GEOMETRY
We are looking at 2D shapes and 3D solids and many of their properties.
3D Solids
Students are building 3D solids to explore the difference between pyramids and prisms as well as review the properties of vertices, edges, and faces. They are enjoying this project tremendously because it combines many things they enjoy....using their hands to build, using technology to document their understanding, and eating a delicious treat.
2D Shapes
The amount of math vocabulary that students need to learn for 2-dimensional geometry is a big jump from grade 2 curriculum. Students need to not only be able to name all the standard shapes (hexagon, triangle, pentagon, etc.) but must know what polygons, quadrilaterals and parallelograms are. They also need to be able to determine lines of symmetry, whether lines are parallel or not and if angles are right angles or greater or less than right. Finally, another knew vocabulary term is congruent. Identifying shapes that are congruent (same shape and same size) or similar (same shape different size) will also be practiced.
Fractions
We move on from division and are taking a look at fractions - of a set of things, of a whole, and how fractions fit in with whole numbers on a number line. We will also be using fractions to determine the probability of an event when looking at fractions of a whole like on a spinner.
Division - Using Multiplication Knowledge to Solve Division Problems
Many strategies to use but they all get you to the same place. Students understand the concept of division as sharing. We will continue to use this knowledge and qpply it in problem situations.
New Links To Practise Multiplication
Using What We Learned About Multiplication To Solve Problems
Exploring What Multiplication Really Means By Using Arrays
I simply asked the question, which grouping has the greatest number of cubes....turn and talk with a buddy. A huge discussion resulted - students agreeing or disagreeing about amount of cubes, sharing of methods for how they determined amount.
From Finding the Sum & Difference To Finding The Product & Quotient
Many students are becoming confident with subtraction using various strategies inlcuding the algorithm. We will continue to practice for the next few days and a short assessment update for both adding and subtracting 3-digit numbers will be sent home to let you know if your child needs to continue practicing at home. By Thursday or Friday, we will begin exploring the various strategies for multiplication (ex. arrarys, repeated addition).
Students discovered after many different mental strategies were shared that even though all strategies work to find the solution, there are some strategies that get you there faster - MORE EFFICIENT. So now that they know many strategies, their next step is to start determining which strategy would most efficient.
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Finding The Difference
During our math talks, we are discovering some strategies that help us do mental subtracting. We have decided on 2 so far.
1. The Separation Strategy (which is similar to the addition TSS)
100-49
=100- 40 - 9
=60 - 9
=51
2. Add On
100-49
49 + 10 + 10 + 10 +10 + 10=99
99 + 1 = 100
10 + 10 + 10 +10 + 10 + 1 = 51
We are also looking at how estimating can help us with quick subtration to see what the difference will be "about".
She has 217 bottles but needs 500....217 is closer to 200/220 (depending if the student prefers rounding to hundreds or tens). ....so she needs ABOUT 300/280 bottles.
Tomorrow we take a closer look at the thinking behind the algorithm so "borrowing" makes sense.
1. The Separation Strategy (which is similar to the addition TSS)
100-49
=100- 40 - 9
=60 - 9
=51
2. Add On
100-49
49 + 10 + 10 + 10 +10 + 10=99
99 + 1 = 100
10 + 10 + 10 +10 + 10 + 1 = 51
We are also looking at how estimating can help us with quick subtration to see what the difference will be "about".
She has 217 bottles but needs 500....217 is closer to 200/220 (depending if the student prefers rounding to hundreds or tens). ....so she needs ABOUT 300/280 bottles.
Tomorrow we take a closer look at the thinking behind the algorithm so "borrowing" makes sense.
Using Estimating
We revisited rounding to the nearest ten and nearest hundred to estimate what the sum could be. Students discovered that they have a preference of what to round to when estimating. They also discovered that if there are multiple numbers, rounding to the nearest hundred is a little bit easier when adding to find the sum.
