Number Sense

Math Mondays

The National Council of Teachers of Mathematics (NCTM) defines Number Sense as "understanding numbers, ways of representing numbers, relationships among numbers, and number systems....understanding meanings of operations and how they relate to one another....to compute fluently and make reasonable estimates."

For early Elementary grades, students should learn and articulate how to break apart and put together numbers. What parts make that number? Here is a great video from Kindergarten Teacher Stephanie Latimer Quick Images: Visualizing Number Combinations found on the Teaching Channel. In this video, the teacher makes her own ten frame on a whiteboard and uses magnets which she can  easily change around on the ten frame. 

To practice subitizing or know the quantity without thinking, teachers can help students practice by showing the students a ten frame with a specific number of dots. They then ask the students, "How many did you see?" and "How did you see them?". Ask several students, give wait time, prompt students to articulate how they saw the amount shown...did they count each dot individually, count by twos, group dots...? Have students come up and show the class how they arrived at their answer. Wrap up by showing the ten frame and restating the the purpose. Have this be a daily five minute routine with three different cards each time. 

A fun game that helps to that build number sense for early Elementary students is "Two Fisted Pennies" where students practice solving addition problems with a missing addend.

• Choose a target number and count out that number of pennies together. 
• Player A hides some of the pennies in one hand and shows the other pennies in the other hand.
• Player B looks at the pennies showing and calls out how many pennies are hidden.

From the Mrs. Jump's class, here are some addition games to build number sense using manipulatives. Although this packet does have a monetary cost, reading through this site you can find lots of great ideas at no cost.

Math Coach's Corner Math games

From Math Coach's Corner, there is a free  I Have/Who Has and Ten-Frame Flash cards. 

Ten Flashing Fireflies Template/Book

Also found at her website are free templates for Making Ten: Ten Flashing Fireflies to go along with the book Ten Flashing Fireflies written by Philemon Sturgis.

Another great Math game is Top-it! There are several variations for this game: Number Top-it, Addition Top-it, Subtraction Top-it, Multiplication Top-it, 2-Digit Number Top-it, and Fraction Top-it.


For Number Top-it: Shuffle a deck of cards and place face down between the players. Each player turns over a card and reads it out loud. The player with the higher number must say, "Eight is more than three" or "Eight is greater than three" (if this terminology has been introduced). That player claims the cards for that round. If there is a tie, players can just flilp another card. (Note: Because students often struggle with the concept of Less, play the game the same way but the player with the smaller number wins.)

For Addition Top-it: Each player draws two numbers and says the equation out loud (i.e.: three and seven are ten). In order to claim the cards for that round, the player with the higher sum then must say, "10 is more than 6." (Don't forget to play the game with the version where the player with a smaller sum claims the cards.)


Thank you for visiting, Tricia

Lattice Math

Math Monday

Multiplication Strategies

There are several multiplication strategies: arrays, equal groups, repeated addition, skip counting, and fact families as viewed in the image on the right. As students progress to multiplying larger numbers with two, three digits or more, another method to use is Lattice Math. This method dates back to the 13th Century.

Let's multiply 216 X 32 using Lattice Math (also called Shabakh, Venetian Squares, Chinese Lattice) as seen in the image below.

Lattice Math method

For multiplying this three digit number by a two digit number using the Lattice algorithm: draw a box with a grid of  three vertical columns and two horizontal columns. Place the number 216 across the top of the box. Place the number 32 along the right side of the box.

Next, draw a vertical line from the bottom left corner to the top right corner of each box to divide the tens from the ones. This will split each box diagonally. As we multiply, the tens will go on top left of the vertical line while the ones will go in the bottom right side of each box.

Starting at the right side of the box, multiply 3 X 2 and place the six in the first box on the left under the 2. With the answer of 6 there is not a ten so place a zero in the upper left side and a six in the lower right side of the box. Continue to the next box to the right and place the answer for 3 X 1.

Continue until all the boxes are filled. The answer is seen in green and read along side the box beginning at the upper left.

216 X 32 = 6, 912.

From E-How Education, here is a video explanation for using  Lattice Math to solve 14 X 56:

For additional practice with multiplying two digit numbers, here is a free template from Teacher Vault:

For additional practice multiplying 3 digit numbers, here is free template from Math Worksheets 4 Kids:

For accommodating students who need additional support, use a multiplication table print out such as this one:

Multiplication Table printable

Thank you for visiting, Tricia

Skittles Math

Math Monday

Skittles...it's the rainbow that works well with graphing, creating patterns, estimating, and analyzing data in the early elementary grades as well as multiplying, dividing, and fractions for upper elementary grades.

For this K/1st grade Skittles Math lesson, give each student an individually wrapped mini-pack of Skittles candy. Worksheets may be found at Teach by Heart.

The lesson focuses on sorting, counting, and graphing and works with these Math Standards noted by Minnesota Department of Education:

Strand: Number and Operations
Standard: Understand the relationship between quantities and whole numbers up to 31 includes:

• K.1.1.2 Read, write, and represent whole numbers from 0 to at least 31. Representations may include numerals, pictures, real objects and picture graphs, spoken words, and manipulatives such as connecting cubes.  
• K.1.1.3 Count, with and withK.1.1.4 Find a number that is 1 more or 1 less than a given number.
• Understand the relationship between quantities and whole numbers up to 31. 
• K.1.1.5 Compare and order whole numbers, with and without objects, from 0 to 20.   out objects, forward and backward to at least 20.

Standard: Use objects and pictures to represent situations involving combining and separating.

• K.1.2.1 Use objects and draw pictures to find the sums and differences of numbers between 0 and 10.
• K.1.2.2 Compose and decompose numbers up to 10 with objects and pictures.   

