Homeschool Math Blog

You might ask, what do these two subjects have to do with each other? Most people probably think that math and crocheting don't have anything in common (well, besides the fact you count your stiches and such). However, the video below shows you a STRIKING connection between crocheting and hyperbolic geometry which has ONLY been found fairly recently. Crochet model of hyperbolic plane by Daina Taimina I found it surprising that mathematicians had thought for years that it wouldn't be POSSIBLE to build a physical model for hyperbolic geometry. Then... the mathematician Daina Taimina found that CROCHETING was the perfect model for it! The essence of the hyperbolic space can be implemented with knitting or crochet simply by increasing the number of stitches in each row. As you increase, the surface naturally begins to ruffle and crenellate. So... what is hyperbolic geometry? You can draw several lines that are parallel to a given line and that go through a ...

Here is the newest worksheet generator that I have added to HomeschoolMath.net: Area and perimeter of rectangles/squares  It is very versatile and makes many different kinds of problems related to the area and perimeter of rectangles and squares. You can make: problems for the area and perimeter of rectangles and squares, with grid images or normal images word problems, including ones asking for a side length when area or perimeter is given problems with irregular rectangular shapes problems to practice distributive property with two-part rectangular areas (required by Common Core Standards in 3rd grade). You can make worksheets with just one type of problems from that list, or mix them up however you want. For example:   (in your browser options, make sure background colors get printed) I especially made this worksheet generator because I feel many children may have some difficulty with the new Common Core Standards requirement for 3rd grade, that is 3.M...

I've just completed making two new worksheet generators for HomeschoolMath.net: Classify triangles   - make worksheets for classifying triangles by their sides, angles, or both. Classify quadrilaterals   - make worksheets for classifying (recognizing, idenfitying, naming) quadrilaterals. There are seven special types of quadrilaterals: square, rectangle, rhombus, parallelogram, trapezoid, kite, scalene, and these worksheets ask students to name the quadrilaterals among these seven types. They look sort of like this: Use the links above to set your options (image size, number of problems, etc.) I had fun making the scripts, though also some challenges. But overall I enjoy such work - programming is similar to problem solving in math. In this case the problems often were math, such as how to make a script that gives me a kite or a scalene quadrilateraly with varying dimensions. I was using php GD library to first create a bunch of images, and then made the...

I got inspired by the blogpost Art School | Geometric Design with Islamic Art where Deborah shows how to make a neat flower design with seven circles , using a compass, and then coloring it using 2, 3, or 4 colors (or however many of your own). I think it ties in neatly with mathematics, and lets students practice drawing circles with a compass.  My girls loved the art/math project. Here are pictures they made: Here are step-by-step instructions for the flower design: 1.  Draw a line and a circle so that the circle's center point is on the line. Then mark the points where this circle intersects the line. 2. Use those points as center points, and draw two more circles. The radius is the same all the time, so make sure you don't change it on your compass!We used 5 cm as the radius, and that made the whole design fit neatly on a regular letter size paper. 3. Now note the two points marked in the picture. They will be used as center points in the next...

I recently put a few exercises about star polygons into the new Math Mammoth grade 5 geometry section that I'm revising, and thought I'd share some printables here as well. What are star polygons? They are polygons that look somewhat like a star. You can form them  by joining the vertices of a regular polygon in a certain manner. For example: I put the star polygon worksheets on this page .  They are PDF files, enabled for annotation, so you can actually fill them in (draw in them) using Adobe Reader on the computer. You will find a worksheet from pentagram (5 points) all the way up to dodecagram (12 points). Here's one example (nonagram worksheet): Then there are also printable worksheets with empty polygons where students can experiment and create their own star polygons. There are more at this link . Lastly, I also made some blank worksheets with various regular polygons. These are for any of you, teachers or otherwise, who would like to maybe hav...

