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Welcome fellow Recovering Traditionalists to Episode 109. Today I’ve got a question for you and it pertains to The Use of AND in Math.
Welcome to Build Math Minds the podcast, where fidelity to your students is greater than fidelity to your textbook. I’m your host, Christina Tondevold, the recovering traditionalist and BuildMathMinds.com Founder, where my mission is to change the way we teach elementary math to our kiddos. Are you ready to start building math minds and not just creating calculators? Let’s get started.
As a Recovering Traditionalist I want you to know that I don’t have it all figured out and it’s okay that you don’t either. I’m still refining my understanding and teaching and it’s been over 17 years I’ve been working on changing my teaching.
So I’m going to start doing a different type of podcast episode every once in a while. I’m calling them my ‘wonderings.’ So today I’m Wondering About The Use of the word AND in Math. Did any of you catch how I said the number of today’s episode?
I see it often on social media and it is very common in my discussions with other math teachers, it’s that the word ‘AND’ should only be used to denote the decimal when saying numbers.
For example, how do you say the number 245?
Do you say “Two hundred and forty-five”?
How about 1036?
Is it okay to say “One thousand and thirty-six”?
A lot of people say “NO!! You cannot do that. You should only use the word ‘and’ when there is a decimal.”
So, according to them we should only use ‘and’ when it’s a number like 12.5…we should say “twelve and five tenths”.
But this is where the Recovering Traditionalist in me comes out. I want to buck tradition. Just because we’ve always used ‘and’ in that way does it mean we HAVE TO????
So here’s what I’m wondering…
Is the use of the ‘and’ just there as a rule to help kids know when to put a decimal instead of helping kids actually understand when a decimal is used?
Are we teaching kids the rule that when you hear ‘and’ that’s where you place a decimal instead of helping them understand place value and that when they hear ‘tenths’ or ‘hundredths’ etc, then that is when you need a decimal??
Let’s put it into context. If I have $134, I have one hundred AND thirty-four dollars. Yes, I can say it as “one hundred thirty-four dollars” but do I have to??? Can’t I say that I have one hundred AND thirty-four dollars?
If I have $134.25, can’t I say “One hundred and thirty-four dollars and twenty-five cents”??? And expect kids, and even adults will understand what that is?
I get that it’s a mouthful and it’s more streamlined to say it without the extra ‘and’s in there, but when we try to make it easy for kids, we often strip out the understanding that goes with it.
When we teach kids that the ‘and’ means ‘put a decimal here’, we aren’t addressing place value with them and that’s a big concern to me.
Yes, we will probably always say ‘and’ when the decimal appears in a number but I don’t want kids to be looking for and listening for the ‘and’ to tell them they need a decimal. I want them to listen to the values of the numbers and when they hear ‘tenths’ or ‘hundredths’ or ‘cents’ when talking about money…basically anything that isn’t a whole number, then that means they need a decimal or it’s written in fractional form.
So those are my thoughts and wonderings, but I’d love to hear what you think on this topic. Like I said this is something I’m wondering about. Is there a reason I’m not seeing that we must only use the ‘and’ when we have a decimal?
Let me know your thoughts on this. You can come over to the show notes page at buildmathminds.com/109 to leave me a comment or I’ll also be posting about this on my social media accounts. You can find me at The Recovering Traditionalist on Facebook and on Twitter and Instagram my handle is @BuildMathMinds. I’d love to hear your thoughts and let me know if my wonderings are correct.
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Saying “and” is an anticipatory action. Rather than using it when saying a number to the left of the decimal (“one hundred and nine”) while waiting to hear the entire number, including the decimal place, using it only to indicate a decimal provides a mental image as the number is described orally. Using “and” anyplace can lead to a number like 109.504 being voiced as “one hundred and 9 and five hundred and 4 thousandths”. That a lot to hold and keep adjusting mentally.
I understand what you are saying. However, I teach my students both ways to understand the math concepts and defend their reasoning. I let them know that although you may put “and” in 134, the “and ” will mean you are placing a decimal in the “and” place when you write the problem. I use the money concept for my examples. I may ask my second graders about this problem for $250.40, which I write on the board. One of the students says, ” 200 and 50 dollars and 40 cents. ask he or she is speaking I write what they are saying on the board. They will tell me, “that’s not what I said.” this is when I start to explain how “and” stand for decimal in math and this is how we will write your answers this way 200.50.40 cents. Then I will say the problem on the board and have them write it as 250and40 cents or 250.40. They start to notice the difference in how both answers are registered, and they start reasoning with each other about why they would change or not change their saying.
