### Home Learning

At Auroa School we have an expectation that each child will complete a weekly home learning programme. We believe that home learning is an important part of your child’s learning as it teaches time management and helps to build on the skills that are taught in the classroom.

Home learning will come home each Monday and is due in on Fridays. It will consist of spelling lists and tasks, home reading and basic facts.
Children who do not complete their home learning will be required to finish it in their own time.

HOME WORK REQUIREMENTS
Spelling
Each Monday your child will have 6 to 8 words to learn. The spelling words will come from the Spelling Lists and your child’s words will be chosen from their current level. The words might seem a little easy at first but they are being tested on every word in their level and words will gradually get harder throughout the year as they move up the lists.
Children will complete the task sheet in order to learn their spelling words.
Every night your child is expected to read a book for at least 5-10 minutes. These books are chosen either by the teacher (will receive 1-2 school books a week) or by your child from home or the library.
Basic Facts
A variety of addition, subtraction, multiplication and division questions to complete.

I do appreciate that your lives and the lives of your children are often busy, which is why it is important to make home learning a regular part of your child’s after school routine. If you have any concerns about R5’s home learning programme please feel free to come in and see me.
Thank you for your support, it is greatly appreciated.

Kind regards

# HOW TO CONQUER THE TIMES TABLE

Here is something to work through with your child which I found on 'Lets Play Maths'.
The question is common on parenting forums:
My daughter is in 4th grade. She has been studying multiplication in school for nearly a year, but she still stumbles over the facts and counts on her fingers. How can I help her?
Many people resort to flashcards and worksheets in such situations, and computer games that flash the math facts are quite popular with parents. I recommend a different approach: Challenge your student to a joint experiment in mental math. Over the next two months, without flashcards or memory drill, how many math facts can the two of you learn together?
We will use the world’s oldest interactive game — conversation — to explore multiplication patterns while memorizing as little as possible.

## Make a Monster Times Table

If she is willing to take the challenge, you will need a way to keep track of your progress. Use a manila file folder or tape two pieces of copy paper together, long sides touching. With a ruler, draw a large, blank times table. Take the chart up to 12 × 12, or even higher (and include a column for zero, if you like). One online friend credits his math skills to working out a 30 × 30 times table as a child.
Your daughter has almost certainly seen a chart like this before, but even so, she will probably find it intimidating. Help her fill in the chart for herself by adding or skip counting the numbers in each row and column.

For instance, to write the times-7 facts, she can imagine using the multiplication ray gun’sReplicate setting to copy a row of 7 blocks, over and over again. As she moves from one row to the next, she will write the total number of blocks, adding seven and seven and seven more…
Be patient. If your daughter is afraid of math, it may take several days to fill in the chart, a little bit at a time.
When the chart is finished, hang it on the refrigerator or some other prominent place. Your daughter will be able to find any particular math fact by looking where the appropriate row and column meet. The answer to $6 \times 7 = ?$ is found where the 6th row meets the 7th column (or the 7th row and 6th column), because it is like counting up six of the sevens.
At first glance, that chart looks like a real pain: 144 math facts to memorize. But we are not going to memorize hardly anything — we’re just going to look for number patterns.

## No Worksheets!

Our goal in these times table conversations is to build up your child’s mental math skills. Therefore, do not resort to worksheets in an effort to teach the math facts. Instead, take the time — and it does take time — to talk through these patterns and work many, many, many oral math problems together. Discuss the different ways you can find each answer. Notice how the number patterns connect to each other.
When you are practicing each family of rules, be sure to experiment with larger numbers, too. Make it into a game, and take turns quizzing each other for just a few minutes at a time. Students love the chance to stump their parents. Try working mental multiplication puzzles while you are doing dishes, or on the way to soccer practice, or whenever you can find a spare moment of time.
Even the patterns which seem easy are worth spending time to master. For instance, the magic power of one — that it can multiply a number without changing the value — is essential to working with fractions and can simplify a multitude of high school chemistry problems.

## The Ones Family

Sit down with your daughter and the chart. Use a highlighter to color in the facts she already knows, making a bright, dynamic statement of how good she is at math. You can mark out the times-1 facts very quickly. Surely your student knows that anything times one is itself, right? With the scale factor set at “1”, the multiplication ray gun won’t change anything.
7 ones = 7
359 $\times$ 1 = 359
etc.
Practice with large and small numbers, fractions, and more:
$\times \frac {1}{2}$ = $\frac {1}{2}$
4.6 $\times$ 1 = 4.6
$\times$ 897 = 897
Now have your child color in the times-1 row and column with the highlighter.