Example: 416 + 369 + 294 + 385
Estimate 400 + 400 + 300 + 400 is easier to add than 420 + 370 + 300 + 390
Example: 416 + 369 + 294 + 385
Estimate 400 + 400 + 300 + 400 is easier to add than 420 + 370 + 300 + 390
Finding Sums and Differences to Three-Digits
Our mental math strategies for addition have made it to 3-digits. We realized today that our mental strategies (e.g. "The Separation Strategy" like 135 = 100 + 35) match what we need to think when using the traditional algorithm. We will continue to use our mental strategies and will officially start to focus on using the algorithm for both subtraction and addition in the context of solving math problems. This means we will be pulling out our KNOWS strategy that we were using before.
Perimeter vs Area
Students practiced finding perimeter (the distance around an object just like a fence to keep the preschool chldren from escaping) in squares and area (covering the inside just like putting down carpet or tiles) in square units. We discussed some strategies to be accurate (e.g. making sure all sides are "fenced in" so sometimes have to count the square for one side and the same square for the next side like the blue tile in the photo) and some strategies to be more efficient (e.g. count by 2's when calculating area when there are rows of 2 or count by 10's if there are columns of 10). Tomorrow we will look at how to find area when information is missing since we've explored what to do when information is missing for finding perimeter (e.g. the top is 10 cm so the bottom of the rectangle must be 10 cm since they are the same length).
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More Mental Math - See How Far They Have Come
Mental Math - Tool and Tutorial
Here is a link that explains a tool that could help develop your child's number sense skills which in turn will help your child progress in addition and subtraction so they can move away from using their fingers when doing computations mentally.
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Mental Math Skills
(For 10 minutes a day, we are training our mental math skill abilities. Students are using many different strategies. We have named 2 (Making Ten and Making A Friendly Number) and today we will name a third strategy that they have started using (Break The Number Into Its Place Value Parts). The way this activity is done is a number sentence is posted and students have think time. Once they have an answer they signal me. When there are many students ready with an answer, all answers are shared. (some students are practicing a 4th strategy by commenting on whether or not another students answer is reasonable ). Then students share their strategies - what was happening in their brain to determine the answer. As students talk, I record their steps using numbers and symbols. The photos below show students' thinking.
Can You Say PERIMETER? The Students Sure Can Determine Exact Perimeters
For the pictures below, students were assigned with the task of designing a fence structure to surround a garden for the Pre-school here at St. James. They were told that the preschool only had 20 m of fence to use. They were allowed to choose any shape as long as it was completely surrounding the garden so no children could escape. Students were creative and accurate with their perimeter of 20 m.
Today students had a similar challenge but this time they had to create a border for a Lego tower and they had 1m of Lego to use to create the border. Students quickly caught on that 1m is exactly 100 cm and worked with those numbers to create a variety of accurate designs. The corresponding photos are above.
Today students had a similar challenge but this time they had to create a border for a Lego tower and they had 1m of Lego to use to create the border. Students quickly caught on that 1m is exactly 100 cm and worked with those numbers to create a variety of accurate designs. The corresponding photos are above.
Measuring With More Accuracy
Students are measuring using meters centimeters. Recording their measurements using numbers and units is an important piece. When the item falls between the whole numbers they have realized that the little mm lines count by ones and that to record halfway between whole number it is recorded by using .5 (e.g. 6.5 cm). They also are combining meters and centimeters when objects are longer (e.g. 1 m 24 cm). We will keep practising and will soon apply these skills to find perimeter.
Our First Step To Explore Meters!
Students have gained a strong grasp of measuring with cm. They practiced using a benchmark of 10 and 30 cm to gain an understanding of how long that really is. The ability to use a ruler (starting at zero and using appropriate numbers for cm) is solidifying as well. We started an activity to begin our "meter" journey but ran out of time. We pick it up tomorrow.
Measurement Continues.....Linear Measurement This Time
Today we explored non-standard measurement (e.g. 5 cubes long), vocabulary (length=long, width=wide, height=tall), and standard measurement (just cm today) using a ruler...."make sure you start at the zero and not the one on the ruler" was heard a few times. Tomorrow, students will continue linear measurement with theirstuffy friends. Watch for photos to show up soon (posted on first page of blog).
