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Prime Climb Round 5

Highlights:

  • Prime Climb Continues!

  • A Challenge for Older Students

If you do not remember what Prime Climb is or you are a new subscriber or viewer then please go back and read the blogs:

  • Prime Climb Round 1: here
  • Prime Climb Round 2: here
  • Prime Climb Round 3: here
  • Prime Climb Round 4: here

These are lessons inspired by Dan Finkel - Math for Love

I was first introduced to Dan Finkel and Prime Climb at a staff meeting one year ago through the video Five Principles of Extraordinary Math Teaching:

I was very curious what my grade three students could tell me about the color circles because through our daily math routine we learn skip counting, factors, multiples and divisibility connected to our school day number.

Here are the colored circles I put up for my Grade 3 students to explore.

My students engaged in this activity about 6 times within a 6 month period and I wrote 4 blogs to share the learning connected to the exploration time. If you haven’t read my blogs, see the links at the top of this post.

Many of my students found the first round quite challenging. There was definitely a productive struggle, but NOBODY was frustrated! When I put up the colored circles for round 2 many cheered and commented how much fun they were having. Our goal was to color in numbers up to 50 by the end of June, however, time ran out. I can tell you they were very disappointed!

The intent of this blog post is to share the learning of  Grade 4, 5 and 6 students who I’ve engaged in Prime Climb through recent subbing experiences.  I am fortunate that teachers who I sub for give me the freedom to plan the math.

Prior to subbing in a Grade 4 classroom I was told the focus of their learning was multiplication and division so without hesitation, I chose Prime Climb. For students to be efficient with these operations they need to have a conceptual understanding of factors, multiples and divisibility of numbers.

I put the colored circles up 1 to 20 and asked the students to look carefully at the circles, numbers and colors.

Here is what the students shared:

  • All even numbers are orange
  • Some circles are fractions-half, thirds

I did ask why certain circles were shared as fractions but they weren’t able to explain and that is okay. This would be something they would need to make the connections to through further exploration.

  • 7 and 14 are purple cause you can count by 7 to get to 14 and 14 is also orange because it is even
  • 5 is blue and 15 is ½ blue and ½ green because 3 x 5 = 15
  • 3, 6, 9, 12, 15, 18 all have green because you are counting by 3
  • Numbers you can count by 5 have blue
  • If you double each number 2 to 9 those numbers have the same colors. Eg. double 2 is 4 so the circle with 4 also has orange, if you double 6 it is 12 so 12 has green, etc
  • 11, 13, 15, 17 are red because there are not any numbers (2, 3, 4, 5, 6, 7, 8 or 9) you can count by to get to them
  • Numbers you can count by 6 to are also green because you can count by 3

I didn’t ask but I should have asked if all numbers divisible by 6 can be counted to by 3? This would have been a great opportunity to see if a conjecture could have been formulated.

I asked why 1 would be gray and nobody was able to explain this to me.

After this discussion, I provided each student with the new blank color circle chart that Dan Finkel has provided which is awesome!

Prime Climb Color Chart

I left the sheets and an explanation of the activity for the teacher hoping she will learn more about Prime Climb for the benefit of students to move into a ‘deep’ phase learning.

Further opportunity for exploration would enhance their learning and understanding of multiplication and division as well as benefit the understanding of fractions.

A few days later, I taught in a Gr. 5 / 6 class as well as a Grade 5 class. Here is their thinking:

