symmetry – Early Math Counts https://earlymathcounts.org Laying the foundation for a lifetime of achievement Wed, 01 May 2024 01:50:07 +0000 en-US hourly 1 183791774 STEM Play With Pattern Blocks https://earlymathcounts.org/stem-play-with-pattern-blocks/ https://earlymathcounts.org/stem-play-with-pattern-blocks/#comments Wed, 01 May 2024 12:00:37 +0000 https://earlymathcounts.org/?p=155986   “Hey, that’s cool. I like your guy!” says four-year-old Jaheem, peering over Michelea’s shoulder as she plays with her pattern blocks. “It’s not a guy; it’s a flower!” Michelea replies, tilting her head to try to see the “guy” that Jaheem is referring to. “That’s the stem and the leaves,” she explains, pointing to […]]]>

 

“Hey, that’s cool. I like your guy!” says four-year-old Jaheem, peering over Michelea’s shoulder as she plays with her pattern blocks.

“It’s not a guy; it’s a flower!” Michelea replies, tilting her head to try to see the “guy” that Jaheem is referring to.

“That’s the stem and the leaves,” she explains, pointing to the green triangles. “And these blocks at the top are the flower.”

Then James weighs in, laughing as he sits down next to Michelea to join in the block play. “I thought it was a guy too—and you forgot to make the other leg!”

“Did you think these were arms?” Michelea asks, giggling. “They aren’t arms; they’re leaves!”

The friends continue to banter good-naturedly as they design with their pattern blocks. The beauty of block play is that it’s hands-on—which facilitates deeper learning and creates a more enjoyable and memorable experience.

We have many different types of blocks in our early childhood classroom, but the pattern blocks—introduced by the Education Development Center in the 1960s to help children develop the spatial reasoning skills they need to master math—have been a part of our play rotation for the past few weeks.

A set of pattern blocks typically consists of six different shapes in six different colors: a yellow hexagon, a red trapezoid, a green equilateral triangle, a blue rhombus, an orange square, and a tan or white thin rhombus. Except for the trapezoid, the lengths of the sides of each shape are the same, which makes it easy for children to fit the pieces together when creating pictures and designs.

Pattern-block play builds inventive and imaginative thinking. These blocks seem to unlock a particular kind of creativity that isn’t always evident in other forms of block play.  

This morning, Jaheem, Michelea and James seem to be creating stories with their pattern blocks while collaborating and mentoring each other in a relaxed and playful way.

“Look!  Michelea tells James, pointing at her latest pattern-block creation. “This is you walking your dog in the sunshine. It took me a long time because I had to figure out how to make the legs. I had them turned in the wrong direction!”

As children discover that they can rotate, flip and rearrange shapes in different ways, they become increasingly aware of two-dimensional shapes. Block play also promotes fine motor skill development as children manipulate the blocks to create their designs.

I watch as Jaheem, James and Michela learn how to measure heights, lengths and areas. Geometric shapes are a kindergarten common core standard, and when children engage in hands-on play with shapes, the learning becomes deeper, more intentional and more relevant.

Geometry is the area of mathematics that involves shape, size, position, direction, and movement. In early childhood education, geometric skills include identifying and comparing shapes, differentiating between shapes, and creating shapes.

The research backing up the importance of spatial skills in early learning is extensive and well-documented:

  • A 2009 Vanderbilt University review in the Journal of Educational Psychology looked at over 50 years of longitudinal research on spatial ability and concluded that “spatial ability plays a critical role in developing expertise in STEM.”
  • In its Learning to Think Spatially consensus study report, the National Research Council underscored the importance of spatial skills, stating that “underpinning success in both mathematics and science is the capacity to think spatially.”
  • A 2017 study from the University of Toronto looked at a spatial-skills intervention implemented in grades K-2. Students were presented with activities that targeted spatial skills, such as finding lines of symmetry, proportional reasoning (the number of tiles needed to fill a space), composition, and visualization. The study found that participating students showed improvement in spatial language, visual-spatial reasoning, 2D mental rotation, and symbolic number comparison.

During today’s pattern-block play session, the three preschoolers are actively exploring combinations of shapes in their constructive play. I watch as they discover that they can combine two squares to make a rectangle and investigate what happens when they turn a shape upside down. (It’s still the same shape even if it looks different!)

