1 sind = 5.6 ricks and 1 sind = 12.88 dalts

2018 Handbook

2018 Test B Math · Question 55 of 57

Also in 2025 Practice Test B Math, question 55.

Question

1 sind = 5.6 ricks

1 sind = 12.88 dalts

Using the conversion above, how many dalts are equal to 1 rick?

A0.43
B2.30
C7.28
D18.48

Show the answer

Correct answer: B

Since 5.6 ricks and 12.88 dalts are both equal to 1 sind, then 5.6 ricks = 12.88 dalts.

To calculate the number of dalts (d) in 1 rick, set up a proportion:

$\frac{5.6}{12.88}=\frac{1}{d}$

$5.6d=12.88$

$d=2.3$

Question analysis

Two made-up conversion facts set 1 sind equal to 5.6 ricks and to 12.88 dalts, and students find how many dalts equal 1 rick. It tests unit conversion with invented units and decimal division. The risk is dividing in the wrong order, since both quotients look like reasonable answers.

NYS standards: 6.RP.3d converting measurement units
6.NS.3 multi-digit decimal operations
Grade level: Grade 6 content, by NYS standard
Compared with grade 7: At grade 7 Converting units with a given rate is grade 6 ratio reasoning. Invented units remove any real-world sense check and the division involves decimals, which matches the care typical grade 7 problems require.
Estimated difficulty: Moderate: several steps, or a close reading with one strong distractor.
Thinking it demands: Depth of knowledge 2, skills and concepts · mainly apply
What makes it hard: Error-prone arithmetic moderate
Solution: 2 steps
Reading level: Question and choices: about grade 3, 15 words.
Students, last 30 days: Not enough answers yet to show (it takes 10).

Why it is hard, traps and wrong answers (shows the answer)

Why it is hard

Because both amounts equal one sind, the problem reduces to 5.6 ricks = 12.88 dalts, but the made-up units remove any feel for which way to divide. The inverted ratio is the strongest pull, while the sum and the difference of the given numbers catch students who combine them without a plan. Checking that 5.6 × 2.3 returns 12.88 confirms the direction.

Error-prone arithmetic moderate Working it out
Dividing 12.88 by 5.6 means dividing by a decimal, best done as 128.8 ÷ 56 = 2.3, where a misplaced decimal point is easy. (Brown & Burton, 1978; Junker & Sijtsma, 2001)

Strategy: Since both amounts equal 1 sind, set the ricks equal to the dalts, then divide both sides by whichever number leaves exactly one rick on its side.

Traps

Wrong operation: Adds instead of multiplying, divides the wrong way round, turns a ratio or rate upside down, or undoes a step in the wrong direction (subtracts what should be added back).
Numbers taken from the question: Combines the numbers in the question without a model of the situation, or is simply a number that appears in the question.

The wrong answers, classified

A Wrong operation (Hegarty, Mayer & Monk, 1995; King et al., 2004)
Reveals partial knowledge Expected pull: strong
Divides 5.6 by 12.88, turning the rate upside down: 0.43 is the number of ricks in one dalt, not dalts in one rick.
C Numbers taken from the question (Hegarty, Mayer & Monk, 1995)
Reveals a surface strategy Expected pull: moderate
Subtracts the two given numbers, 12.88 − 5.6 = 7.28, as if the gap between them were the conversion rate.
D Numbers taken from the question (Hegarty, Mayer & Monk, 1995)
Reveals a surface strategy Expected pull: weak
Adds the two given numbers, 12.88 + 5.6 = 18.48, combining the conversion figures without a model of what they mean.

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Unit rate: $\text{amount for 1} = \text{total amount} \div \text{number of units}$; The total amount is what you have for several units. The number of units is how many of them there are. Dividing shares the total equally, so you get the amount for just one unit.

Sort out what you know
Sinds, ricks and dalts are made-up units. 1 sind is 5.6 ricks. 1 sind is also 12.88 dalts. You need the number of dalts in 1 rick.
Link ricks and dalts
Both 5.6 ricks and 12.88 dalts equal 1 sind. Two things equal to the same thing are equal to each other. So 5.6 ricks are the same amount as 12.88 dalts.
Set up the division
You want 1 rick, not 5.6 ricks. So share the 12.88 dalts among the 5.6 ricks. Use the unit rate formula.
$\text{amount for 1} = 12.88 \div 5.6$
Watch out: do not divide the other way. $5.6 \div 12.88$ is about 0.43. That is ricks in one dalt, choice A. Adding or subtracting the numbers gives D or C.
Do the division
Move the decimal point one place right in both numbers. This makes the number you divide by a whole number.
$12.88 \div 5.6 = 128.8 \div 56 = 2.3$
So 1 rick is 2.3 dalts.
Give the answer
One rick equals 2.3 dalts, written 2.30 in the choices. So the answer is B, 2.30.

Check your answer

Multiply back: $5.6 \times 2.3 = 12.88$ . That matches the dalts in 1 sind. Also, a sind holds more dalts than ricks, so a rick is bigger than a dalt. One rick must be more than 1 dalt. That rules out 0.43.

The original DOE question

Question 112 as printed on page 164 of the DOE handbook. — As printed in the DOE’s Specialized High Schools Student Handbook 2018–2019, page 164, question 112. Open page 164 of the handbook (PDF) The handbook letters this question’s choices E–H; here they are A–D (E = A, F = B, G = C, H = D).