  • The colors are based on multiples. Multiples of 2 are orange, multiples of 3 are green, multiples of 5 are blue, multiples of 7 are purple
  • 12 is both orange and green because 2 x 6 = 12, 12 is also green because it is divisible by 3
  • 12 is shared into thirds because 4 has two orange parts and 3 is one whole green and 3 x 4 = 12
  • 7 is full purple but 14 is half purple and half orange because 2 x 7 = 14
  • Multiples of 10 have blue and orange because they are divisible by 2 and 5
  • 5 x 3 = 15 so 15 is both blue and green
  • 1 is clear (white, gray) and all circles have some white because you can count by 1 to all numbers
  • 2 is full orange, double 2 is 4 so circle has two parts, double 4 is 8 and 8 has 3 parts and double 8 is 16 and 16 has 4 parts. So as you double the number the circle has one more part. It goes whole, ½, ⅓, ¼.
  • Red are prime numbers
  • 10 has two parts cause 5 and 2 are factors and 20 has 3 parts (2 orange and 1 blue) because the two orange represent 4 and the one blue represents 5 and 5 x 4 = 20

Some very interesting thinking was happening. A productive struggle was going on which I think is critical and awesome. A few of the Grade 5 students were asking for ‘answers’ but my reply was, “with further exploration time you will come up with the answers (and conjectures) yourself.”

The educational assistant in the classroom asked the students if there was any pattern or reason for how the circle was colored. For example, if the top half was orange and the bottom half blue could these colors be reversed? Something to ponder.

The teachers of the two classes are going to continue this exploration and purchase the game so I am excited to hear (and hopefully get to see) how the learning grows.

Below you will find a few pictures of the students’ work. I found it interesting how many of the upper elementary students chose to color the numbers out of sequence whereas my Grade 3 students worked in sequence.

The pictures demonstrate the students' recognition of patterns (eg. all even numbers needed orange, all numbers divisible by 5 needed blue). As students were coloring I was moving around the class asking questions to see if any conjectures were being formulated. I didn’t hear any, but deep thinking was happening and I believe if these students are provided further opportunity to explore and continue to color in the chart conjectures will come.

One of the grade 6 boys said to his partner, "Let’s color all numbers divisible by 11 red because 11 is red."

I was thrilled to hear the response of his partner, “No, we can’t do that because 22, 44, 66, 88 are even numbers and 55 is divisible by 5."

Through my classroom experiences, Prime Climb engages students and allows them the opportunity to explore. The learning that emerges is deep, meaningful and rich which is of benefit to understanding number. In turn, this deeper understanding of number will strengthen their conceptual understanding of skip counting, multiples, factors, divisibility, and the operations of whole numbers as well as fractional numbers.

I recommend that you purchase this game for your class or for home, to play as a family. If you can’t find it at a Chapters near you then you can purchase it using this link: 

http://primeclimbgame.com/ 

If you have purchased this game, or choose to purchase this game,  and/or engage your students just using the circles you can retrieve here (link), please comment to this blog and share with us what learning is happening.

I would love to hear from you and I most definitely know Dan Finkel himself would love to hear any feedback!

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Why Incorporate Money Into Math Lessons

Why Incorporate Money and Thermometer into our Mathematics Lessons

Highlights:

  • Why it's important to add money to your math lessons

  • How to use thermometer to support your math lessons

  • Examples demonstrating the need to teach money and thermometer

Despite the fact that the learning of money is minimal in the Alberta curriculum; and thermometer(temperature) completely removed, I strongly believe it is of the utmost importance to add it to our students’ math learning at ALL grade levels.

I have included money and temperature into my Grade 3  math lessons on a daily basis. And because of it, the development of number sense and connection to other outcomes has been incredible!

When writing my Kindergarten through Gr. 6 Math For Success teacher guide books I didn’t hesitate to incorporate both money and thermometer (temperature). I am most definitely including it into my Gr. 7 book, which has been in pilot mode.  Math For Success Guidebooks

I often have been questioned through the years, why I have included money and temperature into the teacher guide books I have written if it is not in curriculum? I have also heard from many teachers since it is not in curriculum they will not incorporate it into their students’ math learning.

I will put forth the following questions:

  • Is money not number?
  • Is money not connected to place value, operations,  fractions, decimals, percentages?
  • Is it not an important life skill that is needed for daily life and decision making?  
  • Is thermometer not a visual representation of a number line that is vertical rather than horizontal?
  • Is it also not part of our daily life with regards to weather and decisions that would need to be made in relation to temperature.