Time To Start TimeWe took some time to review Gr. 1 and Gr. 2 expectations for time - hands, face, o'clock, thirty. Students helped to make a classroom clock by adding the minute lines. This was a great concrete way to have students recognize that there are 5 minutes between each number and that if you count them all the way around the clock it is 60 minutes. We also played an ordering time game to get the feel for linear time. Students are beginning to tell time using specific time vocabulary such as "10 minutes after 5" and "20 minutes before 4". Our next steps will be to review and solidify the understanding of quarter hours and then learn how to determine elapsed time.
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Using An Acronym to Help Show Thinking and Understanding While Problem Solving
Coming Back in January...Money Continued and Time Begins
Which one doesn't belong? How many different ideas can you come up with? Ask your child to explain the ones they came up with and see if your's are the same.
Played the money game to refresh our memories on adding money, making change, using a number line. Fun was had by all ....so much so they didn't realize how hard they were working.
Still Working With Money
Still working on money concepts up to $10.00. Worked on this problem... Abdul has 7 quarters. Sanjeet and Cindy have the same amount of money as Abdul, but Cindy has less coins and Sanjeet has more coins. What possible combination of coins could each have? Here is what students came up with! If a group finished, they were given an alternative problem with a new money combination for Abdul (a loonine and 6 quarters).
Show Me The Money!
Girls and boys have been having a great deal of fun with money. Most already know the names of the coins, their values and the difference of adding dollars or cents so we started with strategies on how to find out how much money you may have. Some of the strategies that they realized worked well are:
-sorting coins into piles of the same coin and then skip counting by that amount e.g. nickels by 5 or quarters 25, 50, 75, 100...a dollar
-making piles of $1 ...again using the first strategy or making 4 piles of quarters or value of 25 cents
-making smaller piles of 25 cents or 5o cents using a mix of leftover coins to help make a $1 pile.
-adding dollars with dollars and cents with cents
This skill is coming along quite well and it is being applied in a variety of problem types.
e.g. I have $5 in my pocket. There are 10 coins and only 3 types of coins. What might they be?
e.g. How many ways can you make $7. 75? Can you make it with the least number of coins and bills?
The problem we tried today was about making change and figuring out strategies to make change.
Mr. Scott went shopping and at the end of the day he had $8.00 left. How much money did he start with and how much did he spend?
Strategies that were used were
-subtracting from amount spent until $8.00 was reached.
-using n open number line (students decide what number the line starts at and where it finishes) to count backwards or forwards by "friendly" amounts to reach the amount spent.
-using algebraic thinking "What amount can be added to $8.00 to get to the amount spent?.... then guess and check
-sorting coins into piles of the same coin and then skip counting by that amount e.g. nickels by 5 or quarters 25, 50, 75, 100...a dollar
-making piles of $1 ...again using the first strategy or making 4 piles of quarters or value of 25 cents
-making smaller piles of 25 cents or 5o cents using a mix of leftover coins to help make a $1 pile.
-adding dollars with dollars and cents with cents
This skill is coming along quite well and it is being applied in a variety of problem types.
e.g. I have $5 in my pocket. There are 10 coins and only 3 types of coins. What might they be?
e.g. How many ways can you make $7. 75? Can you make it with the least number of coins and bills?
The problem we tried today was about making change and figuring out strategies to make change.
Mr. Scott went shopping and at the end of the day he had $8.00 left. How much money did he start with and how much did he spend?
Strategies that were used were
-subtracting from amount spent until $8.00 was reached.
-using n open number line (students decide what number the line starts at and where it finishes) to count backwards or forwards by "friendly" amounts to reach the amount spent.
-using algebraic thinking "What amount can be added to $8.00 to get to the amount spent?.... then guess and check
We Will Be Taking A Look at Money and Time Next!
Grade 3 Curriculum Expectations
-read time using analogue clocks, to the nearest five minutes, and using digital clocks (e.g., 1:23 means twenty-three minutes after one o’clock), and represent time in 12-hour notation;
– solve problems involving the relationships between minutes and hours, hours and days, days and weeks, and weeks and years, using a variety of tools (e.g., clocks, calendars, calculators).
