standard_description: Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
problem_activity: Narrative
The purpose of this Estimation Exploration is for students to think about dividing a unit fraction into smaller pieces. In the lesson, students will be given extra information so they can determine the exact size of shaded regions like the one presented here.
Launch
Groups of 2
Display the image.
“What is an estimate that’s too high? Too low? About right?”
1 minute: quiet think time
Activity
“Discuss your thinking with your partner.”
1 minute: partner discussion
Record responses.
Student Facing
How much is shaded?
[IMG]
Record an estimate that is:
{"table": [{"_attributes": {"border": "1"}, "tbody": [{"tr": [{"th": [{"_attributes": {"scope": "col", "style": "text-align:center"}, "_value": "too low"}, {"_attributes": {"scope": "col", "style": "text-align:center"}, "_value": "about right"}, {"_attributes": {"scope": "col", "style": "text-align:center"}, "_value": "too high"}]}]}, {"tr": [{"td": [{"span": [{"_attributes": {"class": ["math"]}, "_value": "\\(\\phantom{\\hspace{2.5cm} \\\\ \\hspace{2.5cm}}\\)"}]}, {"span": [{"_attributes": {"class": ["math"]}, "_value": "\\(\\phantom{\\hspace{2.5cm} \\\\ \\hspace{2.5cm}}\\)"}]}, {"span": [{"_attributes": {"class": ["math"]}, "_value": "\\(\\phantom{\\hspace{2.5cm} \\\\ \\hspace{2.5cm}}\\)"}]}]}]}]}]}
Student Response
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Activity Synthesis
Display the image:
[IMG]
“How is the tape diagram the same as this area diagram? How is it different?” (Both diagrams show
\(\frac{1}{4}\)
of the whole and then a piece of that
\(\frac{1}{4}\)
is shaded. The tape diagram is long and narrow and the shaded piece is an entire vertical slice. The shaded piece in the area diagram is cut horizontally.)


aligns: no