## The Tens Family

2 tens is 20.
5 tens is 50.
9 tens is 90.
11 tens is eleventy, or 110.
12 tens is twelvety, or 120.
17 tens is 17-ty, or 170.
156 tens is 156-ty, or 1,560.
4,000 tens is 4,000-ty, or 40,000.
Practice the pattern with small numbers, big numbers, and anything in between. Then mark times-10 as mastered, coloring both the row and the column.

## More Easy Facts

You can get rid of nearly half the chart in one sweep of the marker. Does your student know — really, truly, thoroughly understand — that $3 \times 4$ is exactly the same as $4 \times 3$ ? Multiplication iscommutative, which means you can move the numbers around without changing the answer: 3 rows of 4 blocks have the same total number as 4 rows of 3 blocks.
Spend a day (or a week, or however long your child needs) practicing, to make sure this principle sticks thoroughly in mind:
Q: What is 7 $\times$ 8?
A: The same as 8 $\times$ 7.
Q: What is 115 $\times$ 6?
A: The same as 6 $\times$ 115.

78 $\times$ 49 is the same as 49 $\times$ 78.
$\frac {3}{5} \times \frac {4}{13}$ is the same as $\frac {4}{13} \times \frac {3}{5}$.
192 $\times$ 7 is the same as 7 $\times$ 192.
Then you can mark out all the facts on the lower, left-hand section of the chart that have duplicates on the upper, right-hand section.
Don’t try to do too much at once. So far, you have marked off nearly two-thirds of the chart. Good job! Now would be a great time to take a break and do some fun math — like multiplying a batch of cookies.
If you remember, we are in the middle of an experiment in mental math. We are using the world’s oldest interactive game — conversation — to explore multiplication patterns while memorizing as little as possible. Talk through these patterns with your student. Work many, many, many oral math problems together. Discuss the different ways you can find each answer, and notice how the number patterns connect to each other.
So far, we have mastered the times-1 and times-10 families and theCommutative Property (that you can multiply numbers in any order).

## The Doubles

What else is relatively simple? Does your student know the doubles? Doubles are often considered easy, because children do so much counting and addition with numbers less than 20. Even if your child finds the doubles tricky, a little focused practice should fix these facts in mind.
Practice doubling big numbers, too. Use silly numbers to help:
38 $\times$ 2
= double 3 tens + double 8
= “sixty-sixteen”
= 76
And:

Go back and forth, inventing double-puzzles for each other:2 $\times$ 56
= double 5 tens + double 6
= “tenty-twelve”
= 112
3½ $\times$ 2
= double 3 + double ½
= 6 + 1
= 7
And:
$\times$ 47,000
= (double 4 tens + double 7) thousand
= “eighty-fourteen” thousand
= 94,000

## Review Game: Once Through the Deck

The best way to practice the math facts is through the give-and-take of conversation, orally quizzing each other and talking about how you might figure the answers out. But occasionally you may want a simple, solitaire method for review. Here’s how:
• Shuffle a deck of math cards and place it face down on the table in front of you.
• Flip the cards face up, one at a time.
• For each card, say (out loud) the product of that number times the number you want to practice.
• Don’t say the whole equation, just the answer.
• Go through the deck as fast as you can.
• But don’t try to go so fast that you have to guess! If you are not sure of the answer, stop and figure it out.
Brian at The Math Mojo Chronicles demonstrates the game in this video, which my daughter so thoroughly enjoyed that she immediately ran to find a deck of cards and practiced her times-4 facts. (It’s funny, sometimes, what will catch a child’s interest.)
You can use Once Through the Deck as a final check that your student knows the fact family well enough to mark it on your chart. Remember to mark both the row and the column!

## The Times-4 Family

Notice that the answers in the times-4 row are exactly double the answers in the times-2 row. Can your child see why that makes sense? If you have two of something, and you replicate two more of it, then you would have four of that thing, whether it is minions or cookies or numbers.
This means you do not need to memorize the times-4 facts. Just double the number to get the times-2 answer, and then double it again. For example, $7 \times 4$ would mean seven doubled, which is 14, and then that answer doubled again:
$\times$ 4
= 7 $\times$ 2 $\times$ 2
= 14 $\times$ 2
= 28
Practice double-doubling a bunch of numbers. Can you use the double-double trick to figure out something like $53 \times 4$ ?
53 $\times$ 4
= 53 $\times$ 2 $\times$ 2
= 106 $\times$ 2
= 212

This may take a little more time to practice — but that is okay! Quiz each other with unusual numbers, using double-doubling to get the answer. Test yourself with Once Through the Deck, and when you are ready, mark the chart.

