Graphing and Geometry

Can you believe the nice weather?  I’m so happy that the snow that kept us out of school for 3 days last week is melting.  Students were thrilled to be able to go outside for recess in 60 degree weather rather than the below freezing temperatures we have been experiencing.  I for one really hope that winter weather has run its course and that spring weather takes its place!

Since we were only in school for 2 days last week, we are going to finish our graphing unit.  Most students completed their data sheets where they asked 20 random people a question that they constructed, giving a choice of 4 to 5 answers that these 20 people could respond with.  Since a few students were absent last week, math homework tonight was to finish these data sheets if need be.  All data sheets should come to school tomorrow with your child so that we can complete our data graphing projects tomorrow.  Details for this project were explained in last week’s blog if you need any clarification.

We are also going to talk about geometry this week.  Specifically, we are going to be classifying shapes into different categories, such as rhombus, rectangle, triangle, etc.  We are going to look at attributes that are shared among these categories, and look at how these shared attributes, such as a shape that has 4 sides, can lead to a larger category (ex:  quadrilaterals).  This geometry concept is one that students are familiar with, so I foresee that reviewing this topic will only take a few days.

That leads us to the end of the third grade math curriculum.  My homework for the week is going to be to really delve into the fourth grade math curriculum and map out skills that we will work on mastering for the rest of the school year.  Students are beyond excited to jump into fourth grade math, as am I!

Much of our graphing vocabulary is the same as last week, and can be viewed on my blog post from last week.  As far as new vocabulary is concerned, students will recall/understanding the following terms:

Geometry – mathematics that deals with points, lines, shapes and space.

Shape – the form of an object – how it is laid out in space (not what it is made of, or where it is).

Parallel – always the same distance apart and never touching.

Polygon – A plane shape (two-dimensional) with straight sides. Some examples include triangles, rectangles and pentagons.

Quadrilateral – a polygon with four sides (or edges) and four vertices or corners.

Rhombus – a 4-sided flat shape with straight sides where all sides have equal length. Opposite sides are parallel and opposite angles are equal. A rhombus is a type of parallelogram.

Rectangle – a 4-sided flat shape with straight sides where all interior angles are right angles (90°). Opposite sides are parallel and of equal length.

Square – a 4-sided flat shape with straight sides where all sides have equal length AND every interior angle is a right angle (90°). It is a Quadrilateral and a Regular Polygon

Trapezoid – a 4-sided flat shape with straight sides that has a pair of opposite sides parallel. The sides that are parallel are called “bases”. The other sides are “legs” (which may or may not be parallel).

Parallelogram – a 4-sided flat shape with straight sides where opposite sides are parallel. Also, opposite sides are equal in length and opposite angles are equal. Squares, rectangles and rhombuses are all parallelograms.

For additional assistance, please examine the following web sites:

Recognize shape attributes (a LearnZillion video and lesson)

Sort quadrilaterals by their attributes (a LearnZillion video and lesson)

Have a wonderful week!

Groovy Graphing!

Hello, math families! It’s a cold and icy Tuesday, and our students took their first PARCC test today. As I’m working on this blog, I’m cheering on our Maryland Terps basketball team and am very excited with our 60 – 50 win over Rutgers! We are winding up the final units in our third grade math curriculum, and plan on starting fourth grade math concepts when we return from Spring Break. I am so immensely proud of our entire class and the hard work they have exhibited in math this year 🙂

This week, we are reviewing graphing concepts. In third grade math, students focus on bar graphs and pictographs. As our class likes to be challenged, we are also going to study pie charts in addition to bar graphs and pictographs. We began our unit on graphing by sharing words and phrases that students think of when they look at a graph. The class came up with the math terms of data, recording information, collecting, and sharing answers as pictures. We used these thoughts to create a definition of graphing: using data or information that you (or someone else) has collected to record and share an answer in picture form. I was very impressed that the class came up with this definition on their own; I feel that it is rather sophisticated and explains graphing perfectly!

This week, students are creating a fun graphing math project. For homework tonight, I asked students to think about a few questions that you would like to find an answer to in which your answer can be represented through a bar graph, pictograph, or pie chart. Write your question, including at least 4 answer choices that accompany your answer on a planning sheet. Students will use one of their questions as a project that they will compile data for over the next two evenings, asking 20 people their question and recording participants responses on a data sheet. They will then take this data and, for their weekly quiz grade, develop a graph of their choice (bar graph, pictograph or pie chart) to share their information with me and with the rest of the class. Students were excited to get started on this, and I think it will be a meaningful way to learn about graphing.

