· Today we are going to focus on comparing fractions. When we compare numbers there are many things we can focus on to compare them but today we are going to speak specifically about their size.
· Discuss where we’ve been – understanding numbers and where this will take us – to comparing fractions to estimating with fractions
· There are many different ways to compare numbers according to their size. Over the next couple of months as we work with fractions in lots of different contexts we will learn about and develop many ways to compare fractions.
· Today we are going to work on comparing numbers by using benchmarks. The reason we are going to do this is it helps us to reason with fractions mentally and make sense of the size of fractions. As we continue to learn about
· TPS – Where have you heard the word benchmark before? What does that word mean to you?
· In math a benchmark number is a number that serves a reference point. It helps us to estimate the size of other numbers very quickly.
· The benchmarks we are going to use today are 0, 1/2 and 1 – Show a number line to students and have them decide where the number ½ would go – possible TPS.
· Ask students – we are really familiar with the number ½ is there another way to say that number?
· Write down students generated list – ask if there are more or if we found all of the equivalents to ½
· Discuss what is common about all equivalents to half
· Offer an equivalent to half where the denominator is an odd number – or ask to guide them through – I noticed that all the equivalents to have that we were able to come up with have even denominators. Can anyone think of an equivalent to half that has an odd denominator?
· Tell students I’m going to model an example using the knowledge I have gained over the course of the week. We will be thinking through two guiding questions:
o Is the fraction between 0 and 1/2 or ½ and 1?
o Is the fraction closer to 0, ½ or 1?
o USE EXAMPLE 2/5 – focus on the strategy of using equivalent fractions but allow others when students are working – Model how to make the decision if 2/5 is closer to zero or one half
o The first question I want to ask myself is what two benchmarks is this number between – 0 and ½ or ½ and 1?
o Well I see that the denominator in 2/5 is five and I know that half of five is 2.5 so I know that 2.5/5 is the same as half.
o Now when I look at my numerator, I see that 2 is smaller than 2.5 so I know that 2/5 must be between 0 and ½
o Next I want to ask myself Which benchmark is my number closest to?
o I know that two fifths is closer to 2.5 fifths than it is to zero fifths, so I 2/5 is closest to the ½ benchmark.
o Last I can check to see if my reasoning makes sense by using my fraction pieces to prove my answer.
o Use the pieces – draw a number line if needed.
· Review with students – what questions did I ask myself, what process did I go through to compare my fraction to the benchmarks.
· Reveal steps to students
· In pairs students are going to be given two fractions. Students will ask each other the guiding questions to guide each other through comparing to the benchmark and deciding which benchmark it is closest to. PROVIDE DIALOGUE for students- STUDENT A will ask the questions to the partner – STUDENT B will answer for the first set. Then the students will switch
· Student A fraction – 2/10
· Student B fraction – 5/6
· Review students’ results and allow them to explain why they thought their numbers were larger than one, less than one, etc.
· Tell students that they will probably start to notice some patterns when they are comparing fractions to benchmarks and they should note them or remember them for when we come back to discuss
· Discuss the assignment – tell students what I expect to SEE when I come around and what I expect to HEAR when I come around
· Remind students of “S” and “E”
· Give students a worksheet with fractions and a table to decide which interval it is between and which benchmark the fraction is closest to.
· Walk around and ask guiding questions to students.
· Tally what students are talking about
· Together put everything into the chart – discuss how decisions were made. How did we know which fractions went into each bucket – what was our thinking?
· How would using benchmarks help us to compare two fractions that are not ½?
· Exit Ticket.