I begin today by asking students how many quarters in a dollar. I ask them to hold up the right number of fingers to match the quarters in a dollar. We agree that there are 4. I now display 1 dollar and 4 quarters on the Smart Board
We move the 4 quarters over to show that they equal one dollar.
Next I ask how many quarters in half a dollar? Can they show me with fingers. I look to see who understands that there are 2 quarters in half a dollar.
We move the 2 quarters over to show that they equal 1/2 dollar. Can anyone think of another coin that is the same as half of a dollar? (50 cent piece).
If I have 1 quarter from the dollar (I move it over away from the other 3) how many quarters out of the 4 did I take? (1). So I have 1 out of 4 which I can write as 1/4. Can anyone read what I just wrote? (one quarter). Some students may say one out of four and then I will ask if anyone remembers another way to say this from first grade? (I am looking for 1/4) Wow, and what is this coin called? (a quarter) Isn't that cool that 1/4 of my dollar is one quarter.
I move another quarter over and say how many quarters do I have now? (2) Out of how many quarters do you see on the board? (4) So I have 2/4 or 2 out of 4 quarters. ( I use the words 2 out of 4 to helps students conceptualize what the fractions really are, but I also use the correct fractional term two fourths because that is the terminology they will use later on in school.
It is possible when I show the 2/4 of the quarters that someone will notice that I have half of the quarters. I will reinforce that there are two ways to say 2/4 so they are right when they say 1/2. I am not ready yet to teach equivalent fractions, but I acknowledge them as they arise.
I ask students how much 1/4 of a dollar is worth? (25 cents). What about 2/4 of a dollar? (50), What about 1/2 of a dollar (50), what about 3/4 of a dollar (75), and what about 4/4 of a dollar (1.00)
I know pose a question. "I have 1/4 of a dollar. My friend has 3/4 of a dollar. How much more money in cents does my friend have?" I give students a few minutes to figure it out and then we share solutions.
I ask students how many of them have ever heard of the expression "Quarter past the hour", how about half past or quarter of? What do they think these mean? I let students share their ideas about what these terms mean.
I tell them that today we will look at the clock and see if we can make sense of those terms (MP7). I hand each student a blank clock face with no hands. It is marked in 1 minute lines around the clock. I ask them to draw a straight line from the 12 to the 6 and lightly shade in the side of the line that contains the numbers 1 - 6 or the first half of the clock. How many pieces is the clock in now? (2) What would I call each side? (half of the clock). Ok so when I say half past the hour, where do you think the minute hand would be? (on the 6). Right - half past the hour. Lets count to see how many minutes are in this half of the clock. 5,10, 15,20, 25, 30 Right, it is 30 minutes because how many minutes are in an hour? (60) and what is half of 60? (30). So if someone tells you it is half past the hour, you will know it is 30 minutes past or __ :30.
Ok, lets draw another line from the 9 to the 3. Now how many sections does your clock have? (4). When we have four parts do you remember what we call them? (fourths or quarters) Remember how many quarters in a dollar? (4) and now there are 4 parts or 4 quarters in my clock. I say lets pretend that the clock is my dollar. I can put 1 quarter in each section of my clock like so (I demonstrate). Now I want you to shade the section from the 12 to the 3 where one of the quarters is. Use a new color. How many of those quarters are there in the whole clock? (4) So if I say quarter past the hour, what number would the hand point to? (3) And when the hand is on the 3 it is how many minutes past the hour? Lets count 5,10 ,15 Right, 15. (15) So quarter past the hour would be ___: 15.
Then we have quarter to the hour or quarter of. Lets look at 1 quarter before the hour. Where is the hand pointing? (9). Right and how many minutes is that? (45). So if someone says it is quarter of the hour they mean ____:45. In this case it is the hour before they mention so if I say quarter of two I mean 1:45 because we only have a quarter of an hour left to go until 2:00.
I hand each student a slip of paper and a paper fastener. I ask them to cut the paper into a short and a long hand for their clocks. I ask them to fasten the hands in the center with the paper fastener.
I review each of these terms with students by having them set the hands on their clocks as I call out a time. I do this until most students are able to set the clocks to the 3 terms. I know that several students will need a review time with me at a later date to really solidify this concept.
I ask students to take their math journals out and to draw a clock and mark it quarter past two. I ask them to draw a second clock and mark it to half past seven. I use these clocks to assess student understanding of the terms half past, quarter past as fractions of time.