4 - 11 years

The 7 conservation activities that can help your child with math and more

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Picture two 4-year-olds, both with a cookie of the same size. One child’s cookie has been cut in half, while the other’s is whole. Depending on where the children are developmentally (and their personalities), the one with the whole cookie may point out that the other child has “more.” Children at this age are learning how to “conserve,” and may truly believe that the child with two cookie pieces has more—even when the two cookies are halves of the same whole.

Conservation, in child development, is a logical thinking ability first studied by Swiss psychologist Jean Piaget. In short, being able to conserve means knowing that a quantity doesn’t change if it’s been altered (by being stretched, cut, elongated, spread out, shrunk, poured, etc). There are seven Piagetian tasks, generally tend to be acquired in this order: number (usually acquired by age 6), length, liquid, mass, area, weight, and volume (usually acquired by age 10).

Interestingly, research shows that children who practice conservation do tend to learn it more quickly, and children who conserve perform better at certain mathematical tasks. The lesson here is: find opportunities to practice conservation when they come up in everyday life, like cutting food into smaller pieces and pointing out that doing so doesn’t actually change the amount.

*Note: to get the most authentic results possible, don’t do these all in a row on the same child at the same time. The child may get restless and tired of the tasks, and they also start to anticipate which answers you are “hoping” to get—children are really clever that way! Spread the tasks out over days and/or between different children to get the most accurate answers.

Here are Piaget’s 7 conservation tasks in the order most typically mastered:

Task 1: Number

In this task, children are asked to compare rows of small objects. Find 10 small uniform objects like coins, beads, or counters (like poker chips), and make two identical rows of 5 coins, close together and with the coins aligned in parallel like this:

🔵  🔵  🔵  🔵  🔵

🔵  🔵  🔵  🔵  🔵

Put them in front of the child and ask if both rows have the same amount of counters in them. The child may simply respond, or they may count; in either case, mostly likely they will say that yes, both rows are the same. Agree with them. Then, with the child watching, spread out one row while keeping the other the same, like this:

             🔵  🔵  🔵  🔵  🔵

🔵        🔵        🔵        🔵        🔵

Now ask the child if one row has more counters than the other, pointing clearly to indicate what you mean by “row.” If your child has mastered conservation of number, they’ll say both rows still have the same amount; if they haven’t, they’ll say the elongated line has more counters.

You can also keep this task going by first returning the second row to its original, aligned form—and agreeing with your child that both rows have the same amount—and then “shrinking” the second row like this:

🔵  🔵  🔵  🔵  🔵

    🔵🔵🔵🔵🔵

Again, ask if one row has more counters than the other. A child who has not yet mastered conservation will likely say the top row has more, compared to the “shrunken” row—even though they watched you do it and previously agreed they’re equal. 

Task 2: Length 

In this task, children are asked to compare the length of two identical objects. Pick two long, stick-like items that are (ideally) exactly the same in length, width, color, thickness, and other properties so you can control for the variable of length. Two chopsticks are perfect, but pens or pencils can also work. Line them up in front of the child like this:

_______________________________

_______________________________

Then ask—while pointing very clearly—“is this stick longer, is this stick longer, or are they the same?” and wait for the child’s response. If they tell you one of them is longer, ask why they think so. If they say they’re the same—the more likely answer—agree and move on. Slide one stick over so they look like this:

                         _______________________________

_______________________________

And ask the same question as before. If the child has mastered conservation of length, they’ll be able to say that the sticks are still the same length. Ask them how they know! If they haven’t, they are likely to say that the one you moved is now longer. 

Always be sure to ask clarifying questions each step of the way—you’ll learn so much about the way children process information when they’re able to explain their thinking.

Task 3: Liquid

This is the most famous of all of Piaget’s tasks, the most recognizable, and in many ways the most understandable. When children get older, they learn in science class that a key property of liquid is that it changes shapes according to the container it’s in, sometimes making it appear as though there’s now more or less of it—and in this task, that property can be really, really convincing 😉.

Place two large, empty glasses in front of the child doing the task. Have ready a taller, narrower glass (keep that one out of view when you start), and a pitcher of water (with some food coloring in it), juice, milk, or any liquid that’s not completely transparent. With the child watching, fill one glass about half full. Then, tell them you’re going to slowly fill the second glass, and it’s their job to tell you when the two glasses are equally full.

If the child isn’t ready or able to do that, make sure you fill the second glass to the same level as the first. Agree with the child that both glasses have the same amount of water in them; if it helps, line them up right next to each other to show.

