Is a Square a Rectangle?

We started another mini geometry unit today: square and rectangles.

First, we investigated characteristics of square and rectangles.  We decided:

Rectangles

• have four 90° angles
• opposite sides are the same length
• opposite sides are parallel

Squares

• have four 90° angles
• all four sides are the same length
• opposite sides are parallel (from which we deduced that the lines must be straight)
• is a rectangle

This last feature about squares brought this question forth:

The students discussed this and came up with some very valid answers.  They should good critical thinking skills and through debate and discussion were able to decipher that this statement is true and why it is so.

Using Tools to Make Perpendicular Lines

Yesterday students learned about parallel and perpendicular lines, and how to draw them.  The tool we chose to start with was a triangular ruler, that has a 90° angle incorporated in its structure.  This led us to today's goal:

With a bag of different measuring tools in front of them, students first choose the one we know and demonstrated how to use it to create perpendicular lines.  Then, from the remaining tools left on their desks they needed to choose on that they thought they could use to create perpendicular lines.

After some discussion, and trying out one tool which we deemed would not work to accurately create a perpendicular line, they decided that we could use a protractor to help us in this endeavour.  Through a class demonstration, the students agreed that indeed this would work.  So then we set out to practice creating perpendicular lines alternating between the two measuring tools.

Making Lines

Using triangle rulers, students practiced making parallel and perpendicular lines today.  It's nice to start with graph paper to help ensure that our lines are straight and that we do create 90° angles.  When we leave the graph paper, our triangle rulers will definitely help as will using a protractor.  It's amazing how previous unit concepts return to be applied again. ;)

Parallel and Perpendicular Lines

Our next mini geometry unit is about lines; parallel and perpendicular lines to be exact.  Today students first explored concepts and shared what they observed about two separate images of lines.  From doing so and our class discussion, we discovered the properties of parallel and perpendicular lines.  Also, we found that moving the turning or rotating the image did not change the properties of the lines.

Parallel Lines
1. Made by two straight lines / line segments
2. The lines never meet.
3. The distance between the lines remains the same at all points.

Perpendicular Lines
1.  Made by two straight lines / lines segments
2.  The lines meet.
3.  Where the lines meet creates a 90° angle.

After we explored this visually and through discussion, the students then used strips of paper to create parallel and perpendicular lines.  We found that using measurement tools (ie rulers and right triangle rulers) helps to ensure accuracy of our lines.

Protractor Fun

Students are learning how to use a protractor to measure angles.  This can be a very tricky tool to use as it's important to place it on the angle you are measuring properly in order to get an accurate measurement.  Also, angles can be measured from the right or the left, hence a protractor has two sets of numbers.  We have to be very aware of which numbers to use, therefore applying our math thinking and knowledge of kinds of angles.

We are using protractors to both draw and measure angles.  Once we've gotten it, it doesn't seem so tricky anymore. :)  Thankfully Singapore Math has some wonderful online resources for us to use in the classroom.

Angles

Students were learning how to name angles today.  First we reviewed the different types of angles (right, obtuse, straight and acute) and then looked at how to name them using letters.  It's a tricky process, especially when we are looking at naming angles that are part of closed shapes, but the students have a good start!

Measurement Tools

As we've moved into our measurement unit in math, students have had to recall many different terms of measurement, along with conversions within these from one unit to another.  A key tool we often use in 4th grade purple is a flip book with information that we can access when we need.

Adding Decimals

Students looked at how to add decimals today.  First, we took a horizontal equation and attempted to correctly write it vertically then add it.  Next, we took the different answers and placed them on the board.  Then, students voted on the correct answer and volunteers came up to state their reasoning as to why they chose that answer.  Through our dialogue, opinions changed and through proofs students all came to a consensus as to how to write the equation and why, thus deriving at the correct answer.

Fractions as Decimals

Today students learned how to make fractions into decimals when the denominator is not 10 or 100.

Students discovered that in order to do this you need to make an equivalent fraction with a denominator or 10 or 100.  So students had to analyze the fraction and decide whether the current denominator was a factor / multiple of 10 or 100, and then work to convert that fraction into an equivalent one and follow up with then making it into a decimal.

I was pleased at how well the students applied their previous knowledge to this task and took to being able to grasp this concept quickly.