I think sometimes, teachers become too focused on the ‘what’ that is to be taught rather than the ‘how’. I also think that teachers are looking at mathematics as parts/pieces that are taught in an assembly line manner rather than seeing it as an interconnected entity.

BOTH money and thermometer are not only visual representations to develop numerical knowledge; but also, in my opinion are mathematical tools to help students develop number sense; and from that many outcomes are learned and meaningful connections made.

Money

FREQUENT QUESTION ASKED REGARDING THE PENNY:

If the penny has been discontinued why are you including it?

ANSWER:

It is connected to place value and place value in mathematics is the foundation in helping develop number sense.

How it is Used in Teaching

  • Skip counting by 1’s (pennies), 5’s (nickels), 10’s (dimes), 25’s (quarters)- connect it to the hundreds chart or a number line and that will help with the understanding of addition, factors, multiplication, divisibility
  • From skip counting will come the understanding of multiples because if you can count by 1’s and 10’s, connection to counting by 100 (loonies), 1000 (10 dollar bill) is made
  • Connection to place value which is the foundation of developing number sense
  • Decimal numbers
  • Fractional numbers - proper, improper and mixed
  • Percentages
  • Pattern

Real Life Stories Relating the Importance of Incorporating Money

Example 1

At the beginning of July I went to get a coffee from McDonalds. The lady who served me was close to 40 years of age, if not older. I ordered a large coffee which is $1.75. I handed her a $5.00 bill but for some reason she punched into the register $20.00. Of course it showed to give me back $18.25.

I told her I gave her a five, not a 20. She became nervous and I tried to explain to her how much change she needs to give me. She fiddled with the money and proceeded to hand me $15.75 cents. |I was confused as to how she was trying to calculate this. I told her again, I gave her five dollars and she needs to give me $3.25 back because it is 25 cents to 2 dollars (175 + 25 is 200) and 2 plus 3 is 5. (200 + 300 is 500)

She became absolutely rattled and said to me, I will just believe what you tell me and she handed me the $3.25.

I’VE HAD MANY OF THESE TYPES OF EXPERIENCES OVER THE PAST FEW YEARS, AS I AM SURE YOU HAVE AS WELL!

Now, let me give you another story with a very different outcome. It was middle of June and our Gr. 4 students were selling cotton candy as a fund raiser. A Gr. 3 student in my room ordered 2 bags and the cost was $3.50. My educational assistant was standing near the children when the exchange was taking place. My young student (age 8) handed the gr. 4 girls a $5.00 bill. The change given back was less than it should have been. She was able to tell them, without hesitation, as well as with confidence, that what they gave back was incorrect. She also explained to them what they owe her and why.

My educational assistant came to me right away to tell me what had happened and it demonstrated for me the importance of learning money and how it is connected to developing overall number sense!

Example 2

I went to a store at the beginning of September and there was a 10% discount on all products. The clerk was in her mid to late 60’s and she is a very intelligent woman who was a school teacher years ago and has ran a business for 25-30 years.

My total came to $117.50 and she figured something out on paper and asked me if 10% of $117.50 was $7.50? We were so busy chatting about a variety of things that my mind was not focused on what she was calculating; and I have dealt with this business for years, so of course I trusted her.

I left the store and on my way home I started to think, how could that be? 10% of $100.00 is $10.00 and 10% of $10.00 is $1.00 and 10% of $7.50 is 75 cents, so therefore, 10% of $117.50 is $11.75. Or 10% of 11 750 is 1175 but written as a money notation and connecting to place value that would be $11.75.

I turned around and went back and explained my thinking and was reimbursed the shortfall of $4.25.

I am confident that some of my grade 3 students by the end of the year would have been more than capable of figuring this out because of the work we engaged in with money on a daily basis through the math routine in my Math For Success teacher guide books.