My kids have recently fallen in love with lapbooks, and have done several science & history related ones. I got to thinking, there aren't that many MATH lapbooks available... but there IS one math topic that suits lapbooking very well, and that is GEOMETRY . Now, while I don't actually have a geometry lapbook for you, I found some places where you can get one: Geometry Lapbook at Homeschool Bin - this seems to be a completely free download (in several parts). Adventures of  Third Grade Teacher is selling a geometry lapbook for $3. Then, if you feel a lapbook (a foldable) is too extensive a project, here's a simpler one: a geometry notebook or journal . This simply means that for each new TERM in the geometry curriculum or chapter, the student explains that term and draws the corresponding figure, using 1-2 blank pages. In the end, the student will have his/her very own geometry book to keep and show around! Here's one parent's example of doing...

I'm reposting here a nice triangle problem with the permission of Antonio Gutierrez from GoGeometry.com The figure shows a right triangle ABC. The inscribed circle and the hypotenuse are tangent at D. If AD = 2, and CD = 3, find the area of triangle ABC. The solution is now posted here !

I intend to publish several of these "stories" or "reports" from teachers who have been using Math Mammoth. Here's the first one, from Megan in Belgium. She used some lessons from my Math Mammoth Geometry 1 book . Presentation of the Class and the School I am a 1 st , 5 th and 6 th grade teacher in south Belgium. My school is what we call an “immersive school”. The students are taught in French, their mother tongue, 14 periods a week. During the other 10 periods each week, class is given in English – the students are “immersed” in the language from the age of 5 and learn to speak this language in a very natural manner. Because of these awkward hours, we teachers “share” the classes. In order to have a full schedule, I give class in English 10 hours a week in 5 th grade, 10 hours a week in 6 th grade and 4 hours a week in 1 st grade. We also split the subjects between French and English – and Geometry is one of the subjects seen in English. Now,...

I was told about this free download of the book Geometry in Art , by Hilton Andrade de Mello. On the page, you need to scroll down to the words "free downloading". This book is a basic introduction to geometry in art, with topics such as polygons, spirals, polyhedrons, tessellations, perspective, the golden ratio, symmetry, geometry and symbolism, and geometry and informatics. It has lots of illustrations and artwork by various artists, and can serve as a nice introduction for anyone who hasn't studied these topics before.

I have updated the list of online geometry resources and games at HomeschoolMath.net. It became quite a long list of links! The links are categorized by topics, such as Shapes & polygons  Area & perimeter  Angles  Solids, volume, & surface area Coordinate plane  Congruent transformations  Similar figures  Circle / Pi  Constructions  Pythagorean Theorem  General geometry websites  Worksheets  Books  Advanced topics. I hope this is helpful!

I have just finished writing the material for Math Mammoth Geometry 2 book. The material in it is suitable for grades 6-7. Download price is $5.80. The main topics in the book include: * angle relationships * classifying triangles and quadrilaterals * angle sum of triangles and quadrilaterals * congruent transformations, including some in the coordinate grid * similar figures, including using ratios and proportions * review of the area of all common polygons * circumference of a circle (Pi) * area of a circle * conversions between units of area (both metric and customary) * volume and surface area of common solids * conversions between units of volume (both metric and customary) * some common compass-and-ruler constructions. I've included several complete lessons from the book as samples (PDF). Feel free to download these and use with your students! Angles in Polygons Review: Area of Polygons, 1 Surface Area Besides those, there are two other sample pages: ...

I have just posted a comprehensive review of this book that is popular among homeschoolers for a high school geometry course. Click to read: Review of Harold Jacobs Geometry book

This is a set of three geometry videos dealing with angles. First, showing that vertical angles are equal: Next, finding out about the angles in a parallelogram . I start out with two parallel lines and a transversal (line that intersects them both). We explore the angles formed, which some of them are corresponding angles, some are vertical angles. I draw a new line, and get a parallelogram. Lastly, here is a short and easy proof about the angles in a triangle .