For each type of graph, we discussed a distinguishing factor that students need to remember and pay attention to. With a pictograph, students need to look for the key that will share the value of the picture representation of the data. For example, we discussed that a picture of an apple could represent a value of 1, 5 or even 10. The example below shows a paw print having a value of 2.

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When looking at bar graphs, we talked about looking at the two axis (along the bottom and along the side) and that you have to use them together to share data.

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Finally, we looked at pie charts/pie graphs and made the correlation that the pieces of the pie in the chart represent the total number of subjects surveyed to get your answers. We compared it to the denominator in fractions, which I think is a great way to have students think of dividing a pie chart into equal sections that can be colored in to represent data.

pie-chart-movies

For parent assistance, please visit the following web sites:

Draw Scaled Picture and Bar Graphs:  5 video lesson (a LearnZillion resource)

Answer Questions using Picture and Bar Graphs:  5 video lesson (a LearnZillion resource)

Pictographs (a great resource from Math Is Fun)

Bar Graphs (a great kid and parent friendly resource from Math Is Fun)

Pie Charts (another wonderful resource from Math Is Fun)

If you have any questions or concerns, please don’t hesitate to contact me. Have a great rest of the week!

All Kinds of Measurement

Happy Monday, math families!  I was thrilled to actually have class today, as Monday school days have been few and far between this winter.  This week, we are exploring units of measurement.  Keep in mind that there are LOTS of things that can be measured in different ways, which led our class discussion today.  Students shared that they experience measurement of various types every day:  getting to school (distance and time it takes to travel), their weight and height, how much they drink at lunch, when they walk in line to get anywhere in school — the measurement that they inadvertently experience on a daily basis is astounding!

We began by breaking measurement into two categories:  The Metric System, which over 95% of the world uses as their standard measurement unit; and The Customary System, which only 3 countries use:  the United States, Burma and Liberia.  Students were asked to think of the various types of measurement that fall into each of these categories, and they did a great job of brainstorming measurement units.  They knew that the metric system included measurement units such as centimeters, meters, kilometers, kilograms, liters, and grams.  They also were able to identify inches, pounds, feet, miles, cups, quarts and yards as units of measurement that fall under the customary system that we use.

Today, we discussed ways to measure length.  Last week, we reviewed measuring in centimeters when we learned about perimeter and area.  Today in class, we learned about inches, feet, yards and miles.  There’s a wonderful picture representation that I shared with the class that you should have seen as part of their homework that really shows the hierarchy of these customary measurement units of length:

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We had a great conversation that amazed the class regarding the hierarchy of these units of length.  Students learned that there are 12 inches in a foot; three feet in a yard, and (what really amazed them) that there are 1,760 yards in a mile.  We were then able to do a hands on “musical chairs-like” math measurement activity where students measured graphics of shoes to the nearest half-inch.  Tomorrow, we will look more at various measurements of length and will measure to the nearest quarter-inch (gotta love the fractions connections we are making this week).

We will also be looking at metric and customary measurements of volume and mass this week.  The vocabulary that we have learned today and will continue to learn this week are:

Metric System – system of measurement used in most countries around the world.

Customary System – system of measurement that we use in the United States.

Length – the distance from one end to another.

Volume – the amount of space an object can hold; refers to capacity.

Mass – how much matter is in an object; refers to weight.

Gram/Kilogram – metric unit of measurement for weight.  Grams weigh smaller objects, while kilograms weigh larger objects.  1 ounce = approximately 28 grams.   1 kilogram = about 2 1/2 pounds.

Liter/Milileter – volume metric unit of measurement.  Milileters measure very, very small amounts, such as a squirt of soap or a drop of water.  Liters measures slightly larger items, such as soda or a bottle of water.

Inch/Foot/Yard/Mile – units of length in the customary system of measurement.  1 inch can be compared to approximately 2 1/2 centimeters.  12 inches = 1 foot; 3 feet = 1 yard; 1,760 yards = 1 mile.

Ounce/Pound – customary system way of measuring the mass or weight of an object.  16 oz. = 1 pound.

If you would like additional support at home this week with any of these skills, please view the links below:

Learning about US Customary (or Standard) Units of Measurement – a great resource from Math Is Fun.

Learning about Metric Units of Measurement – another great resource from Math Is Fun.

Have a wonderful week.  Stay warm, and please contact me if you have any questions.

Perimeter and Area

Happy cold and snowy Wednesday!