Standard: Recognize, create, complete, and extend patterns.

• K.2.1.1 Identify, create, complete, and extend simple patterns using shape, color, size, number, sounds and movements. Patterns may be repeating, growing or shrinking such as ABB, ABB, ABB or ●,●●,●●●. 

The K/1st Skittles Math lesson asks students to estimate how many Skittles they have then count to see if their prediction was correct. They can make a color pattern. Next, using tallies they show how many of each color they have. Students then put the tallies in number form. They make a bar graph showing how many Skittles of each color they have. Next, the number concepts are reinforced by completing fill in the blank sentences. Most and least concepts are practiced as they note which color had the most or less Skittles. They check in with their classmates to find out which of their color Skittles they had the most of then chart the data. Rather than print out the worksheets, this work could be done in a Math Journal.

Dominoes! Pip, Pip, Hooray!

Welcome to Math Monday 

Most primary students love to work with dominoes! Their eyes light up as soon as the dominoes come out and they can't wait to get started.

Kindergartners, especially, are fascinated and love to count the dots. They will place dominoes end to end across the table to see how many it will take to stretch across the table. They will stack them and build with them. They may line-up just a few or many dominoes one after the other to watch them cascade down the path they so painstakingly set up. It can be an exercise in patience for many students.

Counting the dots on dominoes is a great beginning. Later add in some addition problems by counting the dots on one side of the domino then the other and add them together. For example, 5+1=__  and 5+5=___ . In this video from Mr. Stahl's Kindergarten class, the students are counting the dots or pips on dominoes while they play Domino Parking. An extension of this activity using a recording page will give students practice in creating and recording number sentences with the dominoes.

Mr. Stahl's Kindergarten Class

KinderDoodles offers a free Domino Parking Lot along with a recording sheet at their Teachers Pay Teachers website.

Over at First Grade School Box, Mrs. Berg shares a free template for a Domino Parking lot along with a recording sheet. This activity would be great as individual work or with teams of two students.

Domino Parking Lot Template

Domino Recording Sheet Template

Older students love to work with dominoes, too. There is just something about dominoes that intrigues. Adding, subtracting, multiplying, and working with fractions may all be done with dominoes. For fractions, look at a domino vertically with dots at the top and bottom rather than viewing from left to right. One domino may have a 1 at the top and a 5 at the bottom while another domino may have a 2 at the top and a 5 at the bottom for: 1/5 + 2/5 = 3/5.

One of my favorite blogs, Upper Elementary Snapshots has free for ten Math games working with dominoes. From basic to more challenging, games include even/odd sort, prime/composite sort, coordinating pairs, and ordering fractions.

From Upper Elementary Snapshots

For additional work with dominoes, students may build with and measure the times, learn about perimeters, area, depth, and volume. Here are some additional links for Math games using dominoes for the classroom.

What's more fun than playing, building, or working with dominoes? Watching videos with dominoes, of course! Here is a just for fun video featuring an Amazing Triple Spiral that took 25 hours to build and uses 15,000 dominoes. Can you come up with at least three math questions related to this domino spiral?

Thank you for visiting, Tricia

Growth Mindset and the Power of Yet!!!

WELCOME to Math Monday!

Growth mindset is a powerful tool using the power of "yet" enabling us to believe that we can achieve! 

The opposite of a growth mindset is a fixed mindset where one thinks they are just bad at something or that a subject such as math is just too difficult to learn. 

Bulletin Board from a Fourth Grade Classroom.

With a fixed mindset, you may give up rather than persevering with the belief that you can be successful, you just haven't learned it all yet!

In author Carol Dweck's Ted Talk "The Power of Yet", she discusses how the idea of "not yet....gives you a path to the future".

You can envision being successful with a growth mindset. We all develop beliefs about ourselves as learners. Believe that this is something we can do...always improve...comes from hard work. Effort is essential and it's the path to mastery.

Growth Mindset v Fixed Mindset.

Also, noted in Dweck's Ted Talk and on the website YouCubed, our brains respond significantly better to having a growth mindset with brain scans showing increased activity and growth.


Learning helps new neural pathways in our brains to form, strengthen, and make connections.






Learning as it relates to Math mentioned in YouCubed's Mindset Mathematics:

• "Mistakes, struggle and challenge are the most important times for brain growth."
• "Speed is unimportant in Mathematics."
• "Mathematics is a visual and beautiful subject, and our brains want to think visually about mathematics.

Student generated self-talk ideas on post-it's.

How do we help our students have a growth mindset in math? Visual reminders such as the bulletin board message pictured in this blog of "...Yet" found in a fourth grade class may help.

Self-talk is important as are the words teachers use when discussing progress with their students. If a student hears from their teacher, "Mistakes help us learn and everybody makes them." and "I believe you can learn Math!" then they will begin to internalize that message.

Student reflection on what they can do well and what they need to improve on adds to having a positive growth mindset.

Encourage students to learn and read about others who have experienced success having a growth mindset.
                               
Carol Dweck states that "We are born to learn!". The power of the growth mindset...the power of "yet" is exponential... the more we use it the more it works!

"The Power of Yet" Ted Talk by Carol S. Dweck

Here is a growth vs fixed mind set free digital download for early Elementary classes from Shannon McKay on the Teachers Pay Teachers website. Click on the words digital download to follow the link for this template.

                                       

Here is another free digital download for Elementary students from Teachers Pay Teachers website:

A nice selection of Children's books found on Pinterest featuring growth mindset. More details may be found at Melissa Taylor's blog: Inspiration Soup - Reading, Writing, Learning!

Thank you for visiting, Tricia