Dice Sum Probability

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We have been working on building automaticity with our math facts through a variety of practice modes: chants, games, noticing patterns and strategies, etc.  Today, we shook things up (literally!) and blended our fact practice with an investigation into probability.

Students partnered with each other to conduct the investigation.  First, partner A was the roller and partner B was the recorder.  Partner A rolled two dice and reported the outcome. The students worked together to find the sum, and partner B recorded the sum on a graph.  Once any of the sums had been rolled ten times, partners traded roles.

We met together as a class and recorded which sums each partnership rolled most often. We discovered that most groups rolled a 6, 7, or 8 most often – but not always!  Then, I proposed the idea that we could play a new game: if a 7 is rolled, I win.  If a 2 or a 12 is rolled, the class wins.  Is it fair?  At first, some students thought they would have the advantage because there are sums that would cause them to win, and I only had one.  Then, they noticed that nobody had rolled a 2 or a 12 as their most common sum, but lots of groups rolled 7s most!  They decided it wouldn’t be a fair game because I would be more likely to win after all.

Soon, we will revisit dice roll sums and discover exactly why this occurred! Can you figure it out?

Inch by Inch

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We have begun working on our measurement skills in first grade.  We began by experimenting with nonstandard units including digits (finger widths), hand spans, paces, and more. We discovered that even if we measured the same object, we came out with different measurements.  The class discussed various reasons we may have found different measurements: We have different sized bodies, some people may have left spaces between units or overlapped units, or we may have measured a different part of the object.

Next, we used paper cut-outs of our own feet and a standard foot to compare some lengths and distances.  We learned that when we used our shorter personal feet, we needed to use more of them to cover the same distance.  We also discovered that we were more likely to agree on measurements when we used the standard foot.

Today, we were introduced to the inch.  First, we explored measuring using inch cubes. We learned that there are 12 inches in one foot and that inches help us get more precise measurements, especially of smaller objects or distances.  Students practiced finding the inch edge of their ruler before lining up the end of various objects with the 0-mark.

Next, we will continue exploring using tape measures!

Polygons

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We have been practicing our geometry skills this week in math.  In first grade, much of our geometry work involves not only identifying shapes, but comparing them, categorizing them, and defining them.

Attribute blocks

The students were introduced to a new manipulative: attribute blocks.  These blocks are similar to the pattern blocks with which you may be familiar, but they have subtle differences.  Attribute blocks are various shapes and come in different colors and sizes.  We use attribute blocks to practice identifying attributes!

First, we defined the word “attribute” and gave a few examples.  For example, one attribute that several of our students share is brown hair.  We applied this new vocabulary to our attribute blocks by noticing their shape, size, and color. To practice, we played the Attribute Train Game.  Here’s how to play:

  1. The first player takes a block and puts it down to start a train.
  2. The second player chooses a block that is different in only one way – in shape, size, or color – from the first block.  The second player adds that block to the train.
  3. Players continue taking turns until no more blocks can be played.

An attribute train game in progress

As students placed their blocks, they practiced identifying what was the same and what was different about their block choice.

Next, we used pattern blocks to practice identifying some standard shapes: triangles, squares, trapezoids, rhombuses, and hexagons.  We learned to identify their defining attributes by starting sentences with “All squares have….” for example.  We learned that all of our pattern block shapes belong to a group with a special name: polygons!

Ask your child to give you some examples of polygons along with some examples of shapes that are not polygons.

Today, we got creative and constructed polygons using pipe cleaners and 3 lengths of straws.

A student with her hexagon

Students constructed both regular and irregular polygons.  They had a wonderful time figuring out what the name of their shape would be depending on how many sides it had.  Several dodecagons (and beyond!) were created!

A student with his irregular decagon

A student with her irregular nonagon

A student with his regular pentagon

A student with his irregular pentagon

A student with her rhombus

Finally, students combined pattern blocks and some circle blocks to create composite shapes.  They discovered that not all of their composite shapes fit the definition of a polygon, but some composite shapes did resemble familiar shapes we’ve seen.

Tracing a composite shape made out of three triangles

Discovering a hexagon made out of three rhombuses

Next week, we will be investigating the characteristics of some 3D shapes and learning the vocabulary associated with them.

Patterning Practice

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Today we began our third math unit with an introduction to patterns.  The students practiced repeating our patterning mantra: “The important thing about patterns is that they repeat!”

We spent some time on a pattern hunt around our classroom.  The students found patterns on the covers of books, on bulletin board borders, on posters, and on the American flag!

We played a game with partners where one partner created a pattern using craft sticks, and the other partner continued the pattern.  The students got creative with the orientation of the sticks, even stacking them to add to their designs.

  

After our game, we practiced in our workbooks to digest our learning.