I hope that you had a wonderful long weekend and that you enjoyed our snow day yesterday.  Here’s hoping to it being our last one of the year 🙂

Today in class, I introduced the concept of perimeter to the class.  We talked about what the word perimeter actually means (“the distance around a shape”).  We looked at how different shapes have different sizes in terms of length, and talked about how you can find the perimeter of a shape that has opposite sides equal as long as you know the given length of one of the opposite sides.  We practiced creating shapes and assigning lengths to them, then practiced finding the sum (or area) of all of the sides.  Students did a wonderful job with this!

Tomorrow, we will move on to learning about area.  We will have some hands on practice measuring perimeter and area of various objects in our classroom — desks, notebooks, and Fraction Man posters specifically.  I’m very excited for an interactive assessment that I have planned for Friday.  To review perimeter and area with the class, in lieu of the traditional weekly quiz, students will be assessed on perimeter and area and will complete a math project where they will need to create a robot design using specific specifications for perimeter and area of the robots parts (head, body, arms, legs, etc.).  I think that the class will really enjoy this activity and I think it will be an engaging way to access their knowledge of this week’s topics.

Please familiarize yourself with this week’s math definitions:

PERIMETER – the distance or boundary of a flat closed plane figure; the distance around a shape.

AREA – the amount of space inside the boundary of a flat closed plane figure; the amount of space inside a shape.

If you would like additional support at home this week with any of these skills, please view the links below:

Perimeter and Area Basics (video tutorial from Khan Academy)

Perimeter Practice (an interactive game from IXL)

Area in terms of Units Square (an interactive game from IXL)

Area of Rectangles – length of 2 sides provided (an interactive game from IXL)

Have a wonderful week.  Stay warm, and please contact me if you have any questions.

Adding and Subtracting Fractions

Happy Monday!  Oh my goodness, our math class was so, so excited when they left math class today, due to the exploration that most of them chose to take regarding adding fractions with unlike denominators.  More on that later, though…

This week, we are finishing up our fraction unit with a 4th grade math skill:  adding and subtracting fractions with like denominators.  Our class did such a wonderful job with fractions as a whole that I believe they are developmentally ready to learn adding and subtracting fractions with like denominators.  They have also been asking daily, practically begging me to teach them this, so to find out today that our week’s objective is what they really wanted to learn really motivated them.

First, we discussed the idea that two students each had pizza last night.  We then had to decide how many slices of pizza were in each (whole) pizza; the class decided on 8 pieces in a whole pizza (this became our common denominator).  Then, we talked about how many pizza slices each student ate from their pizza.  In our discussion, Student C ate 5 pieces, while Student J ate 2 pieces.  I asked the students what they thought they should do with these fractions of 5/8 and 2/8 in order to add them.  They all said “just add the numerators and then add the denominators!”.  When we did this, the students noticed that we suddenly had a whole pizza with 16 slices, which is NOT what we started with.  This led to a great discussion about common denominators, and why when you have two denominators that you add, they in reality just stay the same, or stay they way they are.  That was a great a-ha moment for the class, and I was very proud that they understood this.  After that, it was rather simple:  students realized that all you need to do is add your numerators together, and that your denominator stays the same 🙂

After we practiced adding fractions with like denominators (which the students breezed through) I gave the class two options:  continue practicing adding fractions with like denominators and create your own math problems of adding fractions with like denominators; or, work with me for an optional activity where I would teach them a much harder common core skill of adding fractions with unlike denominators.  Our optional math group was made up of 17 very excited third graders who were beyond excited to learn this skill.  As this skill is NOT a third grade skill, students will not be assessed on it, but they still loved the fact that they were learning “really hard math”, to quote what most of them said. ❤

Tomorrow, we will begin looking at subtracting fractions with like denominators:  this is practically the same thing as adding fractions with like denominators, with the exception of subtracting the numerators rather than adding them.  I am confident that the class will excel with this fraction concept in a similar fashion as they have with adding fractions with like denominators.

This week’s weekly quiz will focus on all of the fraction skills that we have learned throughout our fraction unit.  I am confident that students will do an amazing job, and have nothing but pride in all of their hard work with this mathematical concept.

As a reminder, the vocabulary that is needed this week for our fractions focus is as follows:

COMMON DENOMINATOR – a quantity into which all the denominators of a set of fractions may be divided without a remainder. For example, the fractions 1/3 and 2/5 have a common denominator of 15.

PROPER FRACTION a fraction where the numerator is smaller than the denominator.  Examples:  1/2, 3/7 or 7/10.

IMPROPER FRACTION – a fraction where the numerator is larger than the denominator.  Examples:  4/3,  8/5, or 11/7.

MIXED NUMBER – consists of a whole number and a proper fraction.  Examples:  2 1/2, 5 3/5, or 6 2/3.

