## Reflection: Diverse Entry Points How Close Is "Close"? - Section 3: How close is "close"?

During group work, students were in homogeneous groups based on the ticket to go from the previous lesson.  Different groups chose different numbers that they believed to be “close”.  Here is a range of work from a number of groups.

0.05 to 0.50

This group was a group that struggled with the previous lesson.  They chose these numbers and said they were close because they were “both between 0 and 1”.  They only produced a few fractions and decimals, but the work shows that the students are able to change a fraction to a decimal.  One issue is that they listed that 1/50 was equivalent to 0.2.  I suspect that they confused 1/5 and 1/50.  They are also able to simplify fractions.  I watched this group work and their strategy was to come up with the decimal first and then change it into a fraction.

0.4 to 0.5

This group was one of the few groups that chose two “close” fractions, most groups chose to start with decimals.  This group moved from tenths and used hundredths to find fractions that were between four-tenths and five-tenths.  They list all of the hundredths between forty and fifty hundredths.  This was an approach that many groups used.  At the end of the second table, they have exhausted all of the possible hundredths.  At this point, some groups said things like, “There aren’t any more fractions/decimals that fall between our numbers.”  I told them to keep thinking.  This group came up with 0.432.  This took time, but ultimately they were able to see that there were indeed more fractions and decimals between their numbers.

0.5 and 1

This group picked two numbers that were further apart than most groups.  Looking at their fractions, it is clear that they understand that they can create fractions that have different denominators than tenths and hundredths.   They were one of the few groups to create a fraction out of 10,000.  I did check in with the group to let them know that the lower table had to have values that were different than the top table.  One issue is that the group listed 0.5 as falling between 0.5 and 1.

Diverse Entry Points: Choosing "Close" Numbers and Generating Fractions and Decimals

# How Close Is "Close"?

Unit 3: Integers and Rational Numbers
Lesson 3 of 17

## Big Idea: How close is “close”? Students generate fractions and decimals that fall between “close” numbers and are confronted with the density of rational numbers.

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60 minutes

### Andrea Palmer

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