mindset that could be used in classrooms.  At MindsetWorks there is a "growth mindset framing tool" ... a list of statements to help frame instruction and feedback using a growth mindset.  I plan to put the document in my planbook/calendar to use in preparing for classes.

OK ... I said "Last" in the last paragraph ... but one more resource that I found yesterday is Brilliant.org.  "Brilliant.org provides a challenging intellectual environment to anyone with internet access and a passion for mathematics or physics. Brilliant.org aims to become a hub of the world's most promising minds, where motivated thinkers can connect to each other and to opportunities to apply their talents." Registration is free. At registration you take a "test" to determine your level of algebra and physics skill. Each week you are presented with challenges to engage in math problem solving.  This site would be especially helpful if you work with gifted and talented students, a math club, or any group of students who just want to dig deeper in problem solving!


As you can see, I've spent way too much time this week surfing along various math webs.  I may need to unplug for a while but I love the exploration!

Fraction Sums

Looking for extra practice in adding fractions??   Check out this Fraction Sum activity here or here!

Suggestions

· Give students the Total Sum (right bottom corner) to make the puzzles self-checking

· Assign one puzzle a day as a warm-up or for homework

· Allow students to work as partners to complete the puzzles and to explain their work.

· Cut the squares apart to rearrange to create new puzzles

· Ask students to create their own puzzles on index cards for future practice

How do you introduce adding fractions?  

What manipulatives do you use to teach addition of fractions? 

How do you practice?

Happy Birthday Made4Math Monday ... First Day Stations!

Happy Birthday to you!

Happy Birthday to you!

Happy Birthday, Made4Math Monday!

Happy Birthday to you!

I remember last summer well.  I had been out of the classroom for several years.  We moved to another state.  I decided to go back to teaching math ... and I was nervous!  So last summer I scoured the Internet and while surfing, I found this amazing math community.  I participated in the new bloggers initiative and when I could, I contributed to Made4Math Monday and #MyFavFriday!  (I had much more difficulty with the favorite Friday posts.  I think it was because at the end of the week I was exhausted!)

I love Made4Math Monday ... the activities, classroom decor, posters, organizational tools were awesome last year!  I look forward to learning so much more this year.

It appears that I will teach advanced Algebra 2 this year instead of Algebra 1.  My background is in working with gifted learners so I am excited about that part.  I know I'll have much studying to do this year as I spent all last year learning the ins and outs of the Algebra 1 curriculum.

I want to start the year with stations (maybe not day 1 but more like day 2) ... reviewing some basic skills.  I want to observe my students at work.  I'm considering this set of stations although I have some other ideas simmering on the back burner as well.

Here is the link to the document.

What might you do differently?
What activities are you planning for the first day or two of school?

Primary Math Number Mysteries

Do you love a good mystery?

I am less than 100.I am an odd number.
My tens digit is the same as the number of days in a week.
My ones digit is the number of fingers on one hand.

What number am I?

Our math resources sometimes lack enough practice for students to build independent math skills. 

Number Mysteries is a free resource with eight place value mysteries that could be used as extra practice for seat work or a math center.

Download the pdf here or here!

In Number Mysteries, students identify a 2-digit number using clues. Clues involve common numbers such as “half of a dozen” or the “value of a nickel.”

Students could be asked to represent the mystery number using concrete materials, drawings, or in standard form.

After working through these exercises, students should create their own puzzles.  Student-created puzzles with illustrations could be put together in puzzle books and/or hung in math centers to challenge classmates.

Graph Stories

In our Algebra 1 curriculum we focus on graphs, analyzing graphs, identifying domain, range, independent/dependent variables, continuous vs discrete, and interpreting the meaning of graphs.

We try to give students as many different opportunities creating graph stories as we can.  Two resources I use are Annenberg Learner Teaching Math module on representing mathematical stories and Dan Meyer's Graphing Stories.  Illuminations also has a very open-ended activity in which students roll dice to get coordinates, connect those coordinates, and then create stories that go with the graphs.  I recently found the Mars Shell Center unit on interpreting distance-time graphs; it will be useful for extra practice next year.