Research shows that young children’s spatial skills, rather than their numerical abilities, predict their overall mathematics achievement: The key skills are visualizing what shapes will look like when they are combined or rotated (Young et al., 2018). Working with shapes and spaces may provide a more accessible route to math proficiency for some children than focusing only on numbers.

Pattern-block play also promotes creativity and problem-solving—with no rules or guidelines to stop the flow. Children have the freedom to create their own designs and structures without having to worry about “getting it right.”

So dig out those pattern blocks and watch the spatial awareness blossom and the creativity flow!

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Geometry with Chalk Mosaics https://earlymathcounts.org/wheres-the-math-in-chalk-play/ https://earlymathcounts.org/wheres-the-math-in-chalk-play/#comments Fri, 01 Sep 2023 12:00:52 +0000 https://earlymathcounts.org/?p=155500 sidewalk chalk mosaic“Oh, I like your mosaic, Avery!” says Claire, who has wandered over to look at the mosaic that Avery has just created with sidewalk chalk and tape. “Yours only had triangles. We did squares and triangles and those long skinny squares.” “Oh, you mean rectangles! I want to see it!” Avery exclaims. He jumps up […]]]> sidewalk chalk mosaic


“Oh, I like your mosaic, Avery!” says Claire, who has wandered over to look at the mosaic that Avery has just created with sidewalk chalk and tape. “Yours only had triangles. We did squares and triangles and those long skinny squares.”

“Oh, you mean rectangles! I want to see it!” Avery exclaims. He jumps up to compare their creations.

Our days have been full of busy children drawing shapes and creating colorful chalk mosaics on the sidewalk. This activity offers many opportunities to work on shape recognition while extending the learning to the outdoor classroom.

Start by creating a shape on the sidewalk or a flat surface with masking tape. Divide the inside area into smaller shapes. If this is your first attempt at introducing chalk mosaics to your students, I would suggest beginning with a few small areas that measure about two feet by three feet, with smaller shapes inside.

Why start out small? The children can see results faster—and smaller is better for our youngest students, who haven’t yet developed the hand and wrist strength to color in larger shapes. On a more practical note, I’ve discovered that smaller shapes are better when the children are using smaller pieces of chalk.

You can always go bigger as the children get the hang of chalk mosaics. If you have an endless supply of wasabi tape, this easy-to-tear tape enables them to create their own shapes inside the larger shape. 

Leaving a basket of chalk nearby will invite the children to start coloring in the shapes. Once the children have completed the mosaic, simply remove the tape and admire the masterpiece! 

As your students learn to identify shapes, they can use spatial orientation vocabulary to describe the relative positions of the shapes. Preschoolers should understand and be able to use positional words such as above, below, beside, in front of, behind, next to, between, on, over, under and inside.

Shapes are the foundation of geometry. Geometry involves shape, size, position, direction and movement.

In early education, geometric skills include identifying and comparing shapes, differentiating between shapes and creating shapes.

Children need hands-on investigation to understand more than just naming or classifying shapes. Our chalk mosaics introduce children to simple shapes—as well as more advanced concepts such as symmetry, angles and fractions.

“My chalk is shrinking really fast!” giggles Rowan.

Oh, how I love shrinking chalk! Yes, we are definitely collecting data, making observations and noticing cause and effect.

But there’s more happening here than meets the eye. We know that the transition to smaller writing utensils helps promote the development of better gripping skills. As the children continue to draw and their pieces of sidewalk chalk get shorter and smaller, they are effectively transitioning to smaller writing tools and increasing their grip strength.

We try not to rush writing in our young learners. But when it happens spontaneously, we try to promote the use of smaller pieces of chalk, crayons or pencils to help them develop age-appropriate gripping skills.

These are all bonuses for kindergarten readiness—above and beyond the early math learning standards. This is the foundation that we talk about when we play our way into academic life. These small steps will enable our children to succeed when it’s time to sit at a desk. 

I have a few insights into the hidden benefits of chalk play—insights that can be shared with parents who may question the value of outdoor play and its role in advancing their children’s kindergarten readiness. Kindergarten, sadly,  involves a lot of sitting time. Children need strength throughout their bodies—including strong core muscles to sit all day. When children get down on their hands and knees and support their upper-body weight with their arms and hands, this strengthens their core muscles, as well as their shoulder muscles, which are so important for fine motor dexterity.

