Grade 3 Notes


These sheets capture the imagery for key concepts in Grade 3. I have set them into this 3 pages in a “loose” order by which I would focus on them during the year. This is page one and you should note that the first 3 outcomes I am interested in starting the year with involve sorting and thinking about shape and space. My goal is to put students in touch with reasoning skills and to build their confidence and understanding with what it means to reason, how important it is to image and move things in your mind.

Grade 3 distinguish regular from irregular polygons. This is a big idea.

Grade 3 are expected to be able to sort by more than 1 attribute. This skill relates to reasoning through multi step problems, recognizing that there is more than one reason that items go together, recognizing that good evidence for an idea or proof for a solution fits more than one parameter or criteria.

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I would start the year with tasks that link measurement to division and fractions. Spatial reasoning that involves taking apart in equal partitions or sets or groups. Folding paper is about dividing 1 into parts. Literally you are introducing the idea of 1 ÷ 3 = 1/3

While students may not need to write and read the equation, they must understand this as division. It blows all that nonsense about when you divide put the big number first out the window. Understanding division is absolutely foundational to future math. We cannot reduce it to just memorizing some facts.


Centimetres are fractional parts of meters. Centimetres are divisions. Centimetres are proportionally related to meters by a 100 to 1 ratio.

Think of cm as 1 and m as 100. We are practicing place value thinking.

Perimeter is an important thinking idea. It is a measure around but it is still a length. Focus on seeing what perimeter is, not adding sides but composing and decomposing a whole length. The reasoning matters.

Will a 12 cm border fit around this picture? How do you know?

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How about this picture?

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This is page 2 of my Year at a Glance for Grade 3. You should note that there are 3 areas of concern for number.

1.) Students are expected to solidify their understandings of how number properties help them build automatic responses to addition and subtraction equations with single digits.

The goal: Quick response (3 to 5 seconds) to solve addition and subtraction equations with sums to 20.

2.) Mental fluency with predicting and accurately solving addition and subtraction equations or computations with 2 digit numbers. So 36 + 74 = 110 and I know because I thought 30 + 70 + 10. I just know it.

3.) Students make sense of and practice using strategies to confidently solve 3 digit by 3 digit additions and subtractions. I expect they will apply their strategies for 2 digit mental math.

In order to build success with 3 digit number there is NUMBER SENSE work to be done. Fluency with composing and decomposing 3 digit number is a huge part of the work. Adding and subtracting come last. If done well, students generate strategies without us.

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Page 3, below: you will note I leave multiplication and division to the end. Multiplicative reasoning is far more important than memorizing “facts.” We have been working on it all year. These outcomes are now about understanding what multiplication is, how division is related, how both include place value and fractions. The final piece: recalling some facts to 25 is an automatic recognition that is similar to subitizing. All the generative practice leads students to the knowing. These facts must be automatic if students are going to build the multiplicative reasoning they need in Grade 4 and 5.


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Data, pattern and passage of time need to be incorporated through out the year in daily and weekly activities that emerge from the regular day and other topics of study. that is why I have left them to the end.

Pattern in mathematics in grade three is about organizing data into tables and charts to see and explain patterns in the numbers. Generalizing from patterns is a way to practice relationships and “facts”.

What changed, what stayed the same? What’s the math going on?

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What changed, what stayed the same? What’s the math going on?

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