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Fact of the day

See also the article on practice and the related video.

Rapid fact mastery: This structured set of lively, brief, daily exercises quickly gets children to master number facts and mental math skills. Because each day's practice focuses on a non-daunting, manageable set of facts or skills -- small, highly focused, and strategically selected -- and builds directly on the previous days' learning, virtually all children gain real competence rapidly and with pleasure.

At the beginning of the day, the teacher lets children know that day's special number "rule," perhaps also taking a few seconds to let students try out the rule once or twice. These rules -- the "fact of the day" -- might be:

  • "say how many more are needed to make 10" or
  • "say how many more are needed to make 100" or
  • "add 10 to that number" or
  • "multiply this number times itself and give the answer."

After the introduction, this lively exercise uses almost no words at all!

  • The teacher says a number as a "prompt."
  • The child answers back with a number.

That's it! No more words than that! For example, if the fact of the day is "how much more to make 100," then, when the teacher says 80, the child answers 20.

Over the first couple of months of school these highly focused practice activities make the necessary facts and skills instantly available to the children. Very brief (30 second to 2 minute) practices in a playful spirit, a few times a day, are the most effective. To be precise, the so-called "fact" of the day is really the "rule" or "task" or function of the day. A list of these fact-of-the-day practices, in a particularly efficient order, is provided below.

Running a fact-of-the-day activity

First thing in the morning, introduce the fact of the day. You can, of course, introduce the idea to the whole group. Here are some other ideas.

  • One good way is to catch several students as they enter, or go around the room as students are settling in, and let them work a couple of examples so that they are prepared.
  • You may even assign "specialists": "Jackie, I want you to be in charge of 8. If anyone says 'eight' to you, you answer 'sixty-four' because today's rule is to multiply the prompt by itself. So, what is 8 x 8? (64) Right, and so if someone says 'eight' to you, what do you say? (64)"

If you do introduce just a handful of students individually, and perhaps have a couple of specialists, your introduction of the rule to the whole class could be through discovery, letting them figure out the rule from the correct responses of the several students that you "let in" on it.

Differentiated instruction: This is an excellent opportunity for differentiated instruction, too: the students you tell individually -- the ones, therefore, who are able to answer first, before the rest of the class has discovered the rule -- might be ones who need the explicit introduction and a bit of advance practice, or might need to specialize on one fact rather than several, or would have a harder time discovering the rule.

Throughout the day, pop these prompts at odd moments: as children are standing in line for lunch, filing in the door after recess or a special. You can even use the prompts as a playful "secret password" when children ask to get a drink. "Can I get a drink?" "Eight." "Sixty-four." "Ok!"

  • Practices should all be very brief -- one or two prompts to a child at most, and only a few children at a time -- but frequent during the day. The more practice with these facts the better.
  • If you coordinate with other teachers, so that an entire hall or grade is on the same fact for that day, feel free to give the prompts to any child you see, and not just your own. A smile, a wave, and an "eight" to a child in the hall will almost invariable get back another smile and wave when the child answers "sixty-four" (or whatever the rule calls for). It's like a magic password or a secret handshake.

Comment from the designer: Have as many adults in the school participate as possible -- administrators, music specialists, etc. It is even better if you send home notes to the parents so they can practice the Facts at home as well. The kids loved getting prompts from their prior teachers, teachers of their brothers or sisters,... Also, they enjoyed giving us prompts, and seeing adults give each other prompts and responses! And they learned addition, subtraction, and basic multiplication, division, decimal, and fraction skills quickly, so that they could focus their in-class time on higher order mathematical thinking!

Addition and subtraction

Making 10 and adding and subtracting 10

Always keep fact-of-the-day activities light and playful. Use secret-handshake-style (one child, one prompt, two seconds), or 15-second-warm-up style (6 or 7 prompts, whole-group choral responses).

Pairs to 10 Prompt:

A whole number from 0 through 10.

Today's rule: I'll give you a number. You say how much more is needed in order to make 10. Example:

  • Teacher: 6
  • Student: 4

Pairs to 100 Prompt:

A multiple of ten (0, 10, 20, 30...) from 0 through 100 (inclusive). (Only numbers that are multiples of ten are fair game today. A later fact-of-the-day will ramp this up further.)

