These are story problems, and they can all be solved with algebra. My students did not know algebra, but they could still solve these problems. For them, these problems built the basic skills of algrebra without actually talking about variables.
Preliminary Problems
These problems build the basic skill of simply understanding the problem. (If you will, to get them thinking "in the box".) So these are just arithmetic, but it is the arithmetic that will be required in the actual Loox problems.
A box contains 6 ants and 2 dogs. How many legs are in the box? How many heads are in the box?
A box contains 4 boys and 3 spiders. How many legs are in the box? How many heads?
A box contains a centipede and 4 tripods. How many legs are in the box?
Another type of Preliminary Problem (or Advanced Problem)
A box contains 10 legs. How many ants and dogs are in the box?
A box contains 116 legs. How many centipedes and spiders are in the box?
Loox Problems
A box contains 3 ants, 4 giraffes, and one loox. There are 39 legs in the box. How many legs does a loox have?
A box contains 3 cats, 4 dogs, and one loox. There are 17 eyes in the box. How many eyes does a loox have?
A box contains 4 giraffes and 3 looxes. There are 17 ears in the box. How many ears does each loox have?
A box contains 3 giraffes, 4 dogs, and 5 looxes. There are 22 noses in the box. How many noses does each loox have?
Bigger Numbers
A box contains 4 toads and 2 looxes. Each toad has 17 warts. There are 90 warts in the box. How many warts does each loox have?
The box contains 56 warts. What is in the box?
The box contains 67 warts. What is in the box?
The box contains 95 warts. What is in the box?
Easy Problems (for young children)
The box contains 2 girls and a giraffe. How many legs does it contain?
The box contains 1 girl and 1 woompa. There are 5 legs in the box. How many legs does a woompa have?
The box contains 2 girls and 1 woompa. There are 4 noses in the box. How many noses does a woompa have?
The box contains 1 girl and 2 woompas. There are 3 heads in the box. How many heads does each woompa have?
The box contains 1 girl and 2 woompas. There are 4 arms in the box. How many arms does each woompa have?
The box contains 2 girls and 1 woompa. There are 5 eyes in the box. How many eyes does a woompa have?
More Problems
The anaik is a backwards animal found in the jungles of sanso.
A box contains 3 ants, 2 dogs, and an anaik. There are 33 legs in the box. How many legs does an anaik have?
A box contains 12 giraffes and 4 anaiks. There are 20 necks in the box. How many necks does each anaik have?
A box contains 5 dogs and 3 anaiks. There are 19 ears in the box. How many ears does each anaik have?
A box contains 17 dogs, and 10 anaiks. There are 47 noses in the box. How many noses does each anaik have?
A box contains 17 dogs and 173 anaiks. There are no arms in the box. How many arms does each anaik have?
Two-Box Problems
One box contains a dog and a rangabooga. The second box contains 2 dogs and a rangabooga. Which box has more noses?
Box 1 contains 2 dogs. Box 2 contains 2 dogs and a rangabooga. Box 2 has 4 more eyes than Box 1. Do you know how many eyes the rangabooga has?
Box 1 contains 2 dogs. Box 2 contains 2 dogs and 2 rangaboogas. Box 2 has 6 more heads than Box 1. Do you know how many heads the rangabooga has?
Box 1 contains 3 dogs. Box 2 contains 3 dogs and 3 rangaboogas. Box 2 has 6 more arms than Box 1. Do you know how many arms the rangabooga has?
Box 1 contains 1 rangabooga. Box 2 contains 2 rangaboogas. Box 2 has 5 more ears than Box 1. Do you know how many ears the rangabooga has?
Box 1 contains 1 dog and 1 rangabooga. Box 2 contains 2 dogs and 2 rangaboogas. Box 2 has 3 more tongues than Box 1. Do you know how many tongues the rangabooga has?
Box 1 contains 1 dog and 1 rangabooga. Box 2 contains 2 dogs and 3 rangaboogas. Box 2 has 9 more brains than Box 1. Do you know how many brains the rangabooga has?
More Loox Problems for the Beginner: Going Slower
A box contains 3 girls and a shlee. The box has 10 arms in it. How many arms does a shlee have?
A box contains 2 girls, 3 boys, and a shlee. The box has 7 noses in it. How many noses does a shlee have?
A box contains 4 girls, 5 boys, and 2 shlees. There are 24 ears in the box. How many girl ears are there? How many boy ears are there? How many shlee ears are there? How many ears does a shlee have?
A box contains 3 trees, 2 elephants, and a shlee. The box has 5 trunks in it. How many trunks does a shlee have?
A box contains 4 boys, 3 girls, and 3 shlees. It has 23 legs. How many legs does a shlee have.
And Even Easier
At a party, I asked a kindergartner to give me two numbers that added up to three. She suggested 2 and 23. It seemed like a bad strategy to criticize her on our first interaction, so I let it pass and thought up the easiest loox problem that I could: There is a dog in a box. How many legs are in the box?
She again tried the answer 2 and 23. I couldn't let that pass. I scrunched up my face like I was very puzzled, and asked in a kind of puzzled skepticism, "There would be 23 legs in the box?" Wait, she wanted to change her answer, to 2 + 2. That's an odd format, but exactly right. High five!
Two Equations with Two Unknowns
Now there are two types of animals and two boxes. This corresponds to solving an algebra problem with two equations and two unknowns. I have not yet used these problems, and there is a steep gradient from easiest to hardest with some holes in it.
This problem is the same as the simplest of the two-box problems above, except that a known animal is replaced by an unknown animal. This is a conceptual leap, though of course students will differ in how much it is a leap for them. Their problem is that you can't subtract (say) two from both sides, you have to subtract an unknown number.
One box contains 2 brombos. There are 98 legs in this box. Another box contains 2 brombos and a wichitwas. There are 99 legs in this second box. How many legs does a wishitwas have?
One box contains 16 brombos. There are 256 arms in this box. Another box contains 16 brombos and a wichitwas. There are 259 arms in this second box. How many arms does a wishitwas have?
One box contains 2 brombos and a wishitwas. There are 9 ears in this box. Another box contains 2 brombos and 2 wichitwases. There are 14 ears in this second box. How many ears does a wichitwas have? How many ears does a brombo have?
One box contains 2 brombos and a wishitwas. There are 12 noses in this box. Another box contains 2 brombos, 1 wishitwas, and a shlee. There are 14 noses in this second box. How many noses does a shlee have?
One box contains a fribjigger and a frumpsungle. It contains 7 ears. A second box contains 2 fribjiggers and 3 frumpsungles. It contains 19 ears. How many ears does a frumpsungle have?
One box contains 2 brombos and a shlee. There are 16 legs in the box. Another box contains 2 brombos and 2 shlees. There are 20 legs in this second box.
How many legs does a shlee have?
If so, how many legs does a brombo have?