I've created a practice activity for students that could be used as homework or as a formative assessment activity.  <It's no longer available.>

How do you provide reinforcing practice?

Fruity Like Terms

I noticed that some of my students had difficulty with grasping the concept of "like terms."  I needed to find a way to make the concept concrete for them.  I found fruit to be an easy analogy.  Here is the mini-poster I created ...

Fruity Like Terms Printable by Beth Ferguson

You can download the poster from Scribd or from my TpT store ... free!

In my classroom, I enlarged the chart and posted it at the front of the room.  For students who struggled with the concept more than others, I created a handout of the chart and asked them to keep it in their notebook for reference.  In the coming year, when I review combining like terms, I'll bring fruit to the classroom!  Last year, I just used pictures.  But I think if we handle the fruit, it will help the concept to sink in!

How do you make challenging concepts concrete for students?

Tutoring this summer!

I'm going to do some tutoring this summer with elementary students - grades 2, 3, and 5. The school they attend uses the Singapore math books. I'm putting together my manipulative kit ... found

most of what I need at the dollar store!

This is what I have on my list so far ... Sharpie marker, whiteboard, whiteboard markers, dice, poker chips – 4 colors to make place value chips, flat square tiles, index cards to make number bonding cards, and sticky notes. I'd love to find one set of base 10 blocks.

In addition I've been scouring the Internet for engaging learning activities that focus on number sense. I've collected several thanks to the many math bloggers!

I also created an activity - a simple hundred board counting activity where pieces of the board are broken and numbers are missing. Students simply fill in the missing numbers. The focus is on counting by ones but also +10 and -10.



(Download free copy of Hoppy Hundred Board Activity)

What are your favorite manipulatives for helping children with number sense?  Do you have an activity to share?

Powerpoint Game Reviewing Slope/Intercepts

I'm always looking for a way to involve students in mastering content through games.  The following game works well for practicing finding slope and intercepts of linear functions.  The game can be fast paced, and doesn't require extra materials.

Slope Intercept Gameboard by Beth Ferguson

Visit my Scribd site for other free algebra materials.  Also visit my TpT site for engaging algebra materials!

I am thinking of a number ... eureka!

Students love to unravel “I’m thinking of a number” puzzles! 

Use these puzzles to introduce solving equations intuitively. Or use these puzzles after students have learned how to translate words into equations. Either way, your students will enjoy the work while reinforcing basic solving skills.The puzzles relate to these common core math standards:

• CCSS.Math.Content.5.OA.A.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
• CCSS.Math.Content.6.EE.B.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
• CCSS.Math.Content.7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
• CCSS.Math.Content.8.EE.C.7 Solve linear equations in one variable.

Arithmetic by Carl Sandburg

I love children's literature!  I especially enjoy literature that has math content.  The other day I noticed Carl Sandburg's poem, "Arithmetic" on my shelf.  I have a picture book that was illustrated by Ted Rand - the illustrations are intriguing - they are anamorphic drawings.  They add to the whimsical nature of the poem!

I began to think about how I might use this book in my Algebra classes.  Sandburg writes what is called a "list poem" describing arithmetic.  It would be interesting for students to compile a list poem about algebra.  Students could brainstorm in small groups ways that Algebra shows up in the real world.  The challenge might be to create humorous or whimsical examples.  We might post the brainstorming ideas around the room to help fuel students' thinking.  Then groups of students could compile their list of 6 to 8 thoughts in poetry style with illustrations.  I created a simple rubric for scoring.

Poetry Rubric for Math Class by Beth Ferguson

For elementary teachers, I created a document with vocabulary, thin and thick questions, and activities to go with this book (or just the poem).  It's for sale on my TpT site, Algebra's Friend.