Today's rule: I'll give you a number like 30 or 60 or 0. You say how much more is needed in order to make 100. Example:

  • Teacher: 80
  • Student: 20

Review Day

The concept of a review day: Having a review day about once a week or when you finish a block of related Facts is a good idea. Review days give children a chance to be nimble, listen for the question, and "mix facts." They also serve as a useful, occasional breather. Fridays are convenient days to review all the Facts-of-the-Day for that week. Depending on when you start your Fact-of-the-Day program, you may have four facts to review, or, as in the first year we implemented this, only two.

If you are reviewing at this point, the students have two Facts, "numbers whose sums are ten" and "numbers whose sums are 100." Children must be told that the fact of the day could be either rule. The prompt for today can fit either pattern, and the child follows the appropriate rule.

Prompt: Either a number from 0 through 10, or a multiple of (10, 20, 30...).

Do NOT combine the Facts (e.g., giving a number like 32). For these practices to be effective, they must remain focused, and develop mastery of simple but essential patterns.

Today's rule: Today you might be asked either of the facts of the day that you used this week! If the prompt is 0 through 10, say how much more is needed to make 10. If the prompt is 0, 10, 20..., etc., say how much more is needed to make 100. Example:

  • Teacher: 40
  • Student: 60
  • Teacher: 7
  • Student: 3

Chains of 10 Prompt:

Any number from 0 through 70.

Today's rule: When you are given a number, count forwards by tens for three steps. Example:

  • Teacher: 43
  • Student: 53, 63, 73
  • Teacher: 7
  • Student: 17, 27, 37

Teacher story: I was working with a child on Chains of 10, quietly writing the prompt and getting a written response back. The child's first result was incorrect. I waited a little to see if he would catch it on his own, but he didn't. However as soon as I said, "What's the Fact of the Day?" he looked at his work again, said, "Oh right," and corrected the sum. With practice, the Facts get to be old friends.

Chains of Tens Backwards Prompt:

Any number between 30 and 100.

Today's rule: When you hear a number today, count backwards by tens for three steps. Example:

  • Teacher: 94
  • Student: 84, 74, 64
  • Teacher: 30
  • Student: 20, 10, 0

The next two rules - adding and subtracting 10 may seem unnecessary repetition of what children have just done, but there are just enough children who don't connect counting by 10s and adding 10 to make them both worthwhile. Many children will feel (as do most adults) that the two kinds of exercises -- chains of 10 (forwards and backwards) and adding/subtracting 10 -- are really the same, but some will not, and the point of this activity is to let them all see the connection. (The order -- chains before adding or adding before chains -- may be switched.) If these rules are too easy for some children, then ask those children to add (or subtract) 20 or 30 or 40 to stretch their abilities with the notion of adding some multiple of 10. Meanwhile the children who are struggling can stick to adding (or subtracting) 10.

Adding 10 Prompt:

Any number from 0 through 80.

Today's rule: When you are given a number, say how much 10 more will be. Example:

  • Teacher: 43
  • Student: 53
  • Teacher: 7
  • Student: 17

Subtracting 10 Prompt:

Any number from 10 through 90.

Today's rule: When you are given a number, say how much 10 less will be. Example:

  • Teacher: 43
  • Student: 33
  • Teacher: 67
  • Student: 57

Using knowledge about 10 to add and subtract other numbers

Always keep fact-of-the-day activities light and playful. Use secret-handshake-style (one child, one prompt, two seconds), or 15-second-warm-up style (6 or 7 prompts, whole-group choral responses).

Adding 8 using Adding 10

This needs an introduction. Here, in the form of a conversation, is one way of introducing the idea.

  • Teacher: (calls a child to the front of the class Hold out your hand so I can give you some invisible money! (teacher puts some imaginary coins, not real or play money, in the child's hand, and says) OK, there's 53¢. Check carefully! How much do you have?
  • Child: (most likely amused) 53¢?
  • Teacher: Wonderful! Now I'm going to give you 8 more cents. (places an imaginary sum in the child's hand and says) Oops! I gave you 10¢ by mistake. How much do you have now?
  • Child: 63¢
  • Teacher: But I meant to give you only 8¢. How can I fix this mess I made?
  • Child: Take 2¢ back? (note that this uses the pairs to 10 that children have learned cold)
  • Teacher: (takes some imaginary money back) Ok, perfect. Now that's right. How much do you have now?
  • Child: 61¢

Do this several more times, calling on different children, always starting with a sum of money, always saying that you will add 8¢ and then messing up, saying "Oops! I made a mistake and gave you 10¢," always verifying what that result was, and then fixing it. The aim is for children to get very used to adding 8 by adding 10, which they are experts at, and then subtracting 2.

Prompt: Any amount of cents from 0¢ through 90¢.

