Question

card sort
match each situation to a tape diagram.
100%
last year
this year
25%
100%
last year
this year
25%
this year’s blueberry harvest is
75% of last year’s.
compared to last year’s
strawberry harvest, this year’s
harvest is a 25% increase.
this year’s apple harvest is $\frac{3}{4}$ of
last year’s.
compared to last year, this year’s
peach harvest decreased 25%.
this year’s plum harvest is 125%
of last year’s.
there are $\frac{1}{4}$ more raspberries
this year compared to last year.

Explanation:

Step1: Analyze the percentage relationships

• For an increase: This year's value = last year's value + increase. If it's a 25% increase, this year's is 125% of last year's.
• For a decrease: This year's value = last year's value - decrease. If it's a 25% decrease, this year's is 75% of last year's.
• $\frac{3}{4}=75\%$, $\frac{1}{4} = 25\%$ increase (since $1+\frac{1}{4}=125\%$)

Step2: Match the situations

• "Compared to last year’s strawberry harvest, this year’s harvest is a 25% increase" → This year is 125% of last year. Match with the right - hand tape diagram (where this year's bar is longer than last year's by 25%).
• "This year’s blueberry harvest is 75% of last year’s" → Match with the left - hand tape diagram (this year's bar is shorter, 25% less than last year's, so 75% of last year's).
• "Compared to last year, this year’s peach harvest decreased 25%" → This year is 75% of last year. Match with the left - hand tape diagram.
• "This year’s plum harvest is 125% of last year’s" → Match with the right - hand tape diagram.
• "This year’s apple harvest is $\frac{3}{4}$ of last year’s" ($\frac{3}{4}=75\%$) → Match with the left - hand tape diagram.
• "There are $\frac{1}{4}$ more raspberries this year compared to last year" ($1+\frac{1}{4}=125\%$) → Match with the right - hand tape diagram.

Answer:

• "Compared to last year’s strawberry harvest, this year’s harvest is a 25% increase": Right - hand tape diagram.
• "This year’s blueberry harvest is 75% of last year’s": Left - hand tape diagram.
• "Compared to last year, this year’s peach harvest decreased 25%": Left - hand tape diagram.
• "This year’s plum harvest is 125% of last year’s": Right - hand tape diagram.
• "This year’s apple harvest is $\frac{3}{4}$ of last year’s": Left - hand tape diagram.
• "There are $\frac{1}{4}$ more raspberries this year compared to last year": Right - hand tape diagram.