– solve problems that arise from real-life situations and that relate to the magnitude of whole numbers up to 1000 (Sample problem: Do you know anyone who has lived for close to 1000 days? Explain your reasoning.)
– estimate, count, and represent (using the $ symbol) the value of a collection of coins and bills with a maximum value of $10;
-add and subtract money amounts, using a variety of tools (e.g., currency manipulatives, drawings), to make simulated purchases and change for amounts up to $10 (Sample problem: You spent 5 dollars and 75 cents on one item and 10 cents on another item. How much did you spend in total?)
– represent and describe the relationships between coins and bills up to $10 (e.g., “There are eight quarters in a toonie and ten dimes in a loonie.”);
-read time using analogue clocks, to the nearest five minutes, and using digital clocks (e.g., 1:23 means twenty-three minutes after one o’clock), and represent time in 12-hour notation;
– solve problems involving the relationships between minutes and hours, hours and days, days and weeks, and weeks and years, using a variety of tools (e.g., clocks, calendars, calculators).
– solve problems that arise from real-life situations and that relate to the magnitude of whole numbers up to 1000 (Sample problem: Do you know anyone who has lived for close to 1000 days? Explain your reasoning.)
– estimate, count, and represent (using the $ symbol) the value of a collection of coins and bills with a maximum value of $10;
-add and subtract money amounts, using a variety of tools (e.g., currency manipulatives, drawings), to make simulated purchases and change for amounts up to $10 (Sample problem: You spent 5 dollars and 75 cents on one item and 10 cents on another item. How much did you spend in total?)
– represent and describe the relationships between coins and bills up to $10 (e.g., “There are eight quarters in a toonie and ten dimes in a loonie.”);
Graph Checklist - What you need to show all you know about a graph
Data Management Continued
Students are getting pretty solid with creation and analysis of various pictographs, bar graphs and circle graphs. Now we have been working on the final step - application of this knowledge. Here are some sample questions (straight from EQAO from previous years). Take note of the vocabulary used in the questions - JUSTIFY YOUR ANWER... EXPLAIN YOU THINKING. Students not only have to determine what the question is asking them to do, but they must also show the steps used to get there using pictures, numbers and words.
We also are taking a look at Venn diagrams. Today students got their brains going with a math talk about sorting and what their sorting rule was. Then they went off in groups to try and determine sorting rules for creating a venn diagram using various items. They used the app Show Me to document their learning. Here are two examples.
More Data Management
We continue to look at bar graphs, pictographs and circle graphs. We focused a little more on the survey question, how the data can be organized effectively on both a bar and a pictograph (including labelling with titles, creating a key, and detemining a useful scale to show data clearly), as well as comparing the data to draw conclusions. We explored these areas using our small groups on the vertical whiteboards, coming together as a whole group to share our findings, and of course some partner and individual practice.
Use Your Key and Check the Scale of Your Bar Graph
Students practiced using various scales on bar graphs. We took a look at the homework (which many haven't returned yet) and noticed that every square was worth 2 according to the scale shown by the numbers on the bottom. This changed the information drastically when comparing more and less.
To further solidify the various strategies for determining difference between amounts on a graph, students practiced using cubes to create the bars. At first, the cubes were just one. After students were able to voice their strategies (counting up from where the shorter bar ended, counting down until reaching where the shorter bar ended, thinking of what added to the shorter bar's number will give me the difference), the scale was changed on them. Each cube then became worth 5, then 2, then 7. Always using the same strategy to determine difference.
Example Each cube is worth 5. I counted down from the top of the yellow by 5's until I reached the top of the black bar...5, 10, 15, 20. There are 20 more students in the yellow bar. |
The vertical bar graph pictured to the left was used for an "Exit Card" where students had to show their individual understanding by writing 4 sentences about the data on the graph about sleeping animals.
Ex. Chimpanzees sleep 10 less hours than brown bats.
Red fox sleep 6 hours more than giraffes.
Brown Bats sleep the most.