Today's rule: When you are given an amount of money, say how much 8¢ more will be. Example:

  • Teacher: 43¢
  • Student: 51¢
  • Teacher: 7¢
  • Student: 15¢

Subtracting 8 using Subtracting 10

This is very much harder than the adding 8¢. Children tend to "get" the idea right away, but executing the idea (keeping track of the process) is tricky, and children (and adults!) tend to make many mistakes. Take all the mistakes lightly. They'll work themselves out in time, but it will take time. Again, you might introduce the idea with the same sort of invisible money.

  • Teacher: Here's 53¢. Look, did I get it right?
  • Child: (most likely amused) Um, yes!
  • Teacher: So how much do you have there?
  • Child: 53¢
  • Teacher: I need some money myself. I need 8 cents back. (takes some) Omigosh! I took too much! I took 10¢ by mistake. How much do you have now?
  • Child: 43¢
  • Teacher: I'm sorry!! I meant to take only 8¢. How can I fix this mess I made?
  • Child: Give me back 2¢?
  • Teacher: Yes! That'll work! OK! (gives back the invisible 2¢) Now how much do you have?
  • Child: 45¢

Again, repeat until children are comfortable.

Prompt: Any amount of cents from 10¢ through 100¢.

Today's rule: When you are given an amount of money, say how much 8¢ less will be. Example:

  • Teacher: 43¢
  • Student: 35¢
  • Teacher: 70¢
  • Student: 62¢

Nearest multiples of 10

Always keep fact-of-the-day activities light and playful. Use secret-handshake-style (one child, one prompt, two seconds), or 15-second-warm-up style (6 or 7 prompts, whole-group choral responses).

Tens Neighbors Prompt:

Any number between 0 and 100.

Today's rule: When you hear a number, name the two nearest multiples of 10 -- the one just less than the prompt and the one just greater than it. For example, if you hear 72, you'll say 70 (the nearest "ten" just below 72) and 80 (the very next multiple of 10 after 72). If you get a multiple of 10, just repeat the number you were given! Example:

  • Teacher: 34
  • Student: 30 and 40
  • Teacher: 95
  • Student: 90 and 100
  • Teacher: 20
  • Student: 20

It's also ok if the child forgets the special case rule and answers "10 and 30." Anchor Counting Down 10 Numbers

Prompt: Any number between 10 and 100.

Today's rule: When you hear a number today, count backward ten numbers. Example:

  • Teacher: 87
  • Student: 86, 85, 84, 83, 82, 81, 80, 79, 78, 77
  • Teacher: 43
  • Student: 42, 41, 40, 39, 38, 37, 36, 35, 34, 33

Review Students will soon be asked to use the "old facts" to generate new facts. We always want the new facts to feel challenging enough for students to feel proud when they succeed, but we also want to prepare students well enough so that they do succeed. This review helps students solidify what they know. The upcoming facts rely on knowing Pairs to 10 and the related Pairs to 100 "cold," so they must be part of the review. Pick a couple of others to review as well. It is good to have a few Facts happening on Review days. Differentiating instruction without differentiating the students: You know your students. For those who will find these old facts too easy, spice it up by using numbers like 4 1/2 as a prompts for Pairs to 10, or 530 as a prompt for Counting Down 10 Numbers. Just as we don't want to lose children to confusion or frustration, we don't want to lose them to boredom.

Prompt: Either a whole number between 0 through 10 (Pairs to 10), or a multiple of 10 (10, 20, 30...)

(Pairs to 100). (You decide which two or three other Facts in the following list to include in today's Review and give the prompts for those.) Do NOT combine the Facts (e.g., giving a number like 32 and ask for a Pair to 100). For these practices to be effective, they must remain focused, and develop mastery of simple but essential patterns.

Today's rule: Today you might be given a prompt for Pairs to 10, or Pairs to 100, or (you decide what other two facts to add to this). Anchor Pairs to 20

Prompt: A whole number from 0 through 20.

Today's rule: I'll give you a number. You say how much more is needed in order to make 20. Encourage children to use their Pairs to 10 facts to find Pairs to 20. If the prompt is 6, the pair to 10 is 4 and then they need 10 more to make 20. Altogether that is 14. Example:

  • Teacher: 6
  • Student: 14
  • Teacher: 12
  • Student: 8

Pairs to 11 Prompt:

A whole number from 0 through 10.

