Garden Bed Length Cards: Ordering and Adding Tenths and Hundredths
The fourth graders are marking four planting beds along a 1-meter strip and labeling each bed with a length card. The cards read 0.4 m, 0.45 m, 2/5 m, and 0.04 m. Before the beds can be staked, the class must line the cards up from shortest to longest and decide which cards name the same length. Three arguments stall the group. Mia insists 0.45 is greater than 0.5 “because 45 is bigger than 5.” Diego says 0.04 and 0.4 are the same length “because the zero does not matter.” Priya mixed 0.3 m of soil into one bed and 0.47 m into another and wrote the total as 0.50 m, explaining, “3 + 47 = 50.” The teacher has one 20-minute block before the custodian needs the beds staked, so the teacher cannot address all three errors with the whole class and must choose which one to teach now and which to note for small-group work.
1. Order the four length cards from shortest to longest and identify any cards that name the same length. Justify using a common representation.
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Rewrite everything in hundredths: 0.4 = 40/100, 0.45 = 45/100, 2/5 = 40/100, and 0.04 = 4/100. Comparing hundredths gives 4/100 < 40/100 = 40/100 < 45/100, so the order is 0.04 m, then 0.4 m and 2/5 m together, then 0.45 m. On a number line from 0 to 0.5, 0.04 sits just past 0, 0.4 and 2/5 land on the same point four tenths along, and 0.45 stops just short of the 0.5 benchmark. The equivalent pair is 0.4 and 2/5. The key move is that no comparison is legal until both numbers are expressed in the same place value, which is why the benchmark 0.50 settles Mia's dispute instantly.
2. Diagnose Mia's claim that 0.45 > 0.5 and Diego's claim that 0.04 = 0.4. What single idea should the teacher reteach?
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Mia is reading the decimals as whole numbers: she compares the digits 45 and 5 and ignores that 0.5 means 5 tenths = 50 hundredths, while 0.45 means 45 hundredths. Since 45 < 50, we get 0.45 < 0.5. Diego deletes a zero without keeping its place: 0.04 = 4/100, but 0.4 = 4/10 = 40/100, so 0.4 is ten times as long as 0.04 - the zero after the decimal point holds the tenths place and cannot be dropped. Both errors share one root: treating decimal digits as whole numbers. The reteach is writing decimals as fractions over 100 and placing them on a number line before any comparison.
3. Priya wrote 0.3 + 0.47 = 0.50. Find the error, give the correct sum, and suggest a reasonableness check she could have used.
Read the worked answer
Priya added 3 and 47 as if both were hundredths. In fact 0.3 = 3 tenths = 30 hundredths, so the sum is 30/100 + 47/100 = 77/100 = 0.77 m. Her answer 0.50 is smaller than one of the addends, 0.47, which is impossible when adding a positive amount - a total must exceed each part. An estimate would have caught it: 0.3 + 0.47 is about 0.3 + 0.5 = 0.8, and 0.77 fits while 0.50 does not. The fix is a place-value chart with a tenths column and a hundredths column, or converting both numbers to fractions over 100 before adding.