Then, put the taller, narrower glass on the table and say “now, watch what I do.” Make sure they’re watching as you take either glass and pour it into the new one. The water level will be much higher. Ask, while pointing, “does this glass have more water, does this glass have more water, or are they the same?”

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A child who has mastered conservation of liquid will know that the amount of liquid—the volume—hasn’t changed. If the child points to the taller glass, ask why they think it has more water. As with all conservation tasks, feel free to explain the truth! These tasks can be an important part of the learning process; you can pour the water back into the first cup to show the amount never changed, even if the child isn’t developmentally ready to understand why yet.

Task 4: Mass/Matter

In this task, you’re looking to see if a child recognizes that an object still has the same mass (sometimes referred to as “stuff,” a non-scientific way for kids to start to grasp a scientific concept). Get two balls of clay or play-dough (anything easily moldable into the shape of a ball), and place them in front of the child. Ask, while pointing, “does this ball have more clay, does this ball have more clay, or are they the same?”

If the child is a perfectionist, they may point out that one is a little bigger 😉. Work with them to ensure both are the same, according to them. 

Here, you have a choice. With the child watching, either flatten one piece of clay as much as you can (ending up with a wide, flat disc), or work it between your hands to end up with a long, thin, snake-like object. Place it back next to the ball and ask, while pointing, “does this have more clay, does this have more clay, or do they have the same amount?”

Source

This task can lead to a fascinating variety of answers. Some kids will see the wideness of the flattened/stretched clay and say its bigger, others may see the height of the untouched ball and say it’s bigger. Whichever answer you get—or another one altogether—always ask for their reasoning: they may surprise you with their logic.

Task 5: Area

This task requires a little more prep than others. Get some green paper, and cut 12 equal small squares out. For contrast, use two pieces of black paper as a background. If you have two cow figurines, use those; otherwise, drawings or pictures of cows can work.

Set your squares up identically to begin with, in neat 2×3 rows with the squares all touching. Explain that the green squares are grass for the hungry cows to eat, and ask if both cows have the same amount of grass to munch on. Agree that they have the same.

Then, spread the green squares out for one cow, so that they aren’t touching anymore. Now ask, while pointing to each cow’s grazing pasture, “does this cow have more grass to eat, does this cow have more grass, or do they both have the same amount?”

Source

As with mass, the results can differ. Some children see the spread out squares and they look like less, but for some it looks like much more. Children who don’t have conservation of area will not recognize that you haven’t actually changed the amount of “grass,” you’ve simply spread it around.

Task 6: Weight

In this task, you’ll need a balance scale—the kind that has surfaces or containers on both sides that rise and fall with differences in weight. This task can be paired with the conservation of mass/matter, as they both use the same clay or play-dough.

Take two balls of play-dough, ensuring ahead of time that they’re big enough to affect the scale and make it tip one way or another. Place one on each side of the scale, showing that they weigh the same amount. Then, take the balls off the scale and squish one as flat as you can make it.

Without placing the ball and the disc back on the scale, ask if the two pieces will weigh the same—if the scale will balance—or if one will weigh more than the other. As always, ask for their rationale. After their answer, place the clay back on the scale (or invite your child to) to show that the weight and balance haven’t actually changed.

Task 7: volume (aka liquid displacement)

In this task, typically mastered last—generally between age 9 and 11—children are asked to compare the rising liquid level caused by adding  solid objects to two glasses filled with water. Start with two clear glasses with the exact same amount of water in each one (nearly full; leave at least an inch on the top), and two identical balls of clay or play-dough. Make sure the balls are big enough to cause a noticeable change in water level when dropped into the glasses.

Ask: “when I drop these two balls of clay into the glasses, will the water levels rise the same amount, or will one glass be more full than the other?” They will likely answer that both glasses will rise to the same level. You can mark that level with a dry-erase marker to make it clear.

Then, remove one ball of clay from one glass, smush it completely flat, and ask: “when I drop this in, will the water level match the other glass, or will it be higher or lower?” Kids who haven’t mastered conservation will look at the flatness of the ball and predict that the water level won’t rise as much. If they have (or if they’re catching onto your tasks!), they will correctly state that the level will now match the other glass.

Drop the flattened clay into the water, showing that it comes back to the line you drew. One of the wonderful aspects of doing conservation tasks with children is that it can serve as a teaching tool: the more you do them, the more likely they are to understand that objects don’t change their quantity when they are stretched, cut, elongated, spread out, shrunk, poured, etc.

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Posted in: 4 - 11 years, Fine Motor, Math, Playtime & Activities, Cognitive Development, Child Development

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