There’s a lot of math built into our chalk play. Follow the lead of your students, connect the curriculum to the play and you’ll meet your learning standards every day!

Looking for more ways to play with shapes? Extend the learning with these Early Math Counts shape lesson plans!

 

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Geometry With Robots! https://earlymathcounts.org/geometry-with-robots/ https://earlymathcounts.org/geometry-with-robots/#comments Mon, 01 May 2023 12:00:31 +0000 https://earlymathcounts.org/?p=155338

“I-am-a-robot!  I-can-do-anything!” squeaks Terrell in his best four-year-old robot voice.

“Oh, I like that you used that octagon for your robot’s head,” says Michaela. “I am going to try that!” 

We are deep into robot construction this month and robots are popping up all over our play spaces. We are constructing robots from clay. We have block robots. We have MagnaTile robots and button robots. What a great opportunity to work on shapes and spatial reasoning

When children play with shapes, they are building rudimentary skills that lay the foundation for later math learning, as well as reading and writing. Shape recognition and identification can help children understand signs and symbols. Children begin to notice shapes before they have the language to name those shapes. In the toddler and preschool years, children learn to name their first shapes: circles, squares, triangles and rectangles.

Shapes are the foundation of geometry. Children need hands-on investigation to understand more than just naming or classifying shapes. Our robot play acquaints children with simple shapes—as well as more advanced concepts such as symmetry, angles and fractions—as they engage in activities such as measuring, counting or investigating 2D and 3D shapes.

Geometry involves shape, size, position, direction and movement. In early education, geometric skills include identifying and comparing shapes, differentiating between shapes and creating shapes.

During our robot-building bonanza, the children are combining shapes in their constructive play. I watch as they learn that they can combine two squares to make a rectangle. They begin to see what happens when they turn a shape upside down. It is still the same shape even if it looks different. 

Research suggests that preschoolers’ early mathematics learning—including spatial-thinking skills—is related to later success in both reading and math. When children hear us use spatial terms to describe the size, shape and location of objects—and then adopt those words themselves—they perform better in activities requiring spatial skills.

Playing with blocks and puzzles and using spatial words such as above, below, across, on top of, inside and outside enables children to talk about where things are located. This strengthens their understanding of these concepts as they use the vocabulary words repeatedly throughout their play.

Geometric shapes are a kindergarten common core standard, and when children actually play with shapes, the learning becomes deeper, more intentional and more relevant. When children manipulate 3D shapes during hands-on play, they build a deeper understanding of these shapes.

Research has also shown that young children’s spatial skills—rather than their numerical abilities—predict their overall mathematics achievement. The key skill is visualizing what the shapes will look like when they are combined or rotated (Young et al., 2018). A focus on shapes and spaces may provide a more accessible route to math for some children, rather than focusing on numbers alone.

Spatial reasoning develops when children learn how to recognize relationships between 2D shapes and 3D shapes. How is a circle like a ball? How is a square like a box? As children discover that they can rotate, flip and rearrange shapes in different ways to change their possible shape and direction, they become increasingly aware of 2D shapes.

There is a lot of math built into our robot play. Follow the lead of your students, connect the curriculum to the play and you’ll meet your learning standards every day! 

Looking for more ways to play with shapes? Extend the learning with these Early Math Counts shape lesson plans

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Symmetry and Snowflakes https://earlymathcounts.org/symmetry-and-snowflakes/ https://earlymathcounts.org/symmetry-and-snowflakes/#comments Thu, 21 Jan 2016 12:02:16 +0000 http://www.mathathome.org/blog1/?p=3548 Do you remember the day you were told that each and every snowflake in the entire world is unique and that no two snowflakes are alike?  The idea of infinite possibilities still rattles my brain.  How can each of the billions and billions of snowflakes be unique?

