A focused Grade 4 learning session for Fractions with Denominators 10 and 100 using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can connect fractions with denominators of 10 and 100.
Fractions with Denominators 10 and 100 means using equal parts, number lines, and clear fraction language to describe parts of a whole.
Question: Look at the grid below. The shaded squares represent a fraction. Which fraction and decimal both represent the shaded amount?
Why it works: The grid shows 40 shaded squares out of 100 total. This is \(\frac{40}{100}=\frac{4}{10}=0.4\).
Answer: \(\frac{40}{100}\) and \(0.4\)
Question: Look at the model. Which answer uses tenths to match this model?
Answer: \(\frac{5}{10}\)
Question: Look at the number line below. What fraction is marked on the number line?
Answer: \(\frac{3}{10}\)
Question: A student wrote: \(\frac{3}{10}+\frac{3}{100}=\frac{6}{110}\). What is the correct answer?
Why it works: The student tried to add the denominators, which is wrong! The correct way: convert \(\frac{3}{10}=\frac{30}{100}\), then add: \(\frac{30}{100}+\frac{3}{100}=\frac{33}{100}\).
Answer: \(\frac{33}{100}\)
Fractions with Denominators 10 and 100 becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
Equal parts first, fraction name second.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
Which fraction with denominator \(100\) is equivalent to \(\frac{3}{10}\)?
Answer C: \(\frac{30}{100}\)
To write \(\frac{3}{10}\) as hundredths, multiply the numerator and denominator by \(10\): \(\frac{3}{10}=\frac{3\times10}{10\times10}=\frac{30}{100}\).
What is \(\frac{7}{10}\) written as a fraction with denominator \(100\)?
Answer B: \(\frac{70}{100}\)
Let's convert \(\frac{7}{10}\) to a fraction with denominator 100 by multiplying: \(\frac{7}{10}=\frac{7\times10}{10\times10}=\frac{70}{100}\).
Which fraction equals \(\frac{50}{100}\)?
Answer B: \(\frac{5}{10}\)
Both fractions represent the same amount---one-half. We can write it as \(\frac{50}{100}=\frac{5}{10}\).
What is \(\frac{4}{10}\) as a fraction with denominator \(100\)?
Answer C: \(\frac{40}{100}\)
To convert \(\frac{4}{10}\) to hundredths, multiply both the numerator and denominator by \(10\): \(\frac{4}{10}=\frac{40}{100}\).
Which number sentence is true?
Answer A: \(\frac{2}{10}=\frac{20}{100}\)
When we convert \(\frac{2}{10}\) to hundredths, we multiply both numerator and denominator by \(10\): \(\frac{2\times10}{10\times10}=\frac{20}{100}\).
What is \(\frac{9}{10}\) written as a fraction with denominator \(100\)?
Answer C: \(\frac{90}{100}\)
To convert \(\frac{9}{10}\) to hundredths, we multiply both parts by \(10\): \(\frac{9}{10}=\frac{9\times10}{10\times10}=\frac{90}{100}\).
Add: \(\frac{3}{10}+\frac{5}{100}\).
Answer C: \(\frac{35}{100}\)
First, convert \(\frac{3}{10}\) to hundredths: \(\frac{3}{10}=\frac{30}{100}\). Now both fractions have the same denominator, so we add: \(\frac{30}{100}+\frac{5}{100}=\frac{35}{100}\).
Add: \(\frac{1}{10}+\frac{45}{100}\).
Answer C: \(\frac{55}{100}\)
Convert \(\frac{1}{10}\) to hundredths: \(\frac{1}{10}=\frac{10}{100}\). Now add the two fractions with the same denominator: \(\frac{10}{100}+\frac{45}{100}=\frac{55}{100}\).
Which is equal to \(\frac{6}{10}\)?
Answer B: \(\frac{60}{100}\)
To convert \(\frac{6}{10}\), multiply numerator and denominator by \(10\): \(\frac{6}{10}=\frac{6\times10}{10\times10}=\frac{60}{100}\).
What is \(\frac{5}{10}+\frac{25}{100}\)?
Answer B: \(\frac{75}{100}\)
First, rewrite \(\frac{5}{10}\) using hundredths: \(\frac{5}{10}=\frac{50}{100}\). Then add: \(\frac{50}{100}+\frac{25}{100}=\frac{75}{100}\).
Which is true?
Answer B: \(\frac{8}{10}=\frac{80}{100}\)
We can convert \(\frac{8}{10}\) to a fraction with denominator 100 by multiplying both parts by \(10\): \(\frac{8}{10}=\frac{80}{100}\).