Today's rule: I'll give you a number. You say how much more is needed in order to make 11. Encourage children to use their Pairs to 10 facts to find Pairs to 11. Eleven is 1 more than 10, so the child finds the familiar pair to 10, and then says 1 more than that. For example, if the prompt is 6, the pair to 10 is 4, and so the child says 5. Example:

  • Teacher: 6
  • Student: 5
  • Teacher: 2
  • Student: 9

Review Because Pairs to 11 and Pairs to 20 involve keeping two things in mind at once -- the pair to 10 and how much more is needed -- it can be useful to have a review day after just those 2 facts. You may want to include only three Facts this time. Pairs to 10, Pairs to 20, and Pairs to 11. To avoid repetitiveness, this is the last Review Box that we will list. The principle is clear. Use your own judgment about when to put in Review Days. Reasonable places are Fridays, after you have finished working on a section of facts-of-the-day, and as review before introducing new sets of Facts that use an old set of Facts. Also, when children are having a tough time with a concept in their regular math lesson that a previously-learned Fact would make easier, feel free to re-use that fact-of-the-day to bring it back to mind!

Prompt: Say the prompt and which pair you want a child to find.

Today's rule: Today you might be given a prompt for Pairs to 10, Pairs to 20, or Pairs to 11. Example:

  • Teacher: 7 to 11
  • Child: 4
  • Teacher: 8 to 20
  • Child: 12

Sums to 10 and Sums to 100 This is identical with the very first review of the year, but worth returning to. Differentiating instruction without differentiating students: For students who need extra challenge, use halves (e.g., 4 1/2) as a prompt for a Pair to 10, and use two-digit numbers ending in 5 (e.g., 35) as a prompt for a Pair to 100. For the greatest assurance that students succeed at this extra challenge, use the same number as in the previous prompt, but with the extra twist. (For example, if the previous prompt was 6, then pose 6 1/2, or if the previous prompts was 60, pose 65.

Prompt: A whole number from 1 to 9 or a two-digit multiple of 10: 10, 20, 30, 40...

Today's rule: I'll give you a number. You say how much more is needed in order to make 10 (for a single digit number) or 100 (for a two-digit multiple of 10). Giving these two Facts on the same day helps children connect them and use the single digit Fact of Sums to 10 to easily find the double digit one for Sums to 100. Example:

  • Teacher: 6
  • Student: 4
  • Teacher: 60
  • Student: 40

Tens Neighbors, ramped up This extends Tens Neighbors. Some children will be ready for the stretch, but some will need to review the basic fact. It is fine to introduce this ramped up version as the Fact of the Day, but if a child is struggling, it is fine to give them a two digit prompt. You can differentiate the same activity by making a task easier or harder with the prompt you give.

Prompt: Any three-digit-number.

Today's rule: When you hear a number, name the two nearest multiples of 10 -- the one just less than the prompt and the one just greater than it. For example, if you hear 722, you'll say 720 (the nearest "ten" just below 722) and 730 (the very next multiple of 10 after 722). If you get a multiple of 10, just repeat the number you were given! Example:

  • Teacher: 681
  • Student: 680 and 690
  • Teacher: 493
  • Student: 490 and 500 (This is hard because it involves "trading up" to a new hundred's digit.)
  • Teacher: 277
  • Student: 270 and 280

Distance to Tens Neighbor less than the prompt

Prompt: Any number that is less than 100.

Today's rule: When you hear a number, name the nearest multiple of 10 that is just less than the prompt and then say how far away that neighbor is. For example, if you hear 72, you'll say "70 is 2 less." If you get a multiple of 10, you may just repeat the number you were given and say that it is "0 less." Example:

  • Teacher: 34
  • Student: 30 is 4 less
  • Teacher: 95
  • Student: 90 is 5 less
  • Teacher: 30
  • Student: 30 is 0 less It is ok if a child says "20 is 10 less."

Distance to Tens Neighbor greater than the prompt

Prompt: Any number that is less than 100.

Today's rule: When you hear a number, name the nearest multiple of 10 that is just greater than the prompt and then say how far away that neighbor is. For example, if you hear 72, you'll say "80 is 8 more." If you get a multiple of 10, you may just repeat the number you were given and say that it is "0 more." Example:

  • Teacher: 34
  • Student: 40 is 6 more
  • Teacher: 95
  • Student: 100 is 5 more
  • Teacher: 20
  • Student: 20 is 0 more As always, it is ok for a child to say "30 is 10 more."

Distance to Nearest Tens Neighbor This exercise practices the skill that underlies rounding.

Prompt: Any number that is less than 100.

