Math

N2- Represent and describe numbers to 1000 concretely, pictorially and symbolically. Examples would be using standard form (just the digits), base ten materials, place value chart, base ten language ( 6 thousands 5 hundreds 3 tens 4 ones), expanded form (6000 + 500 + 30 + 4).

Some activities:

• Ask your child to count to 1000 by 100s.

• Try rolling a dice 4 times to create numbers in the thousands. See who rolls the bigger/smaller number.

• Talk about when 1000 is a big number and when it is a small number.

• Have your child write down a series of numbers that are read to them. Include numbers that contain zero.

N3- Compare and order numbers to 1000.  

Students should be able to read, write, compare and order two or more whole numbers, each less than 1000. Early instructional strategies will include situations involving hundreds charts and number lines, but then gradually progress towards the use of place value positional names in determining relative sizes.  For example, to compare 667 and 607, students should notice that both numbers have 6 hundreds, but that the 667 is greater than 607 because it has more tens in the tens place. The numbers could also be compared by considering their relative position in the counting sequence: 667 comes after 607, so 667 is greater than 607.

Students should also be able to name numbers  greater than, less than or between given numbers and be able to arrange them in ascending and descending order.

In grade three the symbols " < and >" are introduced to show less than and greater than.

Some activities:

• Play "Guess My Number" with your child using numbers less than 1000.  Use greater than, less than in the response (i.e. "is your number 498?" "No, my number is greater than that.") Continue until the number is guessed and then switch roles.

• Repeatedly roll a die and have your child fill in the digits, one at a time, on a place value chart (hundreds, tens, ones).  Alternate by having them make the greatest number and the least number with the digits. 

• Make up a set of 10 cards with each card having a 2 or 3 digit number on it (you could use recipe cards).  Ask your child to order the number cards from least to greatest and to explain how he or she determined the relative number size.

N4- Illustrate, concretely and pictorially, the meaning of place value for numerals to 1000.

In grade 3, students will come to understand that there is a constant multiplicative relationship between the place values in a multi-digit number; i.e., from right to left, the value increases by powers of 10.  As they develop a deeper understanding of numbers to 1000, students will be able to compose and decompose numbers in more flexible ways.  For example, they will begin to recognize 842 as 84 tens and 2 ones  or 8 hundreds and 42 ones or 800+40+2, or 500+300+20+20+2, etc.

Some activities:

• Ask your child to record the number that is made up of 15 tens and 15 ones.

• Ask your child to build a model or draw a picture using base ten blocks. Ask: What is the value of the drawing/ model?

• Ask your child to model a number such as 507 in a variety of ways.

• Ask your child to model two numbers such as 421 and 139. Discuss which number has more tens, and how they know.

N1- Say the number sequence forward and backward from 0-1000 by:

• 5s, 10s, or 100s using any starting point

• 3s using starting points that are multiples of 3

• 4 using starting points that are multiples of 4

• 25s using starting points that are multiples of 25

In grade 3, students are continuing to develop and understanding of number and counting.  A focus on skip counting in the early years helps them to recognize and apply the patterns in our place value system and prepares them for work involving money.  

Some activities:

• Use a hundred chart (1-100, 101-200 etc.) and have your child colour in the pattern for a given skip counting sequence.

• Have your child count beans in a jar.  Ask him/her how the beans were grouped (5s, 10s, 2s...) for ease of counting.

• Have your child correctly identify the error in a given skip counting sequence such as:  12, 16, 21, 24, 28, 32.

• Play "What's in the Can?"  Tell your child you are going to drop nickels (or dimes or quarters) into a can.  Have your child listen as the coins drop and count to find the total.

N10- Apply mental math strategies and number properties to recall basic addition fact to 18 and related subtraction facts.  Strategies include:

• using doubles

• making 10

• using the commutative property

• using the property of zero

• thinking addition for subtraction

It is expected that by the end of Grade 3 students will have achieved fluency with the addition and subtraction facts to 18.  It is important to provide regular and frequent opportunities to introduce, develop, reinforce and practice thinking strategies using games and meaningful contexts as much as possible.  When recall of facts are automatic, students are no longer using strategies to retrieve them from memory.  It is strongly encouraged that students learn subtraction facts by "thinking addition", rather than starting with a number, counting off what is to be subtracted and then counting what is left over.

Some activities:

• Have your child roll 2 dice (or number cards).  They either add or subtract these values.  Ask your child to make up a subtraction or addition story based on these numbers and write a corresponding number sentence.  

• Play "Missing Part" game for two to practice fact recall.  One player places a number of counters in front of them (i.e., 16) and then the other player covers up some of the counters with their hand.  The first player must determine how many counters are hidden as quickly as possible.

• Provide your child with cards with a subtraction number sentence (13-7=).  Have your child rewrite the sentence as a missing addend number sentence (7 + __  = 13)  and solve it.

N6- Describe and apply mental math strategies for adding two 2-digit numerals, such as:

• adding from left to right

• taking one addend to the nearest multiple of ten and then compensating

• using doubles

N7- Describe and apply mental math strategies for subtracting two 2-digit numerals, such as:

• taking the subtrahend to the nearest multiple of ten and then compensating 

• thinking of addition

• using doubles

Using mental math will focus a student on the relationships between numbers and operations rather than relying on completing the traditional algorithm.  For example, students might solve 49 + 99 mentally by adding 100 to 49, then subtracting 1.  This method involves using benchmark numbers then compensating by adding or subtracting, whichever operation is necessary.  Presenting practice items horizontally rather than vertically will encourage students to look to the numbers first and then think about them in terms of their place value.

I will be introducing computational strategies for mental math in this unit, but students are not limited to those alone.  It is important to note that students are not expected to master all strategies, rather, they are encouraged to try them out and then choose the one(s) that work best for them as an individual.

