In-Class Reference Sheet
Big Idea 1: Fractions are numbers that can represent length and are identified with a position on a number line.
Topic 4: Measuring on a Number Line
Key Concept: Fractions are numbers that can represent length and are identified with a position on a number
line.
Prior Knowledge:
1. Number lines with whole numbers.
2. Understand that a number line is a model that shows length.
3. Understand what the denominator and numerator represent.
Activity 1: Ordering Fractions with Common Denominators (2, 4, 3, 6)
Description
Students place fraction with common
denominators on a number line.
Beginning examples provide extra tic
marks to assist in placement.
Vocabulary
Content: number line
Process: place on, notice, drag
Preparation for
Learning
Teacher/Student
Dialogue
Indicators of
Understanding*
Provide students with sentence strips or paper strips. Each strip represents 1 inch.
• Have student mark the strip with 0 and 1.
• Have students fold the paper in half, draw a line, and mark 1/2.
• Continue folding and marking fractions up to sixths. As students place
fractions, count in sequence, for example 1/4, 2/4, 3/4, 4/4.
Open the Order Fractions on a Number Line tool and make tic marks for fourths.
• Put out fourths, and have students put the fractions on the number line.
• Discuss how the tic marks help with placement.
• Discuss how to sequence with the use of the numerator.
Reset the example and repeat with fourths and no tic marks.
• Discuss strategies for placement without tic marks. Relate to how folding the
sentence strip in half and half again divided it into fourths. Can you visualize
half of a half? To help us place 1/4?
• How do you know where to place 2/4?
While students are working in the software, be sure to circulate and ask:
• Which of the fractions in this example is the same as 1 whole?
• What strategy can you use to help you place the ___ fraction?
• Can you tell me what the marks on your number line are for? What do they
mean?
• Can you count from 0 to 1 in fourths for me?
• Sequentially counts from 0 to 1 in fractions such as fourths.
• Matches a fraction to 1 whole on a number line.
• Identifies where 1/2 is located on a number line.
• Uses the number line with tic marks to identify equivalent fractions for 1/2.
* Indicators of Understanding are in addition to the formative assessment at the end of each activity.
www.conceptuamath.com
© 2010 Conceptua Math LLC
1
In-Class Reference Sheet
Big Idea 1: Fractions are numbers that can represent length and are identified with a position on a number line.
Topic 4: Measuring on a Number Line
Key Concept: Fractions are numbers that can represent length and are identified with a position on a number
line.
Prior Knowledge:
1. Number lines with whole numbers
2. Understand that a number line is a model that shows length
3. Understand what the denominator and numerator represent
Activity 2: Ordering Fractions with Common Denominators 2 (2, 3, 4, 5, 6, 8, 10)
Description
Students place fraction with common
denominators on a number line.
Beginning examples provide extra tic
marks to assist in placement.
Vocabulary
Content: number line
Process: place on, notice, drag
Preparation for
Learning
Teacher/Student
Dialogue
Indicators of
Understanding*
Expand on previous lesson in which students used sentence strips. Have students
continue folding and writing the fraction numbers on their strips for eighths and
tenths.
• Ask students what they observed about the arrangement of the numbers.
• Are there more equivalent fractions for one half?
• Are there other fraction numbers that name the same point on the number
line, for example for 1/4?
Open the Order Fractions on a Number Line tool and put on the tic marks for fourths.
• Put out fractions with eighths. Ask students what strategies they can use to
place the fractions on the number line.
Reset and create a number line with tic marks for fifths.
• Ask them what the tic marks represent.
• Ask students where the 1/2 fraction would be located.
• Make examples placing fifths and tenths.
• Lead students into discovering that there are 2 tenths for each fifth.
• Is this a rule they can use for other fractions?
While students are working in the software, be sure to circulate and ask:
• Which of the fractions in this example is the same as 1 whole?
• What strategy can you use to help you place the ___ fraction?
• Can you tell me what the marks on your number line are for? What do they
mean?
• Can you count from 0 to 1 in tenths for me?
• Sequentially count from 0 to 1 in fractions such as fourths.
• Matches a fraction to 1 whole on a number line.
• Identifies where 1/2 is located on a number line.
• Uses the number line with tic marks to identify equivalent fractions for 1/2.
* Indicators of Understanding are in addition to the formative assessment at the end of each activity.
www.conceptuamath.com
© 2010 Conceptua Math LLC
2
In-Class Reference Sheet
Big Idea 1: Fractions are numbers that can represent length and are identified with a position on a number line.
Topic 4: Measuring on a Number Line
Key Concept: Fractions are numbers that can represent length and are identified with a position on a number
line.
Prior Knowledge:
1. Number lines with whole numbers.
2. Understand that a number line is a model that shows length.
3. Understand what the denominator and numerator represent.
Activity 3: Estimating with Benchmark Fractions
Description
Students select the benchmark
number to which a given fraction
number is closest. A number line
graphic provides extra visual support
and vectors are provided as feedback.
In this introduction, most fractions are
closer to 0 or 1.