Giraffes slept the least.
Even after all the group and partner practice, many still forgot to check the scale of how the graph was counting. Stating things like "Brown Bats have 2 more than red fox." We will continue to practice this skill in reading and creating graphs.
Ex. Chimpanzees sleep 10 less hours than brown bats.
Red fox sleep 6 hours more than giraffes.
Brown Bats sleep the most.
Giraffes slept the least.
Even after all the group and partner practice, many still forgot to check the scale of how the graph was counting. Stating things like "Brown Bats have 2 more than red fox." We will continue to practice this skill in reading and creating graphs.
Sorting Is A Part of Data Management
Students get their brains started by taking a look at some numbers and devising strategies to sort. Amazing the different ways students found to sort them.
Then they were off to sort their pile of Halloween treat wrappers any way they could. Many groups (random groups of 3) came up with 3 or 4 different ways. Can you determine some of the sorting rules pictured?
We came back together as a class and shared some of the sorting strategies. Finally, we decided a common sorting strategy in order to determine an over tally of all the Halloween wrappers.
Starting Data Management-This Week
Overall Expectations
y the end of Grade 3, students will:
• collect and organize categorical or discrete primary data and display the data using charts and graphs, including vertical and horizontal bar graphs, with labels ordered appropriately along horizontal axes, as needed;
• read, describe, and interpret primary data presented in charts and graphs, including vertical and horizontal bar graphs
y the end of Grade 3, students will:
• collect and organize categorical or discrete primary data and display the data using charts and graphs, including vertical and horizontal bar graphs, with labels ordered appropriately along horizontal axes, as needed;
• read, describe, and interpret primary data presented in charts and graphs, including vertical and horizontal bar graphs
Collection and Organization of Data
By the end of Grade 3, students will: – demonstrate an ability to organize objects into categories, by sorting and classifying objects using two or more attributes simultaneously (Sample problem: Sort a collection of buttons by size, colour, and number of holes.); – collect data by conducting a simple survey about themselves, their environment, issues in their school or community, or content from another subject; – collect and organize categorical or discrete primary data and display the data in charts, tables, and graphs (including vertical and horizontal bar graphs), with appropriate titles and labels and with labels ordered appropriately along horizontal axes, as needed, using many-to-one correspondence (e.g., in a pictograph, one car sticker represents 3 cars; on a bar graph, one square represents 2 students) (Sample problem: Graph data related to the eye colour of students in the class, using a vertical bar graph. Why does the scale on the vertical axis include values that are not in the set of data?). |
Data Relationships
By the end of Grade 3, students will: – read primary data presented in charts, tables, and graphs (including vertical and horizontal bar graphs), then describe the data using comparative language, and describe the shape of the data (e.g.,“Most of the data are at the high end.”; “All of the data values are different.”); – interpret and draw conclusions from data presented in charts, tables, and graphs; – demonstrate an understanding of mode (e.g.,“The mode is the value that shows up most often on a graph.”), and identify the mode in a set of data. |
Weblinks For Online Patterning Practice
Boys and girls have a strong abiltiy to make repeating patterns as well as extending them and identifying the attributes. Now they are looking at patterns that grow. Below are photos of the two types they have been exploring.
Not just Repeat Patterns But Growing Patterns and T-Charts
We've updated our anchor chart by labelling the attributes of the repeating patterns. (photos above) Students tried to make their own - ensuring they have 3 attributes from the list. Here are 3 that were accomplished. (photeos below)
Math Talk
This is a quick activity we try to do 2-3 times a week to have students talk about math using math vocabulary as well as learning to discuss with peers ideas even when they disagree-how to do it in a positive, non-threatening, productive way.
Our Anchor Chart So Far For Patterning
Are you able to fill in the attributes for the example repeating patterns on the chart?
Growing Patterns Are Fun....Let's Try Repeating Patterns Too
Today, we took a look at repeating patterns and various attributes. By the end of the block, students were being challenged with creating patterns with at least 3 attributes. They soon realized that an attribute only counts as changing if the change is happening to the same item. (e.g. A big heart and a small cube is NOT a change in size for the attribute size. A big heart and a small heart is a change in size for the attribute size). We will continue exploring growing patterns and repeating patterns all next week.
