Students

Students are expected to read at least 30 minutes each night. Reading is recorded in the agenda. Reading should be enjoyable and relaxing as well as engaging and educational. All kinds of reading are encouraged! Novels, non-fiction, newspapers, magazines, comics, graphic novels, audio books, online reading, listening to someone else read, reading aloud...just read! It's great for your brain!

Students should practice their typing skills as often as possible. Please see the link below for improving typing skills.

Word Study:

Words of the week - Each week we will be looking at 20-25 new words. Students are encouraged to practice these words throughout the week at home so that they can spell them automatically. At the end of each week these words will be placed on the word wall for the entire year to help students with their writing. See Word Study page for list of words.

Math Strategies to Review:

In Mental Math - Any additional practice at home would help reinforce this knowledge.

Making Ten Strategy (1st strategy - focus in early Sept - this will be extended to the 100/1000/10 000)

This is an extremely important strategy that can be difficult for some students. The expectation is that students know single digit numbers that add up to ten.

Example: 0 + 10 = 10, 1 + 9 = 10, 2 + 8 = 10 etc.... The reason that this strategy is important is because it helps to build other mathematical strategies as well as extends this one.

Example: If I know that 8 + 2 = 10 then I can figure out quite quickly the sum of 80 + 30. If I know that 80 + 20 = 100 then I can take 20 from 30 and give it 80 changing the question to 100 + 10 which equals 110. Also, if I know that 4 + 6 = 10 then when completing a question such as 50 000 + 60 000 = that I can take 40 000 from the 50 000 and give it to the 60 000 to make 100 000. Therefore changing the question to 100 000 + 10 00 = 110 000

Doubles Strategy

This is another extremely important strategy that is useful in mental math. Students should be able to recall their double facts to 10 + 10 = .This strategy can then be extended to multiples of 10, 100, 1000 and even 10 000.

Example: If you know that 4 + 4 = 8 then students can should be able to see the relationship between 4 + 4 = 8 to 40 + 40 = 80 and 400 + 400 = 800 and so on.

Doubles Plus One Strategy

This is a strategy that can be used when addition is required. Knowing your doubles facts is a must if you are to use this strategy efficiently. This strategy can also be extended to multiples of 10, 100, 1000 and even 10 000.

Example: If you know that 4 + 4 = 8 then if the addition sentence is 4 + 5 = students should think, "well I know that 4 + 4 = 8 therefore if one addend is one more (5) then my answer (sum) should be one more. Therefore 4 + 5 = 9"

If I know that 40 + 40 = 80 then 40 + 50 = 90

Estimation:

Students need to develop both mental mathematics and estimation skills through context and not in isolation so they are able to apply them to solve problems. Whenever a problem requires a calculation, students should follow the decision-making process as illustrated below.

Students need to recognize that estimation is a useful skill in their lives. However, to be efficient when mentally estimating sums, differences, products, and quotients, students must be able to access a strategy quickly, and they need a variety of strategies from which to choose. Students should be aware that in real-life estimation contexts overestimating is often important.

Front-end estimation:

This strategy is the simplest of all the estimation strategies for addition, subtraction, and multiplication. It involves combining only the digits in the highest place value of each number to get an estimate. As such, these combinations will require only the use of the basic facts. While this strategy may be applied to division questions if the divisor is a factor of the highest place value of dividend, division estimation is better done by a rounding strategy.

− sums (e.g., 253 + 615 is more than 200 + 600 = 800)

− differences (e.g., 974 – 250 is close to 900 – 200 = 700)

− products (e.g., the product of 23 × 24 is greater than 20 × 20 (400) and less than

25 × 25 (625))

− quotients (e.g., the quotient of 831 ÷ 4 is greater than 800 ÷ 4 (200))

Example: 1423 ÷ 70 = ( When looking at 1423 ÷ 70 we would look at the fron end of 1423 and ask ourselves can 14 be divided by 7 evenly? The answer is yes it can. My next question to ask myself is is, should 1423 be rounded up to 1500 or down to 1400? Well, if I look at the back part of 1423 i know that 23 is less than 50 so, I should round down to 1400. Also, 1400 can be divided easily by 7. Therefore 1400 ÷ 70 = 20

Adjusted Front-End Estimation

This strategy is often used as an alternative to rounding to get closer estimates. It involves getting a front-end estimate and then adjusting that estimate to get a better, or closer, estimate by either clustering all the values in the other place values to determine whether there would be enough together to account for an adjustment or considering the second-highest place values. This second method of adjustment often results in a closer estimate than first method and would likely only be bettered by the strategy of rounding to the two highest place values.

Example:

To estimate 3297 + 2285, think, 3000 plus 2000 is 5000, and 200 plus 200 is only 400, which is not close to another 1000; so, the estimate is 5000. However, clustering 297 and 285 would suggest about 600, so another 1000 would be added to give an estimate of 6000.

Compatible Numbers

When estimating the addition of a list of numbers, it is sometimes useful to look for 2 or 3 numbers that can be grouped to almost make 10s, 100s, 1000s (compatible numbers).

Example: 134 + 55 + 68 + 46 =

You can put the 46 and 55 together to make about 100

You can put the 134 and 68 together to make about 200 for a total of 300.

Front End Addition

This strategy is applied to questions that involve two combinations of non-zero digits, one combination of which may require regrouping. This strategy involves first adding the digits in the highest place-value position, then adding adding the non-zero digits in another place value position and doing the needed regrouping.

Example: for 26 + 37 = think 20 + 30 = 50 then 6 + 7 = 13. Therefore we think

50 + 13 = 63.