Real Life Situations Involving the Need to Understand Money

  • Young children earn money for chores/allowances and they may be saving to buy something. Therefore, they would be able to figure out how many chores and the length of time it would take them to earn the amount they need. (or perhaps they are collecting can/bottles to take to the Bottle Depot and keeping track to a specific value)
  • Young children may be given money for a birthday gift or allowance and want to go shopping. They need to know if they have enough money to purchase an item(s) of choice?
  • Children as they grow into young adults need to learn about budgeting their money/earnings.
  • When borrowing money there are interest rates on lines of credit, visa cards, mortgages, loans
  • If there are sales at stores they need to determine if it is a savings and what is the better buy (eg. two for $5.00 or one for $2.75)
  • If there is a discount on sales items and/or extra discounts on already discounted items, is it really a savings and if so how much?
  • They are setting up a lemonade stand to earn a specific amount of money and figuring out that if they sold an x amount of cups of lemonade they would make an x amount of dollars
  • If wanting to make investments understanding of money is needed
  • Making wise and solid economical decisions in life
  • If wanting to start and/or run a business, figuring out prices so materials/products/wages can be paid, but also a profit can be earned
  • Job decision (Eg. Do I take this job that will pay x amount per hour and work 4 hours daily or do I take this other job that will pay x amount per hour but I work 8 hours 3 times weekly?)

I WILL STOP THERE BUT THE LIST IS ENDLESS AND IT APPLIES TO INDIVIDUALS AT EVERY AGE!!

WHAT ELEMENTARY KIDS SAY ABOUT LEARNING MONEY

I asked if I could buy a $6 loaf of bread with $5 and we said no! I asked why they said you don't have enough money, so the discussion went to value of money:

  • We need to know the value
  • It is important to know the value of money
  • We need to save to buy the bread.

Karen Bouliane - Gr. 1 Class

I always ask my kids how important is $ to them...?  They always respond it's very important to them because of all the things they can buy with it.  I then ask then isn't it important to count it and know how much change you should get so you aren't short changed?

Connections, connections connections...!!!!!!!

Mary Schatz - Grade 4 Teacher

  • So we can get food for our body to make us live(survive) and be alive longer
  • Be a banker
  • Buy food for people who are too old to go the the store
  • Make money when people shop
  • To buy stuff to grow

Diane Waldie - Kindergarten Class

  • You need to know how to pay for stuff
  • You have to earn money to buy things you need (house, clothes, car)
  • To buy water, groceries and important things to stay healthy
  • It shows you how to use money

Vanessa Hardy - Gr. 1 Class

  • You need to buy stuff, so you need to know how much it cost.
  • You need to know how much money you have before you can buy something
  • You are learning about the value of money (money and coins)
  • When you are grown up, you need to know how to pay your bills.
  • You need to understand the money to avoid making mistakes when paying for things and getting change.

Elena Reynolds - Gr. 2/3 Class

  • When we get older we will have to do taxes.
  • When we want to buy something we need to know we have enough money.
  • So we don’t get ripped off.
  • So we do not take long when paying.
  • Budgeting
  • To save
  • For working at a store (power off, tips)
  • So we do not go broke
  • Invest
  • You may not have an adult with you
  • To be independent

Dawnna Morgan - Grade 5/6 Class

Thermometer

How it is Used in Teaching

  • Vertical number line
  • Sequencing of number
  • Magnitude of number
  • Intervals
  • Difference between (subtraction)
  • Negative and positive integers

Real Life Situations Involving the Need to Understand Thermometer

  • How to dress for the weather
  • Would you run through the water sprinkler outside in a temperature of -5 degrees celsius?
  • Boiling and freezing temperatures for the purpose of cooking, building (certain materials contract and expand as temperatures drop and rise)  pouring concrete, putting out bedding plants, gardening, hatching baby chickens

I HOPE THESE REAL LIFE EXAMPLES CLEARLY DEMONSTRATE THE IMPORTANCE OF WHY TO INCORPORATE THERMOMETER

Your Turn!