Here are the different attributes students came up with.
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Sort first!
Once students had a pattern, they took a photo. We regrouped as a whole class each time to discuss the following things:
1. Is it a pattern? 2. How do you know?... What type of pattern is it (Repeating or Growing?) 3. How many attributes does it have? 4. What are the attributes? |
Take a look at these photos and go over with your child the same 4 questions we did in class.
Students Go "Paintballing" To Get a Taste of Patterning!
I hooked the students' interest with having them use an imaginary paint ball gun and shooting at a target. Our first shooter was very accurate with her shooting and she got us started with our first quest to figure out what the target would look like by Target #7. Students worked hard to figure it out and with great success. The second one was a little more challenging.
Rounding to the Hundreds
It got a little tricky for some changing from rounding to tens to rounding to hundreds. Students simply need to follow the steps as before but instead of underlining to the tens, underline to the hundreds.... then circle the digit to the right (now circling the tens) and that will help you determine "let it rest" or "raise the score".
Greater Than/Less Than AND Rounding to The Nearest Tens
Get out your "chompers" .... your greater than/less than chompers that is.
Students are strong with their knowledge of which numbers are greater and many can explain why. "I look at the digit on the number on this end (left) and look at the other number to make sure it (the digit) is in the same place (place value spot) as the other number. Then I see which has more. (e.g. 3 groups of a hundred vs 6 groups of a hundred).
Now they simply are learning the symbol to show which number is greater. "The chomper eats the greater number" (e.g. 1,234 < 3,456).
We've also started looking at "friendly numbers" to prepare us for estimating and other computation strategies. We have been using this little rhyme: 4 or less, let it rest....5 or more, raise the score. Strategies also include underlining all the digits until the place you are rounding to (this case the tens), circling the digit to the right, deciding the lesser friendly number and the greater friendly number and putting them at either end on a number line. See the picture below.
Students are strong with their knowledge of which numbers are greater and many can explain why. "I look at the digit on the number on this end (left) and look at the other number to make sure it (the digit) is in the same place (place value spot) as the other number. Then I see which has more. (e.g. 3 groups of a hundred vs 6 groups of a hundred).
Now they simply are learning the symbol to show which number is greater. "The chomper eats the greater number" (e.g. 1,234 < 3,456).
We've also started looking at "friendly numbers" to prepare us for estimating and other computation strategies. We have been using this little rhyme: 4 or less, let it rest....5 or more, raise the score. Strategies also include underlining all the digits until the place you are rounding to (this case the tens), circling the digit to the right, deciding the lesser friendly number and the greater friendly number and putting them at either end on a number line. See the picture below.
Taking What We Know and Using it With Thousands
Groups of a thousand have been added to our number work. It is amazing to watch students order numbers from least to greatest, create numbers themselves and place them on number lines that they have created themselves. We continue to practice odd and even both in the class and in the gym. This would be a good skill to practice at home (e.g. when driving in the car, give numbers to your child and have them tell you if it's odd or even, see a number in a flyer or newspaper and get your child to tell you if it is odd or even). Next week, we will continue to use numbers to 9,999 while we explore rounding to the nearest ten or hundred, as well as the uses for a number line.
Moving on to the Hundreds
Boys and girls are getting quite comfortable with numbers up to 999. We continued with place value, adding/taking away 1, 10, and 100, and now we are moving on to comparing (greater than, less than, placing numbers on a number line).
Digging A Little Deeper
We've continued with hands on exploring of numbers. Here are some of the things that we've been learning and practicing.
Looking At Numbers
We are starting with numbers and all that we know about them using hands-on manipulatives and then representing that information using numerals and symbols (+, -). Students are amazing me with what they know. We will continue to look at numbers into the hundreds - place value, odd vs even, probability with estimating. If you are looking for a way to support your child, practicing addition and subtraction facts to 20 so they have that knowledge embedded (instead of counting on his/her fingers), that would be helpful.