Trailing Zeros

Students should use their single digit multiplication facts to assist in this strategy. This strategy involves multiplying then tacking on the zero.

Example: 3 x 80 = Students should think 3 x 8 = 24. Then all they need to do is tack on the zero from the 80. Therefore 3 x 80 = 240

The same strategy applies if you were to multiply 3 x 800 = 2400.

Compensating Multiplication

Compensating multiplication is strategy that can be used where a factor ends in 9. This strategy involves multiplying by the near multiple of ten and subtract the one extra set to find the actual product.

Example: 39 x 7 = can be thought as 40 x 7 = 280

then 280 - 7 (seven being the extra set) = 273 therefore 39 x 7 = 273 This strategy can be used for any factor that ends in a 9.

Trailing Zeros - (Division)

Students should use their single digit multiplication facts to assist in this strategy. This strategy involves dividing then tacking on the zero.

Example 2400 ÷ 6 = can be thought of as 24 ÷ 6 = 4 then tack on the 2 trailing zeros therefore your answer (quotient) is 400. 2400 ÷ 6 = 400

Breaking Apart the Dividend

The dividend is the amount of something you are breaking/sharing.

Students will use a number of previously taught strategies within this new strategy.

This strategy involves knowing multiplication facts and trailing zero strategy.

Compatibles Strategy

Students should make their job easier by looking for compatible pairs.

Example 5 x 7 x 2 x 6 =

Student should think 5 x 2 = 10 then 7 x 6 = 42 then 42 x 10 = 420

therefore 5 x 7 x 2 x 6 = 420

Example 287 ÷ 7 = (287 is the dividend) you can break apart the dividend to make this easier to do mentally. Take 287 and break it into 280 and 7.

280 ÷ 7 = 40 and 7 ÷7 = 1 then add 40 + 1 = 41 Therefore 287 ÷ 7 = 41

Recognizing Patterns in dividing and Multiplying

Students should be able to recognize and explain patterns in dividing by 10, 100, 100 and or multiplying by 0.1, 0.01 and 0.001

Examples: 2435 ÷ 10 = 243.5 2435 x 0.1 = 243.5

2435 ÷ 100 = 24.35 2435 x 0.01 = 24.35

2435 ÷ 1000 = 2.435 2435 x 0.001 = 2.435

Students should make their job easier! They should be thinking about place value. Each numeral sits in a place (See Place Value chart under documents). When dividing by 10 or multiplying by 0.1 the numeral will move one place value to the right. When dividing by 100 or multiplying by 0.01 the numeral will move two places in the place value chart to the right and so on.

Making Your Own Compatible Numbers

We can make addition sentences much easier if we change the numbers into compatible number (numbers that when added together give us a multiple of 10) then compensate through adding or subtracting.

Example: 25 + 79 = We can change this sentence to make it much more easy to do mentally. We would leave 25 but change 79 to 75. The sentence is now 25 + 75. We know that 25 +75 = 100. But we have to remeber to add on the 4 back on that we took away from the 79 to make 75. Therefore, we then add the 4 onto the 100.

100 + 4 = 104. Therefore 25 + 79 = 104

Example #2: 23 + 18 = We can change 23 to 20 by taking away 3 from 23. This changes the sentence to 20 + 18 = 38. We have to remeber to now add the 3 back onto our answer that we took away from 23. Therefore 38 + 3 = 41. 23 + 18 = 41

These strategies will assist in further strategies in the coming weeks. I would suggest practicing with your child each night for 5 minutes...just running through all the double facts to 10.

Multiplication Strategies

The Nifty-Nine Facts

The introduction of the facts involving nines should concentrate on having students discover two patterns in the answers; namely, the tens’ digit of the answer is one less than the number of 9s involved, and the sum of the ones’ digit and tens’ digit of the answer is 9. For example, for 6 × 9 = 54, the tens’ digit in the product is one less than the factor 6 (the number of 9s) and the sum of the two digits in the product is 5 + 4 or 9. Because multiplication is commutative, the same thinking would be applied to

9 × 6. Therefore, when asked for 3 × 9, think, The answer is in the 20s (the decade of the answer) and 2 and 7 add to 9; so, the answer is 27. Help students master this strategy by scaffolding the thinking involved; that is, practise presenting the multiplication expressions and just asking for the decade of the answer; practise presenting students with a digit from 1 to 8 and asking them the other digit that they would add to the digit to get 9; and conclude by presenting the multiplication expressions and asking for the answers and discussing the steps in the strategy.

Examples:

For 5 × 9, think, The answer is in the 40s, and 4 and 5 add to 9, so 45 is the answer.

For 9 × 9, think, The answer is in the 80s, and 8 and 1 add to 9, so 81 is the answer.

Compensation Strategy for 9 Times Tables

Another strategy that some students may discover and/or use is a compensation strategy, where the computation is done using 10 instead of 9 and then adjusting the answer to compensate for using 10, rather than 9. For example, for 6 × 9, think, 6 groups of 10 is 60 but that is 6 too many (1 extra in each group), so 60 subtract 6 is 54. This strategy can be modeled nicely using ten-frames. Students can build six sets of nine on ten-frames and see that they have almost six full ten-frames (60) but each ten-frame has one counter missing (six less than 60) so there are 54 counters in all. This model can help them to visualize multiples of nine and make sense of this compensation strategy. While 2 × 9 and 9 × 2 could be done by this strategy, these two nines facts were already handled by the twos facts. This nifty-nine strategy is probably most effective for factors 3 to 9 combined with the factor 9, leaving the 0s and 1s for later strategies.

If you have any questions about our mental math please feel free to contact me.