Strategies for basic addition and subtraction facts

In this video I show several strategies for learning the basic addition and subtraction facts:

• finding all the possible sums for a certain number; e.g. for 6, these would be 0 + 6, 1 + 5, 2 + 4, and 3 + 3;
• writing out all the fact families where the sum is a certain number;
• the 9 "trick"; 9 + 7 is the same as 10 + 6 (9 wants so badly to be 10 so that it "steals" one from 7);
• doubles and the accompanying addition facts;
• number rainbows and how to use them to practice subtraction;
• a structured drill for addition facts.
  

Enjoy!



Strategies for Addition and Subtraction Facts - Video

Strategies for basic addition and subtraction facts

In this video I show several strategies for learning the basic addition and subtraction facts:

• finding all the possible sums for a certain number; e.g. for 6, these would be 0 + 6, 1 + 5, 2 + 4, and 3 + 3;
• writing out all the fact families where the sum is a certain number;
• the 9 "trick"; 9 + 7 is the same as 10 + 6 (9 wants so badly to be 10 so that it "steals" one from 7);
• doubles and the accompanying addition facts;
• number rainbows and how to use them to practice subtraction;
• a structured drill for addition facts.
  

Enjoy!



Strategies for Addition and Subtraction Facts - Video

Math Mammoth LightBlue series books as downloads

Great news!

The LightBlue Series books are now available as downloads. These are designed to be a complete curriculum for a given grade. They follow the lesson format of my Blue Series books: explanations, then problems (worktext). In fact, the two series do share a lot of material.

The LightBlue is for you if you need a math curriculum for a given grade that covers all the topics needed. These are practically no-prep for the teacher, and in fact, kids can probably teach themselves the majority of the time (assuming they can read).

Please read more by following these links:

Math Mammoth Grade 1 Complete Worktext

Math Mammoth Grade 2 Complete Worktext

Math Mammoth Grade 3 Complete Worktext

I will have grade 4 ready sometime this spring, February or March I think.

Math Mammoth LightBlue series books as downloads

Great news!

The LightBlue Series books are now available as downloads. These are designed to be a complete curriculum for a given grade. They follow the lesson format of my Blue Series books: explanations, then problems (worktext). In fact, the two series do share a lot of material.

The LightBlue is for you if you need a math curriculum for a given grade that covers all the topics needed. These are practically no-prep for the teacher, and in fact, kids can probably teach themselves the majority of the time (assuming they can read).

Please read more by following these links:

Math Mammoth Grade 1 Complete Worktext

Math Mammoth Grade 2 Complete Worktext

Math Mammoth Grade 3 Complete Worktext

I will have grade 4 ready sometime this spring, February or March I think.

Number rainbows to learn subtraction facts

I thought some of you (those who teach second grade) might enjoy my NUMBER RAINBOWS. The idea is that you connect two numbers with an arc if they add up to the particular number, such as 13.



Then, the child can use it as a reference when subtracting from 13 or when doing subtraction drill. You could first drill subtraction facts WITH the rainbow (such as 13 − 4, 13 − 7 etc.) and then without.



You would also ask the child to reproduce the rainbow - and color it, of course! These make for quite pretty math facts practice, don't you think!

I'm going to add these to my Add & Subtract 2-A book.

Number rainbows to learn subtraction facts

I thought some of you (those who teach second grade) might enjoy my NUMBER RAINBOWS. The idea is that you connect two numbers with an arc if they add up to the particular number, such as 13.



Then, the child can use it as a reference when subtracting from 13 or when doing subtraction drill. You could first drill subtraction facts WITH the rainbow (such as 13 − 4, 13 − 7 etc.) and then without.



You would also ask the child to reproduce the rainbow - and color it, of course! These make for quite pretty math facts practice, don't you think!

I'm going to add these to my Add & Subtract 2-A book.

Does the child need to add completing the ten?

Question:

...have an other question about using your worksheets for my daughter. She is six years old - home schooled.
Currently, we are using Addition & Subtraction 2

She is able to add and subtract any numbers from 1 to 100 but when I try to explain "complete the ten" concept, she doesn't like thinking about it. She would rather solve 9+6 by counting on the finger 6 after 9 ... . She complains that I have to first subtract then add to make 10.

My question is: Should I let her complete the exercises without making her think in this manner?

It is important that she understands the IDEA in completing the ten. I gather that she does indeed understand the idea, but doesn't want to do it, since you'd have to both subtract and add, right? She just likes to do one operation, not two?

The adding though, is really easy, because you add 10 + 5 or 10 + 7 or something to ten. If she's counting with fingers, she's not yet seeing the easiness of this adding. It is also faster to do 9 + 6 by first subtracting one from 6 (getting 5), and then adding 10 + 5, because you can do 10 + 5 really easy: it is one ten and five, or we call that fifteen.

Of course she must understand place value to realize how easy that addition is.

Now, the goal is ALSO to eventually memorize the answers. You might let her know that she can't always count with fingers to find 9 + 6 but a quicker method is needed.

You can let her do some exercises "her way" for now as long as she also is able to understand and do the "complete the ten".

But come back to this idea how completing the ten makes the whole calculation easier and quicker. She WILL need to understand the idea when studying CARRYING in addition, (I mean to totally understand how it works. I realize kids can learn carrying mechanically as well.)

So you can say 1-3 months later reprint some pages and try again.

Does the child need to add completing the ten?