## The Times-8 Family

In the same way that times-4 was the double of times-2, it makes sense that times-8 is the double of times-4. If you have four of something, and you replicate four more of it, then you will have eight of the thing in all. It doesn’t matter whether the thing is books or aliens or numbers. Even fractions: If you have four 1/16 size slices of pizza, and you take four more pieces, then you will have 8/16 of the pizza.
If you need to calculate something times eight, you can double the something, then double again — that makes four times — then double it once more for your final answer:
$\times$ 8
= 6 $\times$ 2 $\times$ 2 $\times$ 2
= 12 $\times$ 2 $\times$ 2
= 24 $\times$ 2
= 48
I find it helpful to count on three fingers, to make sure I don’t forget any of the doublings. Remember to experiment with big numbers, too. Can you double-double-double to figure out $132 \times 8$ ?
132 $\times$ 8
= 132 $\times$ 2 $\times$ 2 $\times$ 2
= 264 $\times$ 2 $\times$ 2
= 528 $\times$ 2
= 1056
It may take a few days or even weeks of practice before you and your student feel comfortable with these. Take all the time you need, and when you both are able to mentally double-double-double almost any number the other can pose, mark off the times-8 column and row on the chart.

## The Times-5 Family

Your daughter can probably count by fives, but many children get confused when trying to skip-count large multiplication problems. A more reliable number pattern for times-5 calculations uses the doubles in reverse. Two fives make ten, so any even number of fives will make exactly half that number of tens:
6 fives = 3 tens
18 fives = 9 tens
24 fives = 12 tens
450 fives = 225 tens
All the odd numbers times five will come out “somethingty-five,” and you can predict what the “somethingty” will be by looking at the next lower even number.
7 fives = (6 + 1) fives = 3 tens + 5
25 fives = (24 + 1) fives = 12 tens + 5
109 fives = (108 + 1) fives = 54 tens + 5
Practice intensively on these until you can both get the answer right every time. Test yourself with a round of Once Through the Deck, and then mark them off.
Wow! Look back and see how much you have learned. You started with 144 facts, and you have narrowed it down to only 21 — and all you had to memorize so far was the doubles! Your child could probably memorize the last 21 facts without too much trouble, but let’s see if we can find a few more patterns to make them easier.

## Square Numbers

Now is a good time to think about the square numbers. Your son or daughter may have heard of square numbers before, but if not, the topic will come up soon. Square numbers will haunt them all through high school, so they might as well get used to them now: A square number is simply a number that makes a square.

$\times$ 1 = 1
$\times$ 2 = 4
$\times$ 3 = 9
$\times$ 4 = 16
$\times$ 5 = 25
$\times$ 6 = 36
$\times$ 7 = 49
$\times$ 8 = 64
$\times$ 9 = 81
10 $\times$ 10 = 100
11 $\times$ 11 = 121
12 $\times$ 12 = 144
Take all the time you need for your student to master these, because the square numbers are important. Remember to take turns. Let your child quiz you to see if you remember what is seven squared.

## Hands-On Learning

Get out blocks or graph paper so you can actually see the squares.
• Make one row of one block for the first square number: 1 $\times$ 1 = 1, and we say, “One squared = one.”
• Two rows of two blocks makes 2 $\times$ 2, or two squared, which is four.
• Three rows of three blocks is 3 $\times$ 3, or three squared. How many blocks is that in all?
• Four rows of four blocks…
• Five rows of five…
• Six rows of six…
Go ahead and build all the square numbers. Make a great pyramid of blocks, one square number on top of another. Or make a poster of graph paper square numbers and hang it on the wall. Be amazed at how quickly the squares grow from tiny to huge.

## Next-Door Neighbors

Once you know the square numbers, simple addition (or subtraction) will help you find some of the hardest-to-remember multiplication facts. For example, $6 \times 7$ is a neighbor to $6 \times 6$ and $7 \times 7$ :
$\times$ 7
= 6 squared + one more 6
= 7 squared − one 7
And 7 $\times$ 8 is a neighbor of 7 $\times$ 7 and 8 $\times$ 8:
$\times$ 8
= 7 squared + one more 7
= 8 squared − one 8
How many next-door-neighbor numbers can you find? How many ways can you calculate them? The more different ways you know, the more likely that you will be able to reason out an answer when your math-fact memory goes blank.
This leaves us with only 13 facts to cover:

Take your time to fix each of these patterns in mind. Ask questions of your student, and let her quiz you, too. Discuss a variety of ways to find each answer. Use the card game Once Through the Deck (explained in part 3)as a quick method to test your memory. When you feel comfortable with each number pattern, when you are able to apply it to most of the numbers you and your child can think of, then mark off that row and column on your times table chart.
So far, we have studied the times-1 and times-10 families and the Commutative Property (that you can multiply numbers in any order). Then we memorized the doubles and mastered the facts built on them. And then last time we worked on the square numbers and their next-door neighbors.

