Ideas for a math lesson

March 14 is International Mathematics Day (IDM). In 2021, a poster competition was also held. The central question was to create a poster that gives an idea of how we can make the world a little better, using mathematics as a universal language. This resulted in a collection of beautiful posters.

The maps we know are a projection of the earth onto a flat surface. The familiar projections distort the size of a country; Greenland is often depicted as much larger than it is in comparison to Africa, for example. There are maps that give a more accurate representation of countries. It may even be better to let children look at a globe to give them an idea of the real size of a country.

However, maps can also be drawn on other grounds. Max Roser redrew the continents and used the number of inhabitants as a measure of a country's size. This gives a different picture of Europe. Compare these two maps.

The Netherlands has suddenly become a lot bigger. Norway, Sweden, and Finland, which appear so large on the standard map, are suddenly a lot smaller than the Netherlands. In the map on the right, each country is made up of squares. What is the value of each square? How large should China, India, Indonesia, or Nigeria be depicted?

You can also let children draw their own maps. There are many ways to make a map. Let all the children, either alone or in groups, make a list of all the countries in Europe. From memory, of course. The point is to include every country they know. We can then color Europe according to how well known each country is. The most well-known country is dark green, and the least well-known country is very light green. The children have to decide for themselves how they will use shades of green.

Closer to home, you can have the classroom mapped in various ways. See here how this has been used. The children can color the map of the classroom from least busy to most busy, least messy to most messy, least distracting to most distracting, best place to worst place...

Or let the children try to make a map based on travel time by public transport, a so-called isochrone map. According to the travel planner, you can travel from Utrecht to Zwolle in 0:50 (or longer). From Utrecht to 't Harde, you travel in 1:01. On this map, 't Harde is therefore further from Utrecht than Zwolle. From Utrecht to Zaandam Kogerveld takes 1:00. Zaandam Kogerveld and 't Harde are therefore equally distant from Utrecht on this map (on the same circle). You could take a series of places around your school and have the children create a travel time map of their surroundings.

The SASMO is an international math competition organized by a group in Singapore. Many of the problems are more like puzzles than mathematical research. These are problems that can be fun to present to the class every now and then and let the children puzzle over. Focus more on reasoning than on arithmetic with these questions. For example

Look at the following series of additions

11+12+13+14+15+16+17+18+19+20=155

21+22+23+24+25+26+27+28+29+30=255

31+32+33+34+35+36+37+38+39+40=355

41+42+43+44+45+46+47+48+49+50=455

51+52+53+54+55+56+57+58+59+60=555

What is the sum of the numbers 101 to 110?

Or, for example, this puzzle: what should be in place of the question mark?

6	8	11
12	15	19
8	?	15

In the SASMO test, they also give four possible answers (9, 12, 11, 13). I don't know if I would include those.

The idea behind this question is not immediately obvious. It requires seeing a pattern in the differences between the numbers.

	2		3
6	→	8	→	11
	3		4
12	→	15	→	19
	□		□+1
8	→	?	→	15

Now you need to look at the jumps in the bottom row.

Converting measurements

Cooking involves recipes and measurements. Some recipes call for grams and ml, others for teaspoons or tablespoons. What exactly is what? It can be quite difficult to determine exactly how much you need. 1 teaspoon (tsp) is 5 ml and 1 tablespoon (tbsp) is 15 ml. So 3 teaspoons is 1 tablespoon. But not everything weighs the same. Roughly speaking, 1 tablespoon of salt is about 10 grams and 1 tablespoon of rice is around 12.5 grams. Cooking becomes even more complicated when you look at an American recipe. Suddenly, it's all about cups, pounds (lb), ounces (oz), quarts, and pints. It's enough to drive you crazy. That's why many people don't use spoons but measuring spoons and measuring cups. Then you can be sure you're doing it right. It's a shame because it involves a lot of ratio calculations.

This table shows that it's not easy for Americans either. It also shows that creating such a chart can be a nice challenge for students.

oz.	tbsp.	cups	pints	quarts	gallons
1 oz.	2	⅛	-	-	-
8 oz.	16	1	½	-	-
16 oz.	32			½	-
		4			¼
			4	2
		16	8		1

The table is only half filled in. Can you fill it in completely?

We can also create a table like this for well-known Dutch measurements. For example, the number of grams that certain products weigh. For ease of calculation, I have included cups and fractions of cups in the table.

Ingredient (g)	1 cup	¾ cup	⅓ cup	1 tablespoon	1 teaspoon
Sugar			64		4
Butter	240		80
Salt				18	6
Flour	144			9	3
Raisins		120		10
Mayonnaise	224			14

Posters about recipes

The IDM 2021 also produced some beautiful posters about cooking and mathematics. On their website, you can also view other posters and read about who the creators are and what they thought about the poster.

Baking cake

Take a look at Baking cakes is mathematics.

Folding a cube and more math crafts .