4th Grade Geometry - Pi and the Geometry of Circles

Last week in Geometry the students did a hands-on activity where they measured the circumference and diameter of a variety of circular shaped objects.  The students worked at measuring old coffee cans, rolls of masking and duct tape, Frisbees, and hula hoops.  They then divided the circumference by the diameter and came very close to calculating Pi!

This week students used their new found knowledge of Pi to calculate the circumference and diameter of other circles.  This presented new challenges as they began using calculators to figure multiplication and division using Pi or 3.14.  Working with decimals and calculators like this can lead to issues of lack of or over confidence.  Many of the students are apt to take whatever answer comes from the calculator as correct no matter how outrageous.  We are working on estimating the answer to the problem in an effort to check the answer from the calculator.  Often students have hit the wrong keys on the calculator and by estimating they hopefully will see that some answers don't make logical sense.

After 3 or 4 successful calculations the students find this to be just as routine as all of the other work we have done.  With hard work and a cycle of success, the students are ready for increasingly difficult challenges.

Some students have asked for a challenge problem to work on at home.  Below you'll find an archery target.  Calculate the circumference of each zone of the target including the yellow or gold center.

Remember that the formula is:

C = d X Pi       and        Pi = 3.14

4th Grade Geometry & Origami

Today's lesson was chopped up a bit by having all three classes at different points in the scope of the class and a morning safety drill.  This means that each class did a little something different, but each class had time for a little geometry taught through origami.  I have a link below to an origami website with a lot of models you can make with your child.  Be sure to ask them about congruent vs. similar triangles, bisecting angles, and quadrilaterals.  You'll enjoy making the models and talking with your child about what they've been learning.

 

Origami of all Kinds! 

4th grade Geometry & Origami

Today 2nd hour Geometry class finished a little early with the lesson and I had an opportunity to share something I really enjoy - Origami.  How do origami and geometry fit together in one class you ask...

I also shared the work of Robert Lang and I think he does a great job of explaining how the two are very good fit for one-another.  Check it out!

Robert Lang TED Talk

http://www.langorigami.com/ 

4th grade Geometry - Area of Triangles

Today in class we extended last week's lesson on are to include the area of triangles.  One powerful moment for most of the students was the demonstration shown below.  This example visually shows how the formula makes sense and makes it more tangible for the students.

An extension you can try at home is to cut up some rectangles and rearrange the leftover pieces to make the triangle.

4th Grade - Geometry - Area notes & practice

In class today all of the students started learning about area of quadrilaterals.  This is a bit basic for some students, however we are establishing a procedure to follow when solving unfamiliar problems.  Things will get more complicated pretty quick but if the kids stick to the procedure they will feel like it's no big deal.

Here are some notes that might help and a few practice problems:

 

4th Grade Geometry - classifying triangles

One class I have always been amazed by is my 4th grade Geometry class.  These students learn middle school math in 4th grade!  We start small but by the time the end of the semester these kids are rocking some real skills - in just 17 classes.

One of the 5th & 6th grade skills we start with is classifying triangles based on their angles and the lengths of their sides.  Most of the students are doing well with this, however some need more practice.  Here is a study guide that you can work on with your student to help them master this content: