Week of June 27th – June 29th 2016:
Students will round out their year in Math exploring a variety of “virtual” (and real) fractions activities, and continuing to work towards mastery in various skills in their IXL accounts.
Week of June 20th – June 24th, 2016:
Last week, we took a look at ways to represent decimals to tenths… now that we’ve explored the idea that there are numbers bigger than zero but smaller than one, we’ll dig into that further with a look at fractions.
Week of June 6th – June 10th, 2016:
This week, we’ll continue with our work on Equality – solving equations using a variety of strategies, but we’ll also spend some time looking at coordinate graphing.
Week of May 30th – June 3rd, 2016:
This week in Math, students will extend what they know about equality to modeling and solving single-variable equations, using a variety of strategies and tools, including Algebra Tiles, Number Lines, bar models, and using the opposite operation.
Students can explore algebraic thinking in Math Playground, which has a number of games that require algebraic reasoning, such as this one:
Week of May 23rd – May 27th, 2016.
This week, we’ll be wrapping up our work in Measurement – I feel that I have enough information about the students’ learning from my conversations with them during class, observations during work time, and the completed tasks that they’ve sent me on Showbie, to inform my judgement when it comes to assessing their understanding and skill level, so I’m not planning on scheduling a “unit test”.
I would encourage students to complete the sections in their IXL accounts:
These skills are listed under “Geometry” on IXL, but they fall under the strand of Measurement in the Ontario Curriculum:
By Thursday or Friday, my plan is to begin to investigate some concepts in Algebra – starting with an exploration of Equality.
Students can get a head-start on some of the topics we will consider, on this section in their IXL Accounts:
Week of May 16th – May 20th, 2016
Last week, we spent time exploring the concepts of Area and Perimeter – ending with a game of “Capture the Array” on Friday – check out my blog post on the main page for photos, and instructions for how to play.
This week, we’ll spend some time working within problem-solving contexts to apply what we know about area and perimeter and… by Friday, will begin to explore volume of rectangular prisms.
Please check out the Illuminations website for an interactive activity that has students building rectangular prisms, using virtual cubes, to determine the volume of a given shape. Here’s the link:
Week of May 9th – May 13th, 2016
Last week, we reviewed what we had learned in previous grades about linear measurement – we covered things like:
- when you measure something, you have to measure in a straight line from one point to another
- when you use a ruler to measure something, you have to start at the zero, and count the spaces
- we use small units (like mm and cm) to measure small things, and bigger units (like metres and kilometres) to measure larger things
- I can use my body to estimate measurements – for example, my arm span is about 1 metre, and the width of my index finger is about 1 cm
This week, we’ll be investigating how to find area and perimeter of regular and irregular shapes. You can practice on IXL, or on these interactive sites:
Week of May 2nd – May 6th, 2016:
Last week we did a whirlwind tour of concepts like reading time to the minute, and counting money… all expectations in the Grade 4 curriculum in the Measurement strand of Math – but most of which have been thoroughly addressed in previous grades – so I didn’t think there was a need to spend a lot of time on it. I will be working my way through the work that the students handed in while I was at the ConnectEd Conference in Niagara last week, and catching up with anyone who needs further instruction.
It would be a good idea for students to work their way through the exercises in IXL on Time and Money – they will have some time in class to work on the program, but would benefit from a little bit of time spent at home.
This week, we’ll be exploring linear measurement – looking at the units that we use to measure length and how they are related, learning to to use a ruler or metre stick to obtain accurate measurements, and learning strategies for estimating the length, width, or height of an object. Depending on how we progress, we should start to talk about perimeter by the end of the week.
Week of April 25th – April 29th, 2016:
This week, we’ll be exploring the Measurement strand in Mathematics – with specific focus on time and money. We’ll review what students know about reading time on an analogue clock, and work on some problems that involve representing and counting Canadian Currency. Students are encouraged to work towards mastery in their IXL accounts – particularly the sections on Time and Money.
Week of April 18th – April 22nd, 2016:
Last week, we used what we knew about multiplication, to help us divide – students quickly caught onto the idea that division is simply the sharing out of a “whole” into equal groups – they can all divide a 2-digit number by a 1-digit number by drawing a model with equal groups, and many can use the Partial Quotients method (see the video I linked in last week’s update below) – I still need to teach that method to a number of students, and will pull them in small groups over the next few weeks.
This week, we’ll focus on putting what we understand about multiplication and division into a problem-solving context. Students will work through a problem-set (the assignment is on Showbie), and demonstrate their understanding and ability to solve problems using mathematical operations.
Week of April 11th – April 15th, 2016:
I feel fairly confident that everyone has at least one strategy they can rely upon to multiply a 2-digit number by a 1-digit number and, more importantly, that they understand the concept.
I’m less confident, unfortunately, that everyone is continuing to work towards mastery of multiplication facts… I keep making the point that knowing those facts “automatically” is going to make many future concepts in math much easier to learn… but I suspect that, by now, all they’re hearing is the Charlie Brown teacher voice (whaaa…. whaaaa whaa whaaaaa) – so if parents don’t mind reiterating the message at home – that would help 🙂 – we’ll keep re-testing every Friday morning to see how we’re improving with multiplication fact mastery.
This week, we’ll explore the concept of division (which, btw, is much easier if you know your multiplication facts… just saying…. whaa whaaaa whaa wha) – I won’t be teaching the students the “standard algorithm” that we learned in school, because it “unteaches” place value concepts that we work for years to consolidate. Instead, we’ll focus on the idea of division as repeated subtraction (taking away groups of the same number, until you can’t take away any more), and distribution amongst groups of equal size. With students who demonstrate readiness, I’ll introduce something known as “continental division” (because it’s taught in Europe) or “partial quotients” method of division – which is similar to the standard algorithm, but makes much more sense in terms of place value.
Below is a link to a screencast that I’ve created to demonstrate how to use the partial quotient method:
Week of April 4th – April 8th, 2016:
Today I sent some feedback to every student in their Showbie account – in the assignment titled “Multiplication Feedback” – please take a look if you haven’t already.
Last week we progressed through a sequence of learning activities to help us understand multiplication of 2-digit by 1-digit numbers. Everyone has mastered the skill of using an open array to multiply, and this week we’ll move to the standard algorithm.
Students are encouraged to continue to practice their multiplication facts, and we’ll complete a timed test (facts from 2 x 2 through 10 x 9) on Friday, to see how they’re coming along.
Week of March 28th – April 1st, 2016:
While we will have minimal time to practice multiplication facts during class time (there will be a few minutes, here and there, as I pull small groups of students together to work with me on different needs,) – students are expected to continue to practice on their own. There are both paper copies of practice questions, as well as the practice apps on the iPads. I plan to do a “check-in” every Friday, in the form of a timed test, to monitor how the students are progressing with improving speed and accuracy in learning their multiplication facts.
This week, students will work their way through a sequence of learning tasks designed to move them from a very basic understanding of multiplication to a more abstract grasp of the concept.
Past experience has taught me that jumping straight to the standard algorithm (which is how multiplication has typically been taught through the years) may have students “presenting” as though they understand the concept, but what many of them really have, when taught this way, is rote memorization of a series of steps, without deep understanding.
I understand that new and different ways of teaching mathematics can be unfamiliar and a little disconcerting to parents, so I have created a document, posted below, that outlines the sequence of skills and concepts that I plan to work through this week with the students – it’s not a document I would use with the kids, but might be helpful in clarifying, for parents, how their children are learning. Take a look, and please e-mail or call me with any questions:
Week of March 21st – March 25th, 2016:
This week, we’ll continue to learn strategies for mastering the multiplication facts.
Below, I’ve posted the slideshow that I’ll be using with the students so that they can review it on their own as needed.
After Monday, we won’t be dedicating any more in-class time to mastering the multiplication facts, although students are strongly encouraged to continue to practice them in their spare time. They have access to iPad apps, as well as pencil & paper drills to practice at school, whenever they have a few minutes, and can practice at home on their IXL accounts.
On Tuesday and Wednesday, I’ll be asking the students to complete a “diagnostic” assessment for multiplication and division – Tuesday’s portion of the assessment will be straight calculation, while Wednesday’s will be problem-based. (Students who attend the SOAR program on Wednesdays will have the opportunity to complete both parts of the diagnostic assessment on Tuesday, or to finish it on Thursday.)
The purpose of the diagnostic is to help me see who needs instruction in which skills, so that I can tailor the students’ learning experiences to match their unique needs.
The Ontario Curriculum Expectations for this topic, state that, by the end of Grade 4, students will:
- multiply to 9×9 and divide to 81÷9, using a variety of mental strategies (e.g., doubles, doubles plus another set, skip counting)
- solve problems involving the multiplication of one-digit whole numbers, using a variety of mental strategies (e.g., 6 x 8 can be thought of as 5 x 8 + 1 x 8)
- multiply whole numbers by 10, 100, and 1000, and divide whole numbers by 10 and 100, using mental strategies
- multiply two-digit whole numbers by one-digit whole numbers, using a variety of tools (e.g., base ten materials or draw- ings of them, arrays), student-generated algorithms, and standard algorithms
- divide two-digit whole numbers by one- digit whole numbers, using a variety of tools (e.g., concrete materials, drawings) and student-generated algorithms
On Thursday, I am at a planning meeting at the Education Centre, and Ms. Poole will be teaching the Grade 4 students how to use Base Ten Materials to multiply a 2-digit number x a 1-digit number. Below, I’ve posted a “screencast” video – created with Explain Everything, that models this process with Base Ten Blocks:
Week of March 7th – March 11th, 2016:
Last week, I had the opportunity to do small group assessments with every student, based on the concepts we’ve been studying in Geometry – feedback about student progress in this strand will be available in Showbie soon – I’ll send out an e-mail when the feedback forms have been completed.
When we come back from the break, we’ll be starting on Multiplication and Division of whole numbers. The learning expectations for Grade 4 are that students will be able to:
- multiply to 9×9 and divide to 81÷9, using a variety of mental strategies (e.g., doubles, doubles plus another set, skip counting);
- solve problems involving the multiplication of one-digit whole numbers, using a variety of mental strategies (e.g., 6 x 8 can be thought of as 5 x 8 + 1 x 8);
- multiply whole numbers by 10, 100, and 1000, and divide whole numbers by 10 and 100, using mental strategies (e.g., use a calculator to look for patterns and generalize to develop a rule);
- multiply two-digit whole numbers by one-digit whole numbers, using a variety of tools (e.g., base ten materials or drawings of them, arrays), student-generated algorithms, and standard algorithms;
- divide two-digit whole numbers by one- digit whole numbers, using a variety of tools (e.g., concrete materials, drawings) and student-generated algorithms;
This week, we’ll start with some diagnostic assessment to see where students are in terms of knowing their multiplication facts to 9×9. I will teach them strategies for learning the facts, but I can’t emphasize enough the importance of practice to gain automaticity – students who rely on strategies (doubles, clock facts, using the distributive property etc.) will be able to figure out the product of 2 numbers, but it will take so much time they’ll have difficulty with higher order skills like problem-solving and showing multiple representations of multiplication situations.
I have downloaded 2 apps onto the classroom iPads, that help students to practice memorizing the multiplication facts. They are:
Math Cards Flash My Math App – Flashcards
One requires students to select the correct answer from 8 options, and the other requires them to type in the correct response – both are excellent for building automaticity in multiplication facts. Students who use personal devices at school may wish to download one or both of these for a few weeks – they are both available for free on the App store.
Students can also practice multiplication facts in their IXL accounts – Section D1 – congratulations to the 7 students who have already mastered this skill in IXL – nice work!
Once the students have had an opportunity to work towards mastery of facts to 9×9, we’ll move on to exploring different strategies for multiplying 2-digit numbers by a 1-digit number, solving problems that involve multiplication of whole numbers, and looking at the relationship between multiplication and division – all after the break.
Week of February 29th – March 4th, 2016:
This week we’ll practice solving multiple choice questions on Geometry concepts – with a focus on learning how to tackle multiple choice questions by paraphrasing the question, eliminating impossible answers, and proving that the chosen answer is the correct one.
Students will also be given time in class to work towards mastery in the Geometry Section (Section P1 through P18) in IXL, while I do some assessment of their understanding of the concepts we’ve covered in Geometry, in small groups.
Week of February 22nd – February 26th, 2016:
This week we’ll resume the work we started earlier on Geometry – with a focus on properties of 2D shapes. Students will sort and classify shapes according to various geometric properties.
Week of February 15th – February 19th, 2016:
This week we move from building, extending and stating the pattern rule for linear growing patterns, to working with composite patterns (2 step functions).
Students are encouraged to work on Section H.1 (Functions – Input/Output Tables) in their IXL Math Accounts, and to practice solving Functions with the Function Machines on Math Playground and Top Marks (links below)
We’ll also be learning some strategies for solving multiple choice questions, using patterning problems as the basis for practice.
Week of February 8th – February 12th, 2016:
We’ll continue our work with patterns this week; we’ll concentrate on learning the difference between an additive pattern rule (one where you predict the next number by looking at the way in which all the previous numbers change) and a multiplicative pattern rule (one where you can predict the value of any number anywhere in the sequence, by looking at the term number (or position number.)
In this pattern: 2,4,6, 8…. I can predict that the next number will be 10… The additive pattern rule is “Start at 2 and add 2 each time”…. but to tell you what the hundredth number is in this pattern, using the additive rule, I would have to figure out all the numbers in between…. very tedious and time-consuming!
That’s where multiplicative rules are useful…. I take this pattern and put it into a table:
(The number 2 is in the first position, so it is Term #1, the number 4 is in the second position, so it is Term # 2, etc.)
When the numbers are written like this, I can see that the number in the second column is always double the term number…. The multiplicative rule for this pattern is “Position Number x 2) – once I know that, I can figure out the value for any position – the 100th term would be 200 (double the position number); the 40th term would be 80….etc.
There are some great interactive games on the web to practice this skill… and it’s fun because it’s a challenge to figure out the rule, based on the sequence of numbers. Here are 2 links you could try: (they’re both “Flash” run sites, which means they won’t work on an iPad)
We’ll also work on representing patterns with manipulatives – for example, the pattern shown in the table can be represented like this:
The fourth position would have…. how many tiles?
Week of February 1st – February 5th, 2016:
This week, we’ll take a short break from our work in Geometry (we’ll return to it in a couple of weeks) to do some exploration of patterns. We’ll look at what defines something as a pattern, patterns on a hundreds chart, growing and shrinking patterns, and pattern rules.
FunBrain has a good online game that challenges students to find the missing numbers in a sequence, and then state the pattern rule – you can access it by clicking the link below.
Students can also work on patterning skills on their IXL accounts – specifically – section J – “Patterns and Sequences”
Week of January 25th – January 29th, 2016:
The tests on Problem-Solving – Addition and Subtraction have been marked, and feedback provided to students’ Showbie accounts. Please check Showbie – 4A Math – the Assignment titled : “Problem Solving – Addition & Subtraction – Assessment Task” for feedback on your work. Those of you who opted to complete the task on hard copy (pencil and paper) will have those returned to you on Monday.
Last week, we explored ways to measure angle size, using “non-standard” tools – that is, we used the smallest pattern block (the tan rhombus) to determine the size of the angles in all the other pattern blocks. This week, we’ll be looking at using a more standardized tool (a protractor) to measure angle size.
If you’re looking for some extra practice estimating and measuring angle size, using a protractor, try this website – the more you do the more accurate you get at reading the angle measures.
Week of January 18th – January 22nd, 2016:
On Friday, students completed an assessment task, designed for them to demonstrate their skill in solving addition and subtraction questions (up to 4-digits) in a problem-solving context. I plan to work my way through those this week, and will post feedback on Showbie as I go. For students who opted to write the test on paper, feedback will still appear in Showbie, in the form of a “comment box” – but the paper copy of the assessment will also be sent home. Students who chose to complete the task on their iPads, can access it in their Showbie Accounts.
This week, we’ll be using a variety of tools (Anglegs, pattern blocks, transparency protractors) to work towards these learning goals:
- identify benchmark angles (straight angle, right angle, half a right angle)
- compare angles to benchmarks (i.e. 2 of the angles on the red pattern block are smaller than a right angle, and two are bigger)
- relate the names of the benchmark angles to their measures (e.g. an acute angle is between 1° and 89°; a right angle is 90°; an obtuse angle is between 91° and 179°, and a straight angle is 180°)
Week of January 11th – January 15th, 2016:
This week, students will complete their rotations through 4 Learning Centres that are designed to help them meet this learning goal: “Draw the lines of symmetry of 2-dimensional shapes using a MIRA, grid paper, and paper folding.”
They will also complete an assessment task on Friday morning, where they will have the opportunity to show what they know about problem-solving with addition and subtraction. We will continue to review 4-digit addition and subtraction at the beginning of each math class, but students are strongly encouraged to prepare for the test with some extra practice on IXL, specifically on topics B.2 (Add Numbers up to 5-Digits – Word Problems) and C.2 (Subtract Numbers up to 5- Digits – Word Problems)
Week of January 4th – January 8th
We’ll continue to review strategies for problem-solving involving 4-digit addition and subtraction – please keep practising on your IXL Math Account.
Students will complete an assessment to demonstrate their skill with this concept next Friday, January 15th.
This week, we’ll begin to explore concepts in 2D Geometry – starting with an exploration of the properties of 2D shapes, and line symmetry.
Week of December 14th – December 18th, 2015
After a lot of hard work, perseverance and effort, it looks like most of the students have grasped the concept of subtraction with regrouping. To make sure the skill is locked in, I strongly encourage everyone to spend time on IXL Math – on the Addition and Subtraction sections (Sections B and C) and work towards mastery of these skills. Since you can’t write on the screen on IXL (unless you’re using your iPad – then there is a pencil that opens up a “scratch pad”) – I recommend you have a whiteboard, or scrap paper handy when working out the problems.
This week, Ms. Bossence will introduce the skill of subtraction across zero, using a strategy that is hinged upon a solid understanding of place value, and the ability to “rename” numbers.
A student who has a good grasp of this concept would be able to look at the number 4, 502 and say: “I can compose (build) that number using 4 thousands, 5 hundreds, no tens and 2 ones.
… OR, I could build it with 45 hundreds, no tens, and 2 ones,
OR… I could build it with 450 tens and 2 ones etc.
The strategy is called “Squaring Off”, or is also sometimes referred to as “Boxing Out” – check out the video below for an explanation:
Week of December 7th – December 11th, 2015
Ms. Bossence will continue to be in charge of instruction in Mathematics; this week the focus will be on using the standard algorithm for subtraction, and learning to subtract across zero. Watch the blog for updates on student work, anchor charts and screencasts.
Be sure to get some extra math practice on your IXL account – I’ll send out an e-mail to parents this week with your child’s IXL login and password.
Week of November 30th – December 4th, 2015
This week, Ms. Bossence will take over instruction in Mathematics, and lead the students as they develop their own methods for subtracting a 4-digit number from another 4-digit number, in a problem-solving context.
Please keep practising your mental math skills (adding and subtracting 2-digit numbers in your head), and your addition – remember to work on your IXL Account – the “B” section is all about addition.
Week of November 23rd – November 27th, 2015
This week, we’ll continue to exercise our brains by using strategies to add and subtract numbers in our heads, and we’ll explore different strategies for adding 4-digit numbers with pencil and paper, and teach each other to use them in a problem-solving context.
Week of November 16th- November 20th, 2015
This week our student teacher, Ms. Bossence, will be taking over Math class. She’ll guide students as they continue to practice strategies for mental addition, and she’ll help them discover some strategies for subtracting numbers in their heads.
Got a long drive ahead of you this week? Try practising some mental arithmetic with your kids. Ask them to explain the strategies they’re using to add and subtract 2-digit numbers in their heads
Week of November 9th- November 13th, 2015
I’ve been working my way through the Place Value assessments that the students completed last week – I have about a 1/2 dozen left to go. Those students who chose to complete the task on “hard copy” will have theirs returned to them; everyone else has access to their completed test on Showbie. Feedback forms will be uploaded to Showbie when completed – please check your child’s Showbie account for details about strengths and next steps.
This week, we’ll begin working on strategies for Mental Addition. Students in Grade 4 are expected to be able to “add and subtract two-digit numbers, using a variety of mental strategies” (Ontario Curriculum 1-8, Mathematics p. 67).
We’ll use “Number Talks” to develop a range of strategies, starting with “Making Ten”.
Students should be familiar with this already, so we won’t spend much time on it – just a quick review and a game to practice.
Making Ten is a pre-cursor skill to another mental addition strategy – “Friendly Numbers” . We use friendly numbers to add larger numbers, by “adjusting” one number to make it a “friendly number”
For example: To mentally add 38 + 44, I would move 2 from 44 (making it 42) over to the 38 to make it 40 (a “friendly” number) – adding 40 and 42 in my head is easier than adding 38 and 44.
We’ll also use the “Doubles / Near-Doubles” Strategy. Human brains are hard-wired to seek out and recognize symmetry, so we find it easy to add doubles. (e.g. 33 + 33, 25 + 25, etc.)
An example of sum that could be found using the Near Doubles Strategy is 44 + 48. Double 44 to get 88, then add 4 to get 92.
The last mental addition strategy that I hope to spotlight this week is the “Breaking Numbers into Their Place Values” strategy. This is a “default” strategy that many students (and adults) use intuitively.
It works like this:
87 + 56 (think of the numbers in their place value positions: 80 + 7 + 30 + 6)
80 + 50 = 130
7 + 6 = 13
130 + 13 = 143
We’ll be spending lots of time this week talking about the strategies we use to solve addition problems mentally; we’ll practice doing it using the PingPong and Nearpod Apps, and we’ll use playing cards to practice mental addition.
Week of November 2nd- November 6th, 2015
This week we’ll wrap up the work we’ve been doing on understanding Place Value, and the students will have an opportunity on Wednesday to show what they know on our unit assessment. My apologies to students who participate in the SOAR program – I realize I keep scheduling Math tests on the day that you are away! I promise this will be the last time – Day 1’s are the best day in the cycle for any kind of assessment, because we’re together the whole morning, and we have time in the computer lab at the end of it – which means I can give you as much time as you need, and those of you who are finished can work in the lab. Next week, Day 1 will fall on a Thursday, and will stay that way till the end of December. Thanks for your understanding 🙂
Below is a link to a PDF file – a “parent guide” to the content we’ve been covering in Math – with information about what knowledge and understanding the students should be able to demonstrate
On Thursday, we’ll revisit using estimating skills to add numbers quickly.
Week of September 21st – September 25th, 2015
This week we’ll be working on creating Pictographs, using the data the students collected when they surveyed one another about their favourite things. This assignment has been posted on Showbie, and students will be learning to use the app to download instructions and work samples, and to photograph and upload their own work.
We’ll also begin to work on the final curriculum expectation for the data management strand in Grade 4 – using experimentation to gather, organize and interpret data. Students will be conducting and participating in a number of “experiments” (taste tests, endurance tests, strength tests, memory tests), logging the data and using it to make comparisons and draw conclusions.
Week of September 14th – September 18th, 2015
We spent some time last week learning how to read and interpret data in a chart, and gathering information about the members of our classroom community (who plays sports, what everyone likes to read, when everyone’s birthday is, etc.) with survey questions.
This week, we’ll review how to read and interpret bar graphs, and then use the class “data set” (the information gathered in the surveys) to construct bar graphs of our own. Students will also generate their own survey questions to find out more about one another – a focus on “favourites” – foods, hobbies, sports, movies, books, etc. and collect some more data that we’ll use to create pictograms
We are learning to use the interactive apps “PingPong” and Nearpod to generate discussion about our mathematical thinking – the kids are picking up how to use the technology very quickly – we are getting closer to having 1:1 iPads in the class – thanks to those who have already decided to allow their children to “BYOD” – if anyone out there still has questions about the BYOD option, please let Mrs. Meadows or myself know.
Week of September 8th – September 11th, 2015
We will begin the school year with the “Data Management” strand of Mathematics, making use of surveys, questionnaires and experiments to learn about everyone in our classroom community, and then organizing the data that we collect in a variety of charts, graphs and tables for analysis.