I do not have a problem with them saying “and,” however, I do want them to know the concept of “and” in math, so when they get to a higher grade, they can better defend their reasoning for saying “and.”
When speaking about quantity, I understand that my first graders may say one hundred and thirty-four for (134) because we often practice grouping quantities that way with our counting collections. However, when reading numerals, I would hope they would say one hundred thirty-four.
Since I don’t do much with decimals at this level, I hadn’t given much thought to the use of the word “and” as an identifier of a decimal point, but can see how that trap would be easy to fall into.
I agree. I feel that way also. I too work with primary grade kids and I think it prepares them better for upper grades and the decimal. It also helps their understanding of money.
Hi Christina, I really enjoyed your podcast today because I’ve had the same wondering. Simply, I think it’s fine to use “and” but I model not using it without pressing the matter. My second graders don’t yet know about decimals and I just don’t want to make things complicated. Most of them use “and” when saying 3-digit numbers and that’s okay!
I am so going to post this as a number talk activity for my class to first see how they say the number I wrote, then I will make it a learning moment.
My 6th grade students really struggle with understanding decimals (and fractions). They struggle with understanding that a decimal amount is less than one whole. So I often talk with them about how number that has a decimal means you have a whole number AND a little bit more. 5.3 is 5 wholes and a little bit more. Even 5.99 is five wholes and a little bit more because it isn’t even one whole more. So for this reason, I encourage students to use the word AND to think about what a decimal means. However, I also wonder about saying AND in 109 because it helps with the understanding that it is 100 + 9. So I guess I’m still wondering….
Hi Christina,
I agree with you that we should be able to use the word ‘and’ in saying a number that does not require the decimal point. For 134, I would say one hundred and thirty four. This is important for students learning the place value of each number. The ‘and’ emphasises the difference between the hundreds and the tens for young students. I would like to say, ‘One hundred and thirty and four.’
I also agree that students should not be listen for ‘and’ to denote a decimal point. Students need the understanding why there is a decimal point in some numbers. Rote learning does not help understanding it only produces misconceptions.
In the UK they say the and in numbers that are not decimals, so I have adapted as an international school teacher to introduce both.
Wow! Wondering why I did not wonder about this before. As always, thank you Christina for helping us think about why we do the things we do.
I learned it as a rule and one that I worked really hard with my students to read numbers ‘properly’. Upon listening to this episode, it may me question is it really necessary?, does it really matter?, especially when so many people use AND when reading/speaking about numbers.
I think it is. I think using AND to represent a decimal helps students see the different parts of the number in context – the wholes and the parts – for example when used discussing money – its dollars and cents, for distance it represents different units such as m and cm.
It was the part you said about place value that really had me thinking, and I agree having students understand place value is huge. That said I don’t think we want students using AND between each place value as the numbers get larger as it would be pretty cumbersome. One of the numbers you mentioned was 1035 as One thousand AND thirty five – but really is that helping students to learn the place when we are lumping the tens and ones together?
Great wonder to get people thinking! Thanks!
As a teacher of special needs students, I approach the AND questions depending on what I am teaching. If I am teaching place value, I make a big deal out of the AND being the signal for a decimal point especially since my students often have difficulty articulating tenths and hundredths. As a drill to reinforce place value, I will have a student read a number and I will write what they say on the board. Then ask the class to explain why or why not the numbers match.
If I am teaching another topic and a student puts in extra ands, I will let it slide or repeat with the correct tenths and hundredths
I never thought about AND as being an indicator for the presence of decimal but ironically I actually teach it as such without realizing it.
I’vejust begun to teach decimal sounding it the way you indicated. I actually used to say decimal numbers the traditional way. 12.45, I used to say it as twelve point four five.
However, I go with the use of AND in numbers such as 109 because it is an indication of a combination of both a hundred place and a unit place, therefore, it is a hundred and nine units.