This week your child works with inequalities in two variables — questions
whose answer is not a number but a whole region of possibilities. It is a real shift.
Up to now, solving meant finding the answer. Here, listing five answers is not
finishing; there are always more. Ten minutes with a household budget makes that concrete.
The activity — ten minutes, one sitting
What you need: paper, a pencil, and two things you actually buy — say eggs and pandesal —
with their prices.
Set a budget out loud: “We have one hundred pesos. Eggs are ten
each, pandesal is five each. What can we buy?”
Let them give one answer. Write it down. Then ask for another. And another.
“Give me one more.” Keep going until they notice they
could go on.
That noticing is the lesson. The answer is not a list — it is
everything the list is part of.
Ask “Can we spend less than a hundred?” Yes. So the
answers are not just the ones that spend exactly a hundred.
Draw two lines on the paper, one across and one up, and mark a few of their answers as dots.
They will see the answers filling a corner rather than sitting on a line.
Last question: “Is buying ten eggs and nothing else allowed?”
Exactly a hundred. Whether the edge counts is the difference between
at most and under — and at school, between a solid line and a broken one.
Three things to avoid
Do not accept a list of answers as the answer. Ask for one more, then one more. The
point lands quickly and it lands better than being told.
Do not teach “greater than means shade above”. It is a rule that fails,
and this week is partly about watching it fail. Test a point instead.
Do not treat the edge as decoration. Whether an answer that lands exactly on the
limit counts is a real question with a real consequence — and it is what the solid and
broken lines in their book are recording.
How to tell it is working
Asked for a solution, they ask which one — they have understood there are many.
They check an answer by trying it, rather than by looking at the sign.
They notice on their own whether the boundary itself is included.
If they are stuck, drop to one item. Just eggs, one hundred pesos, ten pesos
each. How many can we buy? Any number up to ten — already a range rather than a single
answer. Add the second item only once that feels ordinary.