Question:

...have an other question about using your worksheets for my daughter. She is six years old - home schooled.
Currently, we are using Addition & Subtraction 2

She is able to add and subtract any numbers from 1 to 100 but when I try to explain "complete the ten" concept, she doesn't like thinking about it. She would rather solve 9+6 by counting on the finger 6 after 9 ... . She complains that I have to first subtract then add to make 10.

My question is: Should I let her complete the exercises without making her think in this manner?

It is important that she understands the IDEA in completing the ten. I gather that she does indeed understand the idea, but doesn't want to do it, since you'd have to both subtract and add, right? She just likes to do one operation, not two?

The adding though, is really easy, because you add 10 + 5 or 10 + 7 or something to ten. If she's counting with fingers, she's not yet seeing the easiness of this adding. It is also faster to do 9 + 6 by first subtracting one from 6 (getting 5), and then adding 10 + 5, because you can do 10 + 5 really easy: it is one ten and five, or we call that fifteen.

Of course she must understand place value to realize how easy that addition is.

Now, the goal is ALSO to eventually memorize the answers. You might let her know that she can't always count with fingers to find 9 + 6 but a quicker method is needed.

You can let her do some exercises "her way" for now as long as she also is able to understand and do the "complete the ten".

But come back to this idea how completing the ten makes the whole calculation easier and quicker. She WILL need to understand the idea when studying CARRYING in addition, (I mean to totally understand how it works. I realize kids can learn carrying mechanically as well.)

So you can say 1-3 months later reprint some pages and try again.

Curriculum focal points

I'm going to talk again about the new report released by NCTM, Curriculum Focal Points.

For each grade, it describes THREE focal points, and also explains to which other mathematical topics these focal points connect to.

By familiarizing yourself with these few points, you can see the basics of school mathematics unfold before your eyes. Knowing the basic goals is essential for being a good teacher.

By the way, these aren't the only things kids might study on a given grade. They are the focus areas. Many of the other topics would connect with these.

Go look at the pics at textsavvy.blogspot.com about the way textbooks and programs typically present the topics, versus a "VISION OF CURRICULUM" laid out by the Focal Points document.


On grade 1, the focus is on

• addition/subtraction: basic basic addition facts and related subtraction facts. Learning to add and subtract two-digit numbers.


• Understanding whole numbers in terms of tens and ones


• Composing and decomposing geometric shapes

Measuring and simple bar and picture graphs are presented as applications of these.


On Grade 2:

• Understanding the base-ten numeration system and place-value concepts at least till 1000.


• Quick recall of addition facts and related subtraction facts and fluency with multidigit addition and subtraction.


• Measurement: Developing an understanding of linear measurement and facility in measuring lengths.

Skip-counting is also included, and prepares children for 3rd grade and multiplication.


On grade 3:

• Understanding multiplication and division, and strategies for basic multiplication facts and related division facts.


• Understanding fractions and fraction equivalence


• Geometry: Describing and analyzing properties of two-dimensional shapes.

Measuring using fractional parts ties nicely in with the second point.

So we get started on multiplication and division. Notice on next grade, one of the focal points is "developing quick recall", or basically memorizing multiplication/division facts.


On grade 4:

• Developing quick recall of multiplication facts and related division facts and fluency with whole number multiplication.


• Understanding decimals, including the connections between fractions and decimals.


• Measurement: Developing an understanding of area and determining the areas of two-dimensional shapes.

Well, reading these makes teaching school mathematics sound almost easy to teach - compared to reading a big laundry list of objectives and thinking, "Oh well, I'm supposed to cover all that".

You can find the other grades at Curriculum Focal Points by Grade.

Curriculum focal points

I'm going to talk again about the new report released by NCTM, Curriculum Focal Points.

For each grade, it describes THREE focal points, and also explains to which other mathematical topics these focal points connect to.

By familiarizing yourself with these few points, you can see the basics of school mathematics unfold before your eyes. Knowing the basic goals is essential for being a good teacher.

By the way, these aren't the only things kids might study on a given grade. They are the focus areas. Many of the other topics would connect with these.

Go look at the pics at textsavvy.blogspot.com about the way textbooks and programs typically present the topics, versus a "VISION OF CURRICULUM" laid out by the Focal Points document.


On grade 1, the focus is on

• addition/subtraction: basic basic addition facts and related subtraction facts. Learning to add and subtract two-digit numbers.


• Understanding whole numbers in terms of tens and ones


• Composing and decomposing geometric shapes

Measuring and simple bar and picture graphs are presented as applications of these.


On Grade 2:

• Understanding the base-ten numeration system and place-value concepts at least till 1000.


• Quick recall of addition facts and related subtraction facts and fluency with multidigit addition and subtraction.


• Measurement: Developing an understanding of linear measurement and facility in measuring lengths.

Skip-counting is also included, and prepares children for 3rd grade and multiplication.


On grade 3:

• Understanding multiplication and division, and strategies for basic multiplication facts and related division facts.


• Understanding fractions and fraction equivalence


• Geometry: Describing and analyzing properties of two-dimensional shapes.

Measuring using fractional parts ties nicely in with the second point.

So we get started on multiplication and division. Notice on next grade, one of the focal points is "developing quick recall", or basically memorizing multiplication/division facts.


On grade 4:

• Developing quick recall of multiplication facts and related division facts and fluency with whole number multiplication.


• Understanding decimals, including the connections between fractions and decimals.


• Measurement: Developing an understanding of area and determining the areas of two-dimensional shapes.

Well, reading these makes teaching school mathematics sound almost easy to teach - compared to reading a big laundry list of objectives and thinking, "Oh well, I'm supposed to cover all that".

You can find the other grades at Curriculum Focal Points by Grade.