Spatial awareness or concepts about space and shape, are pretty interesting to young children.  Snowflakes are one way to explore shape in an engaging and meaningful way, especially if you live in a part of the world that is filled with the cold, white stuff a good part of the year.  Also, as children begin working on their cutting-with-scissors skills, creating snowflakes is great way to practice.  Some kinds of paper are harder to cut than others but the easiest paper to cut is also the most likely to tear.  I like simple copy paper for snowflakes as it is sturdy enough to withstand some three-year old torture, but light enough to cut easily with children’s scissors.

Begin by folding the paper in half and then in half again.  018The difficulty in cutting increases with the number of folds, so fold the paper to meet each child’s individual developmental needs.  One fold reveals the least interesting patterns and more folds reveals more complicated designs.  Ask the children about the shapes they have created.  Show them that they can fold the paper back up and continue cutting, if they so choose.  The snowflakes will just become more interesting.

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If you want them to look more like snowflakes, and you think the children may enjoy it, you can begin with circular paper.  Again, fold at will, but the thicker the folded paper is, the more difficult it is to cut. 023 024

 

 

 

 

If you are working with older children, snowflakes are also a great place to discuss symmetry.  They provide concrete examples of “mirror images” that are easily (maybe not easily) seen. Notice how unique and distinct each of the children’s snowflakes are. No two are alike and that is what makes them special.

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Snowflakes and Symmetry https://earlymathcounts.org/january-means-snowflakes/ https://earlymathcounts.org/january-means-snowflakes/#respond Thu, 26 Feb 2015 12:00:59 +0000 http://www.mathathome.org/blog1/?p=1045 There is something fascinating about snowflakes.  I still don’t really believe that each one is different from all others.  Really?  All of the billions and billions of snowflakes out there and no two are the same?

Even the youngest children can make snowflakes out of white paper and a pair of scissors.  It is a great way for them to work on their fine motor skills and they can be fairly successful at making approximations of snowflakes.

Take thin white paper and fold it in half.  Fold it in half again.  Then let the children have at it.  You can show them how to make small cuts in the paper or larger cut-outs.  When the paper unfolds, the paper looks like a snowflake.

When the children unfold their snowflakes, you can help them identify the different shapes they have cut out.  You can also show them that there may be “symmetry” in their snowflakes.  Each side is a mirror image of the other.  This is a great “math” word that you can introduce when making your snowflakes.

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Spring Cleaning https://earlymathcounts.org/spring-cleaning/ https://earlymathcounts.org/spring-cleaning/#respond Fri, 24 Jan 2014 11:17:33 +0000 http://www.mathathome.org/blog1/?p=2373 I don’t know about you, but I am already thinking about the end of winter!  I love breaking out my winter boots in December but by mid-January, I am desperate to pack them away again.

This got me thinking about Spring Cleaning and the opportunity for children to help us sort and pack, as well as clean and organize. Young children have not decided that chores are a drudgery and should be avoided at all costs.  In fact, if presented in the right way, many young children will enjoy these activities as much as an other, as long as they are free to play within them.

Noah could sweep a room all day.  If we gave that boy a broom, a mop, a Swiffer, or a Dustbuster, he could keep himself busy for hours.  Larry and I would sit back and watch him clean.  It was like having our very own Roomba.   Unfortunately, that stage didn’t last as long as I would have liked.  I think that if we had participated with him rather than simply watching him, he would not have realized so quickly that we were using him as unpaid child labor.  Oh well.  He has made up for it in his teenage years by rarely lifting a finger to clean anything.

Spring cleaning means sorting through gloves and mittens, hats and scarves, boots and woolen socks.  Finding pairs is a great game for children.  Have them match up the items that look alike (by color or type) and then find the pairs within the groups.  It is more effective if you ask them to look for one attribute at a time since young children have trouble/cannot think about 2 aspects of a problem simultaneously.  First, have them separate the gloves from the mittens and then find the pairs.  Separate the white socks from the colored socks, and then find the pairs.  You can show the children that shoes, boots, mittens, and gloves are mirror images and even though they look almost the same, they are  not exactly the same.  This will give you an opportunity to talk about symmetry and how the human body is symmetrical, so the clothes that fit them must be as well.  Encourage the children to put a left glove on their right hand to see if it works, or the right shoe on the left foot.  This will reinforce the concept that they are the same but different because they will feel the difference.

This is what was left over at my house at the end of last winter.  Where did all of the matches go?  Another great unsolved mystery!

Gloves

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