Some activities:

• Provide a set of practice questions and ask your child to circle the ones they would like to solve mentally and have them describe the strategy they would use.

• Ask calculations such as the following (orally or on paper), and ask your child to write only the answer.  Allow only a few seconds for each question (i.e. 300+600, 200-40, 200+80+30, 220-40)

• Ask:  How many different ways can you add 19 to 63 in your head?

• Ask:  How many different ways can you subtract 19 from 63 in your head?

• Have your child list doubles facts that might help him/her solve expressions such as 28+29 and 40-20 or 57-29.

*Remember to check the "resources" tab to see the anchor charts we use in math class!

N9- Demonstrate an understanding of addition and subtraction of numbers with answers to 1000 (limited to 1, 2 and 3-digit numerals) by:

• using personal strategies for adding and subtracting with and without the support of manipulatives

• creating and solving problems in contexts that involve addition and subtraction of numbers concretely, pictorially and symbolically.

Students are expected to apply what they know about the addition and subtraction of single digit numbers and the meanings of these operations to 2- and 3-digit numbers.  As their understanding of these processes and of place value deepens, they will begin to record their work in ways that make sense to them.  One of these ways may look like the traditional right to left, borrow/carry but there are other methods that are just as acceptable.

In Grade 3, students are expected to be able to interpret  word problems involving missing parts of the number sentence or answer, and write number sentences that represent these story situations.  They are also expected to create their own word problems given an addition or subtraction number sentence.

Some activities:

• Use the following digits to create two, 2-digit numbers that have the greatest possible sum: 2, 3, 4, 5.  Use the same digits to create the greatest difference..

• Set up a "store" at home and have your child take turns being the cashier.  Model for them how to "count on" when making change.

• Continue practicing mental math strategies.

N8- Apply estimation strategies to predict sums and difference of two 2-digit numerals in a problem solving context.

Estimation strategies include rounding to the nearest multiple of ten or 100, front-end estimation or a combination of the two.  Exploring the proximity of the estimates to the exact answers and making comparisons to the numbers and the operation used with enable students to become more efficient in their ability to estimate.

Some activities:

• Play "A Fast Ten" with your child.  Turn over 2 playing cards ( a deck of cards numbered 1-9 only) to build a two-digit number.  The player who determines which multiple of ten that number is closest to gets the cards.  This game could be extended to add or subtract estimates of two pairs of cards.

• Tell your child that the sum of two numbers has been estimated to be about 120.  Ask your child to list four possible pair of numbers that might have been added.

• Have your child use estimation in real life "story problems" you encounter as a family. For example, "Mom spent $58 at the Superstore and Dad spent $45 at Sobeys.  About how much did we spend all together?"

N11- Demonstrate an understanding of multiplication to products of 36 with single digit factors by:

• representing and explaining multiplication using equal groupings and arrays

• creating and solving problems in context that involve multiplication

• modeling multiplication using concrete and visual representations, and recording the process symbolically

• relating multiplication to repeated addition

• relating multiplication to division

It is important that students understand the "groups of" meaning for multiplication and to recognize that the answer may be found in a number of ways, including:

1. repeated addition- 4+4+4 can be written as 3x4

2. making sets of equal groups- students can create equal sized groups with actual items

3. the total number in an array

It is not intended that students automatically recall the basic multiplication facts in grade 3.

Some activities:

• Using counters of any sort, have your child build as many arrays as possible for a given number, and write it's corresponding equation.

• Create arrays on cards and cut off a corner so that some counters are missing but the intended number of rows and columns remain clear.  Show cards to your child and ask them how many counters the card had initially if all the rows and columns had the same number of counters.

• Have your child create a realistic story problem to go with a given number sentence (i.e. 4x5) or describe a situation for which you might have to find the answer to 5x3.

N12- Demonstrate an understanding of division by:

• representing and explaining division using equal sharing and equal grouping

• creating and solving problems in context that involve equal sharing and equal grouping

• modeling equal sharing/grouping using concrete and visual representations, and recording the process symbolically

• relating division to repeated subtraction

• relating division to multiplication

It is important that students see that division can mean:

-equal sharing: 16 divided by 4= 4 is the amount each person gets if 16 items are shared equally among 4 people.

-equal grouping: 16 divided by 4 = 4 is the number of equal groups of you can make with 16 items

-repeated subtraction: 16 divided by 4 = 4 is the number of times you can subtract 4 from 16 before you reach zero.

Multiplication and division are inverse operations so as students master clusters of multiplication facts, it is appropriate for them to learn the corresponding division facts as "think multiplication".

Some activities:

• Give your child some toothpicks and ask him/her to use 12 to make 4 identical shapes.  Ask your child what division and multiplication sentences could describe the creation of the shapes.

• Set up a 3 x 4 array and ask your child to give two multiplication and two division sentences that describe it by looking at the array from different perspectives. 

• Ask your child to write word problems in which one has to multiply or divide to find the answer.  Have him/her illustrate the solutions and describe the multiplication/ division relationship.

N13- Demonstrate an understanding of fractions by;

• explaining that a fraction represents a part of a whole

• describing situations in which fractions are used

• comparing fractions of the same whole with like denominators

In Grade 3, the focus is on students developing a beginning understanding of fractions less than one, relating fractions to authentic situations, and comparing fractions with the same denominator.

Some activities:

• Ask your child to fold pieces of paper into equal parts (halves, fourths, eights etc.)

• Have your child model on a number line to 100 where 1/2, 1/4, 3/4 would be

• Ask your child "Is half a lot or a little?" Have them explain their thinking

• Ask your student to identify the numerator or denominator of a given fraction