  • Ask your students why it is important for them to learn money and share the responses with us.
  • Incorporate the learning of money into your classroom and share the learning that came from it?

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Assess While Making Math Alive

Highlights:

  • The importance of starting early 

  • Number sense activities

  • The importance of engagement = fun 

How have you or how are you starting your math class this Fall?

  • Paper and pencil assessment
  • Teach a lesson and have students practice by completing a worksheet or questions out of a textbook or workbook
  • Printables to make math fun. Eg. Coloring in numbers on a hundreds chart to create a picture
  • Mad minutes
  • Games  
  • Or have you even started yet because you are doing ‘get to know you’ activities

I start engaging my students in math from Day 1 of school with the following intentions:

  • Setting classroom norms regarding expectations of what math class will look like
  • Getting them excited about math by making it active and alive
  • Checking in on their understanding of number as well as a few other concepts.

I understand if your district or school has given clear direction to complete an assessment with the purpose to identify students requiring targeted instruction. However, can you also include ‘informal’ activities (assessment) in which you engage your students in a way they don’t even realize they’re doing math?

I know from many years of experience that if you can get your students hooked right from the get go, you will have them eating out of the palm of your hands and success will follow.

I have provided you with a few different number activities to  engage your students. Whatever level you are teaching, each and every one of the  activities can be modified or adapted.

Activities

Activity One

 

Ask students where numbers are important to them in their lives?

 

  • Birthday, age, house number, street number or number of family members
  • A lock code or password
  • Amount of money in their piggy bank or bank account
  • Earning a specific amount of money to purchase an item

Write this out on a piece of chart paper and post in your classroom

Activity Two

Give students a number and ask what they know about this number or how it can be represented mathematically

Eg. Five (5)  

  • 3+2
  • Number of fingers on one hand
  • Number of toes on one foot
  • Half of 10
  • The value of a nickel
  • Years in one half of one decade
  • Comes after or to the right of 4
  • Comes before or to the left of 6

Activity Three

Put a few numbers up and ask, What can you tell me about these numbers?

9, 7, 13, 3, 33, 35, 21, 5

  • All are odd numbers
  • 3 is a factor of 33
  • 3 groups of 7 is 21
  • 5 is 1/7 of 35
  • 33 and 9 are multiples of 3

Activity Four

Write a few numbers and ask, "Which of the numbers does not belong and why?"

28, 20, 10, 16, 24, 36

Possible answer: 10 doesn’t belong because it is a multiple of 2 but not a multiple of 4

Activity Five

Can you determine my secret number from the following clues:     

Eg. My secret number is:

  • A two digit number
  • Greater than 35 but less than 48
  • Not odd
  • A multiple of 2, 3, 6 and 7
  • The difference between 100 and 58

Answer: 42

Eg. My secret number is:

  • Less than 5
  • More than 2
  • A number I can count by 1’s and 2’s to get to when I start counting at 0

Activity Six

Give students a hundreds chart and ask the following questions

  • Is the sum of 1 and 99, 100?
  • Is the sum of 2 and 98, 100?
  • Is the sum of 3 and 97, 100?
  • Is the sum of 4 and 96, 100?
  • Is the sum of 5 and 95, 100?
  • Are you noticing anything with the addends?
  • Without writing all the word sentences or equations out, is there a way to determine how many two addend equations have a sum of 100?   
  • Can a relationship/connection be made to subtraction? Eg. Is the difference between 100 and 1, 99? Is the difference between 100 and 2, 98? Is the difference between 100 and 3, 97? Is the difference between 100 and 4, 96? Is the difference between 100 and 5, 95?
  • What are you noticing? Is there a pattern?

Grade 5&6 Math About Me September 2017

The number of activities to engage our students in is endless.

Do you want your young students to be excited and engaged in mathematics class?

OR do you want your students bored and disliking math?

Your Turn!