EQUIVALENT FRACTION – Fractions that have the same value, even if they look different.  Example:  1/2 has the same value as 2/4.

NUMERATOR – the top number of a fraction.  It tells you how many parts are being counted.

DENOMINATOR – The bottom number of a fraction. It tells you how many parts make up a whole.

If you would like additional support at home this week with any of these skills, please view the links below:

Add Fractions with Like Denominators (a LearnZillion video tutorial)

Subtract Fractions with Like Denominators (a LearnZillion video tutorial)

Adding Fractions with Different Denominators (from the website Fractions Made Easy)

Have a wonderful week, and please contact me if you have any questions.

Proper Fractions, Improper Fractions and Mixed Numbers

Happy Monday, math families!  This week we are venturing into the world of not only proper fractions, but of improper fractions and mixed numbers.  In class, we talked about the vocabulary associated with these math terms and came up with examples as well.  We were able to do some hands-on practice where we counted and examined groups of shapes that were divided into parts, enabling us to determine both the improper fraction and mixed number associated with each shape group.

Tomorrow and Wednesday, we will continue or exploration of improper fractions and mixed numbers.  Students will participate in a hands-on BINGO game where they will need to identify improper fractions and mixed numbers from a group of shapes and then locate those numbers on a BINGO board.  The students were very excited to learn about this BINGO game and were asking about possible prizes that might be awarded for the winners 🙂

Please continue to reinforce the following fraction vocabulary terms with your child:

PROPER FRACTION a fraction where the numerator is smaller than the denominator.  Examples:  1/2, 3/7 or 7/10.

IMPROPER FRACTION – a fraction where the numerator is larger than the denominator.  Examples:  4/3,  8/5, or 11/7.

MIXED NUMBER – consists of a whole number and a proper fraction.  Examples:  2 1/2, 5 3/5, or 6 2/3.

EQUIVALENT FRACTION – Fractions that have the same value, even if they look different.  Example:  1/2 has the same value as 2/4.

NUMERATOR – the top number of a fraction.  It tells you how many parts are being counted.

DENOMINATOR – The bottom number of a fraction. It tells you how many parts make up a whole.

If you would like additional support at home this week with any of these skills, please view the links below:

Mixed Numbers/Mixed Fractions – a tutorial and explanation from the website Math Is Fun.

Improper Fractions – a tutorial and explanation from the website Math Is Fun.

Fraction Fling – a fun fraction game from ABCya.com where you can choose to “hit” mixed number fractions that are represented by a visual model.  Lots of fun and educational as well 🙂

Math Man – a great fraction game that has students convert mixed numbers to improper fractions and vice versa.  Lots of fun and educational as well 🙂

Have a wonderful week, and please contact me if you have any questions.

Continuing Equivalent Fractions

Happy Wednesday — I can’t believe that it’s Wednesday, can you?  I’m sure that students loved our two snow days, but they were literally running into math class today and got to work immediately.  I’d like to think that they missed learning about fractions and were ready to have some fun in math class today 🙂

This week, we are continuing our exploration of the concept of equivalent fractions. We looked at how our Build A Fraction chart from last week could help us find fractions that are the same as 1/2.  Then, we had a great discussion as to what 1/2 really is, and students discovered that any fraction that is the equivalent of 1/2 has a numerator that is half of its denominator/a denominator that is twice the value of its numerator.  The amazing “ah-ha!” moment that students had when they realized this was so worthwhile to see!

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We’ll continue to look at equivalent fractions this week, will also begin to explore simplifying fractions, and will prepare to discuss the Fourth Grade Common Core math concept of adding and subtracting fractions next week. Please continue to reinforce the following fraction vocabulary terms with your child:

EQUIVALENT FRACTION – Fractions that have the same value, even if they look different.  Example:  1/2 has the same value as 2/4.

NUMERATOR – the top number of a fraction.  It tells you how many parts are being counted.

DENOMINATOR – The bottom number of a fraction. It tells you how many parts make up a whole.

If you would like additional support at home this week with any of these skills, please view the video below:

Identify Equivalent Fractions:  Fraction Models (a LearnZillion tutorial)

Identify Equivalent Fractions:  Using Fraction Strips (a LearnZillion tutorial).  I really like this video, as it uses manipulatives similar to our Build A Fraction resource sheet that I referenced and shared a photo of earlier in this post.  🙂

Identify Equivalent Fractions:  Use an Equation (a LearnZillion tutorial)

As always, please let me know if you have any questions or concerns.  Have a great (short) week!