## The Distributive Property

This brings me to one final trick: the Distributive Property. The Distributive Property converts a tough multiplication problem into an easier addition problem. Like square numbers, the Distributive Property will follow your son or daughter throughout their school math career. Now is a good time to figure out how it works.
Assume we have two numbers to multiply, say, 62 $\times$ 25. We can break one of the numbers into two (or more, but let’s not make it difficult!) chunks that are easier to multiply. We could break them into any chunks we wanted, such as 25 = 17 + 8 or 62 = 39 + 23.
Since our goal is to make the calculation as simple as possible, however, let’s try chunking it like this:
25 = 20 + 5
Which turns our multiplication problem into:
62 $\times$ 25 = 62 $\times$ (20 + 5)
The Distributive Property says that the first product, 62 times the whole 25, is the same as the sum of the two partial products, 62 times each part of 25. This is how the distributive property turns multiplication into addition:
62 $\times$ 25
= 62 $\times$ (20 + 5)
= (62 $\times$ 20) + (62 $\times$ 5)
[Do you remember that 62 fives = 31 tens?]
= 1240 + 310
= 1550
The Distributive Property is the key to understanding the traditional pencil-and-paper rules for multiplying large numbers. But it is also a very important principle for working with mental calculation. You can break all of our remaining times-table numbers into easily-multiplied chunks.

## The Times-3 Family

For instance: 3 = 2 + 1. If you have two of something, and you get one more of that thing, then of course you will have three of that thing. Three puppies are the same as two puppies plus one more puppy. Three pizzas are the same as two pizzas plus one more pizza. And three of any number is the same as two of that number plus one more of it.

And:3 $\times$ 6
= two 6s + one more 6
= 12 + 6
= 18
12 $\times$ 3
= two 12s + one more 12
= 24 + 12
= 36
Take turns with your child, giving each other numbers to multiply by three. Be sure to include some bigger numbers.
$\times$ 55
= two 55s + one more 55
= 110 + 55
= 165
Or:
41 $\times$ 3
= two 41s + one more 41
= 82 + 41
= twelvety-three
= 123

## The Times-11 Family

Similarly, the Distributive Property tells us that 11 of anything is the same as “ten and one more” of that thing. Eleven tigers are ten tigers and one more tiger. Eleven cars are ten cars and one more car. Eleven pencils are ten pencils and one more pencil. It is the same with numbers.
11 $\times$ 11
= ten 11s + one more 11
= 110 + 11
= 121
Or:
11 $\times$ 15
= ten 15s + one more 15
= 150 + 15
= 165
Take turns quizzing each other on these facts, and be sure to try it with bigger numbers, too.
11 $\times$ 36
= ten 36s + one more 36
= 360 + 36
= 396

## The Times-9 Family

In the same way that 11 is one more than ten, nine is one less than ten:
12 $\times$ 9
= ten 12s – one 12
= 120 – 12
= 108
Big numbers will stretch your child’s mental math skills, but isn’t that the point? Remember your mental math tricks and subtract in chunks:
$\times$ 27
= ten 27s – one 27
= 270 – 27
= 270 – 20 – 7
= 250 – 7
= 243

## Times-6 and Times-7 Families

We left these fact families for last, since many children (and adults!) find them difficult. But notice: Most of the numbers in these families are already colored in. That means the Distributive Property simply deepens our understanding by giving us another way to view the facts we already know.
You can break both six and seven up into two easily-multiplied chunks:
6 = 5 + 1
7 = 5 + 2
So anything times six is the same as “five and one more” of that thing, and anything times seven is the same as “five and two more” of that thing. Since the times-1, times-2, and times-5 facts are among the easiest to remember, we can use the Distributive Property to make our calculations simple:

And:12 $\times$ 6
= 12 $\times$ (5 + 1)
= (12 $\times$ 5) + (12 $\times$ 1)
= 6 tens + 12
= 72
12 $\times$ 7
=12 $\times$ (5 + 2)
= (12 $\times$ 5) + (12 $\times$ 2)
= 6 tens + 24
= 84
Take at least a week on each of these: one week for times-6 and one week for times-7. Build up your mental math skills with big numbers, too. Add in chunks, finding the highest place values first.
34 $\times$ 6
= 34 $\times$ (5 + 1)
= (34 $\times$ 5) + (34 $\times$ 1)
= 17 tens + 34
= 204
Or:
128 $\times$ 7
=128 $\times$ (5 + 2)
= (128 $\times$ 5) + (128 $\times$ 2)
= 64 tens + 256
= 896
With that, we have made it through the whole times table chart, and we only had to memorize the doubles and squares. We did everything else with logic and number patterns!