I've finally ventured into geometry topics with my latest video: It shows how to use a protractor to measure angles . I show where the "base line" of the protractor is for three different protractors, and use it to find out the angle measure of different kinds of angles (including a reflex angle).

Have you ever wanted to fold a pyramid or some of the other interesting polyhedron out of paper? At least, take a look at the pictures! www.korthalsaltes.com provides hundreds of free printable paper models for various solids, including platonic solids, pyramids, and lots of polyhedra. Some are available as colored versions also. Folding and gluing one or two is a great summer math project also, and will keep kids busy for a while.

I have a collection of interesting links for you today; mostly some picks from Math Teachers At Play #2 blog carnival, which you SHOULD visit. Denise always has good stuff and really nice photos to spice up the reading. Here's a neat way to practice multiplication tables by Math Mojo. I also liked some simple dissection puzzles ; you'll even get a free worksheet download. Nick has posted two geometry "Wrapper" problems This one is hilarious - lots of pictures of mathematical clocks! Those were all from the carnival; please check out all the other posts as well ; it is a good carnival! Lastly, I visited this yesterday, and I think ALL of us should check out what a trillion dollars looks like .

UPDATED! Today I have a geometry problem for you. Just yesterday I showed you a proportion problem and its solution. (I want to insert a note here, especially for parents reading this. Don't feel that you always need to use the problems I present here with your students. Instead, as a homeschooling parent, consider them part of your "math teacher training" that you never got. Reading through problems and their solutions will help you become a better math teacher. Consider yourself an apprentice observing a master completing a task, in this case mathematics problem solving. It just takes you a minute or two to read this, think it through, try it - and understand (I hope). Your students' or child's book will have similar problems later on when it's time for geometry studies, but if you read these that I present, you will have learned more and can better tackle those problems at that time.) OK, here we go. Look at the tiling below. Here you can see the tiling in...

64 pages (of which 37 are lesson pages) Price: $2.50 download Buy at Kagi (PDF download) Sample pages (PDF) Contents and Introduction Shapes Right Angles Line Symmetry Perimeter Solids 1. Math Mammoth Early Geometry covers geometry topics for the early elementary grades (approximately grades 1-3). The first lessons in this book have to do with shapes - that is where geometry starts. Children learn the names of the common shapes, and also put several shapes together to form new ones , or divide an existing shape into new ones. They practice using a ruler to draw various shapes and are introduced to tilings. Next children learn the concepts of parallel lines and lines that are at a right angle (perpendicular lines). The book also has beginner lessons about symmetry, area, perimeter, and solids . After studying these early geometry lessons, you can continue the study of geometry with Math Mammoth Geometry 1 book . In it, children will learn to classify figures (dur...

These are answers to my earlier pos t where I asked if certain figures necessarily are parallelograms. The question was: Does the given information in each diagram guarantee that each is a parallelogram? Figure 1: This one you can't get around; it ends up being a parallelogram, actually a dandy rhombus. Let's prove it. You can notice it has lots of sides of the same length. If we draw a diagonal, we get two triangles with all kinds of same sides: The two triangles ABD and BCD end up having all three sides the same. So by the SSS triangle congruence theorem, they are congruent triangles. Hence, their corresponding angles are the same. I've marked the corresponding angles with the same colors. Actually the triangles are even isosceles so the blue and purple angles are even congruent... but we don't need that fact. To prove ABCD is a parallelogram, we need to prove its two sides are parallel. And for that, it's often handy to use the corresponding angle theorem: if c...

Continuing with the idea in my post about Squares that aren't squares? , let's look at the following "parallelograms". The question is the same: Does the given information in each diagram guarantee that each is a parallelogram? If you don't think so, your mission is to draw a quadrilateral with the given information but that clearly does NOT look like a parallelogram. Figure 1: Figure 2: Figure 3: Figure 4: Again, these problems let students practice logical reasoning, and also learn about parallelograms, of course. See answers here .