Comparing Decimals

Students are getting to the point in their math decimals unit where they are comparing fractions.  Therefore, they are looking at 0.1 more/less and 0.01 more/less, along with then increasing this amount to find numbers that fit their clues.  Today we introduced this concept using place value mats, with places consisting of tens, one, tenths, hundredths, and place value chips.  First we practiced building given numbers using these tools, and then we extended this knowledge of find more and less than numbers with clues.  Using manipulatives helps us build our understanding of the concept, and to see it visually before we enter the abstract math world.  Comparing numbers will also have us ordering and using our >, <, and = signs again.

Comparing Decimals

Students had an introductory lesson on how to compare decimals today.  We started by comparing tenths to tenths, then hundredths to hundredths.  We found that comparing decimals is just like comparing whole numbers: pay attention to the place value of each digit.  Students extended their comparison to comparing decimals with similar tenths but different hundredths, and hundredths to numbers with only tenths.  We realized that it's not hard; we just have to remember that 0.9 is equivalent to 0.90 and this knowledge helps us in our comparisons.

Decimals

This week the students have been learning about decimals.  We've started out with tenths (the first place value after the decimal point).  The students have learned that we use a base 10 system so our magic number is 10 (that's how many fractional parts are in a tenth), how to convert a fraction to a decimal and vice versa (both improper, mixed and regular fractions), how to read and write in words a decimal, and how to accurately place it on a number line.

Math Review

In anticipation of our math assessment tomorrow, students did some review work in class today.  One activity was a quick matching activity whereby we were renaming mixed numbers as improper and vice versa.

Fraction Fun

With Salty Cats being cancelled, 4th Grade Purple put into place their back-up plan for the day.  Part of the plan included.....Fraction Fun!  In 3 pods, students practiced making fractions with dice and cards, comparing fractions, and using fraction pieces to create mixed fractions for which their partner needed to represent with numbers and symbols.  This was a great way to continue to practice our fraction knowledge in various settings that felt more like fun games than learning. ;)

Mixed Fractions on a Number Line

Today we took our knowledge of number lines & fractions, and combined them to put mixed fractions on a number line.  Working in teams of two (doctors and prep surgeons) one student had to accurately prepare the number line for the doctor to come in and do surgery (place the number on the line).  So far, many lives have been saved today.

Adding & Subtracting Unlike Fractions

Students are learning how to add and subtract fractions with unlike denominators.  This can be a tricky tricky process.  We've used both fraction strips and numbers & symbols to do these processes.  We are only looking at changing one fraction to have a similar denominator as the other, where the larger numbered denominator is a multiple of the smaller numeral (ie 1/2 to 3/6 - sixths, as opposed to 1/2 and 1/3 to a common denominator).

By using two different methods, students: a) develop better conceptual understanding, and b) show how they can prove their answer is correct.

Here are some links that we've used in class:

Virtual Fraction Strip manipulatives

Adding Fractions Notes - Math is Fun website

Subtracting Fractions Notes - Math is Fun website

Data Analysis Scavenger Hunt

On Monday the students have a math test on their data analysis unit.  In order to prepare for this, not only do they study at home but we also review in class.  We've currently been working on word problems and taking them apart to solve.  Today, we did a scavenger hunt activity that used our graphing skills along with recalling mean, median, mode and range.

The scavenger hunt was broken up into 4 parts (or different graphs).  The students would take 1 slip of paper then have to find the graph that goes along with it.  Once they did, they used the graph data  to answer questions.  This was a great way to review concepts and the students had fun while moving around.  They also got instant feedback on their work as they had to show me one slip, get it corrected and then get the next one ONLY if they didn't have corrections.  At which point, they'd go back to seek out their error.

Probability Terminology

The students are learning about probability and the terminology that goes along with it.  Terms we'll encounter while we look at probability include: impossible, certain, more likely, less likely, equally likely and outcomes.  To help us, we added a flip book with these terms and their corresponding definitions to our interactive math notebooks.  The students used the glossary at the back of their math textbooks to locate all the definitions.  They then created their flip book and put it in their math notebook to use for future endeavours.

Data Analysis

Data analysis: our next unit in math has us learning about mean, median, mode and range.  The students are starting with mean (or average): a calculated central value of a set of numbers.

To find the mean (average) you:
1) add up all the numbers in the set
2) divide by the number of items in a set

For more information on the definitions and to see some examples, please see one of the links below:

Math Is Fun - Mean

Math Is Fun - Average

We also watched a cute video that gave us information about these terms and got stuck in our heads.  Hope you enjoy it as much as we do.

Math Collaboration

4th Grade Purple is encouraged to talk about and collaborate during math.  Turn and talk, learning from one another, group work and sharing ideas are all ways students learn with and from one another.  In today's class, students worked with a  partner to solve questions about table data and then correctly construct a bar graph from it.