Vocabulary
Content: benchmark, closest to
Process: No new vocabulary
Preparation for
Learning
Have students take out their sentence strips or create strips as described in Activity 1.
• Discuss what is meant by estimating and how estimating can be helpful. Have
students provide examples of times they have estimated an amount, size, etc.
• Introduce that we can also estimate the size of fractions.
Define Benchmark numbers as 0, 1/2, and 1.
Have students list ways that the numeral 1 can be written as a fraction.
• Have students write the fractions in the list as 1 less unit. (write 6/6 as 5/6,
write 8/8 as 7/8). Identify the closest benchmark for each.
• Have students draw number lines with vectors that represent each fraction and
identify the benchmark that is closest.
Have student list equivalent fractions for 1/2. Note that students may need to refer to
their sentence strip manipulatives.
Teacher/Student
Dialogue
While students are working in the software, be sure to circulate and ask:
• What strategy can you (did you) use to help you estimate?
• Can you tell me how many___ are equivalent to _____?
Indicators of
Understanding*
•
•
•
Can represent one whole as a fraction.
Can partition a number line equally to represent fractions.
Can state a strategy for estimating.
* Indicators of Understanding are in addition to the formative assessment at the end of each activity.
www.conceptuamath.com
© 2010 Conceptua Math LLC
3
In-Class Reference Sheet
Big Idea 1: Fractions are numbers that can represent length and are identified with a position on a number line.
Topic 4: Modeling Part/Whole Relationships
Key Concept: Fractions are numbers that can represent length and are identified with a position on a number
line.
Prior Knowledge:
1. Number lines with whole numbers.
2. Understand that a number line is a model that shows length.
3. Understand what the denominator and numerator represent.
Activity 4: Ordering Fractions with Common Numerators
Description
Students place fraction with common
denominators on a number line.
Beginning examples provide extra tic
marks to assist in placement.
Vocabulary
Content: number line
Process: place on, notice, drag
Preparation for
Learning
Teacher/Student
Dialogue
Expand on previous lessons in this topic in which students used sentence strips and
order fractions with common denominators.
• You may want to review with the strips depending on student performance on
previous activities.
Open the Order Fractions on a Number Line tool and put out 5 unit fractions.
• Discuss how students can determine placement. How does comparing
denominators help?
• Order the fractions above the number line first, then place them on the
number line.
• Help students discover the rule that when they are placing fractions with
common numerators, the smaller the denominator the larger the number.
Show examples of comparing unit fractions, fractions with common
numerators of 2, etc.
While students are working in the software, be sure to circulate and ask:
• What strategy can you use to help you place the ___ fraction?
• Can you tell me how you can use the tic marks to help you determine where
to place this fraction?
Indicators of
Understanding*
•
•
•
Can use tick marks to place fractions that fall on the tic marks and those in
between two tic marks.
Explains placement of a fraction by number of parts in the length between 0
and 1.
Explains the rule that the smaller the denominator the larger the length, so the
further from 0 the fraction number will be located.
* Indicators of Understanding are in addition to the formative assessment at the end of each activity.
www.conceptuamath.com
© 2010 Conceptua Math LLC
4
In-Class Reference Sheet
Big Idea 1: Fractions are numbers that can represent length and are identified with a position on a number line.
Topic 4: Modeling Part/Whole Relationships
Key Concept: Fractions are numbers that can represent length and are identified with a position on a number
line.
Prior Knowledge:
1. Number lines with whole numbers.
2. Understand that a number line is a model that shows length.
3. Understand what the denominator and numerator represent.
Activity 5: Estimating with Benchmark Fractions
Description
Students select the benchmark
number to which a given fraction
number is closest. A number line
graphic provides extra visual support
and vectors are provided as
feedback.
Vocabulary
Content: benchmark, closest to
Process: No new vocabulary
Preparation for
Learning
Have students take out their sentence strips or create strips as described in Activity
1 in this topic.
• Discuss what is meant by estimating and how estimating can be helpful.
Have students provide examples of times they have estimated an amount,
size, etc.
• Introduce that we can also estimate the size of fractions.
Review the definition for Benchmark numbers as 0, 1/2, and 1.
Have students list ways that the numeral 1 can be written as a fraction.
• Ask students if the fraction for 1 was one unit less, what benchmark would it
be closer to?
• Have students draw number lines with vectors that represent fractions, for
example 2/3, 4/5, 5/6.
Have student list equivalent fractions for 1/2. Note that students may need to refer to
their sentence strip manipulatives.
Teacher/Student
Dialogue
While students are working in the software, be sure to circulate and ask:
• What strategy can you (did you) use to help you estimate?
Can you tell me how many___ are equivalent to _____?
Indicators of
Understanding*
•
•
•
Represent one whole as a fraction.
Can partition a number line equally to represent fractions.
Can state a strategy for estimating.
* Indicators of Understanding are in addition to the formative assessment at the end of each activity.
www.conceptuamath.com
© 2010 Conceptua Math LLC
5