Today's rule: When you hear a number, say how far away the nearest multiples of 10 is. For example, if you hear 72, you'll say 2. If you hear 36, you'll say 4. If you get a multiple of 10, you'll say 0! Example:

  • Teacher: 17
  • Student: 3
  • Teacher: 95
  • Student: 5
  • Teacher: 10
  • Student: 0

Language and place value

Always keep fact-of-the-day activities light and playful. Use secret-handshake-style (one child, one prompt, two seconds), or 15-second-warm-up style (6 or 7 prompts, whole-group choral responses).

Using the Language of Place Value to Subtract

Prompt: Any number two-digit number minus that number's units digit.

See The Way We Name Numbers and Using Those Number Names to Aid Subtraction to see what language skill underlies this exercise, and how to make this intuitive for children who are still using counting-backward strategies. For children who catch onto this right away and find this too simple to be interesting, you can up the challenge by giving them a three digit number and have them subtract the units digit. If that is too easy, give them a three digit number and have them subtract the tens digit. For example, "three hundred seventy four" minus "seventy." Because of the way English numbers are constructed, all children need to do is know to take out the "seventy" and leave everything else. That gives them "three hundred four." This should ALL be done verbally/mentally, not with anything written.

Today's rule: I'll give you a subtraction sentence and you tell me what it equals. Example:

  • Teacher: 17 minus 7
  • Student: 10
  • Teacher: 95 minus 5
  • Student: 90
  • Teacher: 21 minus 1
  • Student: 20

Subtracting 8 breaking it apart

Using money as imagery, an earlier fact introduced the idea of Subtracting 8 by subtracting 10 and then adding back 2. Another way to Subtract 8 is subtract it in two easy parts. For example, if we want "37 minus 8," we can start with 37 minus 7, which is 30. (That's just language, and we worked on that in our last fact!) Now we only have to subtract 1 more. 30 minus 1 is 29. (That's using the Pairs-to-10 facts we know so well.) So, 37 minus 8 is 29. Introduce this method for Subtracting 8 by demonstrating, perhaps having some children help, and let all children practice this briefly. If, during the day, children give you the correct answer, but use the earlier strategy of subtracting 10 and then adding back 2 that is fine. The idea is to introduce another strategy so that children will have it in their "tool kit" if they need it, not to force them to use it.

Prompt: Any two-digit-number between 10 and 90.

Today's rule: ! Example:

  • Teacher: 68
  • Student: 60 (68 minus 8)
  • Teacher: 42
  • Student: 34 (42 minus 2, then minus 6)
  • Teacher: 27
  • Student: 19 (27 minus 7, then minus 1)
  • Teacher: 29
  • Student: 21 ("twenty" followed by 9 minus 8)

Extending the addition facts

Always keep fact-of-the-day activities light and playful. Use secret-handshake-style (one child, one prompt, two seconds), or 15-second-warm-up style (6 or 7 prompts, whole-group choral responses).

Extending Facts

Extend the previous Facts by introducing larger numbers or other numbers. For example:

  • Have children find Pairs to 1000 if they are given a multiple of 100
  • Have children add (and, later, subtract) 9 or 7 from a two-digit number using the same strategy they used for 8.
  • Have children find pairs to 12 the way they did Pairs to 11
  • Have children find pairs to 30 or 40 the way they did Pairs to 20

The idea is to make it interesting, but not to get too complex. The power of these Facts lie in their being quick to do!

If children are tired of addition Facts, stop and go to multiplication Facts. It is not necessary to finish addition before you go to multiplication. It is actually good to go back and forth. Try to maintain the order within each topic.

Multiplication and division

A few of the following boxes include information for several days worth of Facts. It is very important to do only one thing in one day! For children who find the Day's Fact too easy, think of a way to have them practice the same idea but with bigger numbers or starting with a mixed number instead of a whole number or... Keep kids excited. Being too hard is not good, but being too easy is also not good!

Depending on the grade you're working with, your children may not be ready for every fact in the following sequences. Introduce the new Facts in order. Sometimes kids surprise you, so it is fine to introduce a Fact that you aren't sure about. When you reach one that the kids really struggle with, let them build more confidence the next day -- or go back to the easier ones from earlier in the same category, or use the Review Day model (a couple of facts that day). Then decide if you want to try the "difficult" one again the day after the Review or if you want to go to a new category and revisit this category a later. Either is fine!

Always keep fact-of-the-day activities light and playful. Use secret-handshake-style (one child, one prompt, two seconds), or 15-second-warm-up style (6 or 7 prompts, whole-group choral responses).

Doubling and halving: a foundation for multiplication, division, and fractions Anchor Doubling

This is a six-day sequence of fact-of-the-day activities.

  • DAY 1: Start first with a one-digit number that is equal to or smaller than 5.
  • DAY 2: Start with a two-digit number, both digits smaller than 5: like 43, 21, 32.
  • DAY 3: When students are swift and confident with those, use three-digit numbers, all digits smaller than 5: like 412, 343, 341...
  • DAY 4: Return to one-digit numbers, but now include numbers that are larger than 5.
  • DAY 5: Return to two-digit numbers, but use all multiples of 10: 80, 60, 70, 40, 60, 50, 30...
  • DAY 6: Use any two digit numbers.

Prompt: Numbers as specified above.

Today's rule: When you are given a number, double it. Example:

Day 1

  • Teacher: 3
  • Student: 6

Day 2

  • Teacher: 41
  • Student: 82

Day 3

  • Teacher: 324
  • Student: 648

Day 4

  • Teacher: 8
  • Student: 16

Day 5

  • Teacher: 70
  • Student: 140

Day 6

  • Teacher: 28
  • Student: 56

Halving even numbers As with doubling, this spreads out over many days.

  • DAY 1: Start first with one-digit numbers between 2 and 8 that are even.
  • DAY 2: Start with two-digit numbers, both digits even: like 46, 28, 64.
  • DAY 3: When students are swift and confident with those, use three-digit numbers, all digits even: like 462, 848, 628...
  • DAY 4: Return to two-digit numbers, but use all multiples of 10: 80, 60, 70, 40, 60, 50, 30...
  • DAY 5: When students can easily halve numbers like 30, 50, and 70, give them multiples of 100: 800, 600, 700, 400, 600, 500, 300...
  • DAY 6: Return to two-digit numbers, but progress to even numbers with an odd 10s digit: like 74 (for which they think "half of 70 and half of 4"), 56, 92...

Prompt: Numbers from the sets described above.

Today's rule: When you are given a number, you give back half of it. Example:

Day 1

  • Teacher: 64
  • Student: 32
  • Day 2
  • Teacher: 28
  • Student: 14 ...and so on.

Halving odd numbers Introduce by halving even one-digit numbers like 8 and 6, then introduce odd one-digit numbers, then numbers up through 20.

Prompt: Any number from 0 through 20.

Today's rule: When you are given a number, give back half! Example:

  • Teacher: 8
  • Student: 4
  • Teacher: 9
  • Student: four and a half

Other foundation-building multiplication facts Anchor Square Numbers

To see how knowledge of the square numbers can help students practice and remember all their multiplication facts, see Difference of squares.

Prompt: Any number from 1 through 10.

Today's rule: When you are given a number, you say its square: that is, multiply it by itself. Example:

  • Teacher: 10
  • Student 100 (10x10)
  • Teacher: 4
  • Student: 16 (4x4)

Square Numbers more advanced DAY !: Start with any number from 1 through 12. DAY 2: Start with two-digit numbers, but use all multiples of 10: 80, 60, 70, 40, 60, 50, 30... Example:

  • Teacher: 8
  • Student 64 (8x8)
  • Teacher: 12
  • Student: 144 (12x12)
  • Teacher: 80
  • Student 6400 (80x80)
  • Teacher: 20
  • Student: 400 (20x20)

Multiplying by 10 Prompt:

Today's rule: Example:

Multiplying by 5 Note how this makes use of the doubling that students have mastered. Think of multiplying by 10 and then taking half of that result. Introduce the idea by giving consecutive problems n x 10 followed by n x 5, so that students "feel" the idea that multiplying by 5 gives half of what you get when you multiply by 10.

Prompt: Any number that students can take half of.

Today's rule: When you are given a number, multiply it by 5. (You can multiply by 10 and then take half, if you like.) Example:

Square Numbers the other way Prompt: The square of any number from 1 through 12: 1, 4, 9, 16, 25 36 ... 144

Today's rule: When you are given a number, say what it is the square of. Example:

  • Teacher: 144
  • Student 12
  • Teacher: 25
  • Student: 5

Square Numbers the other way -- more advanced

Prompt: The square of any two-digit multiple of 10: 100, 400, 900, 1600, 2500, 3600 ... 8100

Today's rule: When you are given a number, say what it is the square of. Example:

  • Teacher: 900
  • Student 30
  • Teacher: 2500
  • Student: 50