 

Give one of the above activities a try with your students and comment to this blog.

Tell us what you did and how you changed or modified it to your grade level. Tell us how your students reacted. Tell us what the outcome was. Did it give you insight about your students’ number sense?

I know from many years of experience that if you can get your students hooked right from the get go, you will have them eating out of the palm of your hands and success will follow.

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Staff Development Conference – Las Vegas July 2017

Staff Development for Educators Conference, Las Vegas, Nevada, 2017

For the first time, I attended the SDE conference July 11 and 12th at the Palazzo/Venetian Hotel in Las Vegas. I enjoyed it and found it valuable. I always can walk away from a conference/workshop/session with at least one new idea, but what I found this conference did for me was reaffirm and confirm I am/have been doing great things for student and teachers learning.

I attended one morning keynote speaker and 7 sessions within the 2 days. I am going to provide you the highlights of each session as well as a wrap up of what messages I found to overlap in all sessions.

KEYNOTE SPEAKER: JO BOALER- MATHEMATICAL MINDSETS

Jo Boaler’s key message is that ALL students can learn mathematics. Mathematical ability is NOT heredity, nor is there smart math students and weak math students. Their success is the outcome of the teacher’s messages of encouragement and empowerment as well as the teacher’s instructional methods and practice.

SESSION 1: COMPUTATION: FROM CONCEPTUAL UNDERSTANDING TO PROCEDURAL UNDERSTANDING by Jana Hazekamp

  • Number sense is developed, it can’t be taught.
  • Visual learning of number is a necessity. Students need to visualize the decomposition and recomposition of number, first numbers to 5, then 10, then 20 and so on.
  • It is important to introduce math words before symbols.

SESSION 2 AND 3: ALL ABOUT ADDITION AND ALL ABOUT SUBTRACTION by Jana Hazekamp

Although these two topics were presented separately, it is crucial to connect subtraction to addition when decomposing and recomposing number. This connection will enhance basic fact fluency which impacts multi-digit addition and subtraction.

Horizontal adding from left to right forces place value which is the foundation to developing number sense.

Strategies for addition:

  • Part part whole
  • Friendlies
  • Hundreds chart
  • Compensation
  • Open Number line
  • Traditional algorithms

Subtraction in not just ‘take away’ and ‘minus’, it is about the ‘distance’ and ‘difference’ between numbers.

Strategies for subtraction:

  • Part whole
  • Place value (pull apart the value of each digit and/or two digits)
  • Hundreds chart
  • Open number line
  • Compensation
  • Traditional algorithm

SESSION 4: TAKE THE NUMB OUT OF NUMBER SENSE (K-2) by Eileen K. Ryan

There are 5 competencies of mathematics that create problem solvers

  • Number sense
  • Visualization
  • Generalization
  • Metacognition
  • Communication  

The key to developing number sense with our primary students is understanding number through the decomposing and composing of number.

SESSION 5: DEVELOPING MATHEMATICAL THINKERS(K-2) by Eliza Thomas

  • Talk to your students, give them the opportunity to share their thinking.
  • Pull out/see mathematics everywhere in our world.
  • Vocabulary needs to be an instant piece of their repertoire because it develops mathematical thinking.
  • Focusing on spatial awareness is also important in mathematics.

SESSION 6: FILLING IN KNOWLEDGE GAPS (Gr. 3-5) by Cassey Turner

  • Students must develop number sense before being taught the algorithms.
  • Decomposition and recomposition is crucial to all operations with all types of numbers.
  • The Japanese believe division is the final step in teaching place value.
  • Equivalent fraction knowledge is the foundation to all fraction learning.

SESSION 7: EARLY ALGEBRAIC THINKING by Kar Hwee Koh

Without an understanding of number-eg.  patterns, relationships, place value, regrouping, add, subtract, count on, problem solving- students will not be able to do algebra later on in the middle school and high school years.

WRAP UP/OVERLAP MESSAGES

  • Empower students
  • Engage students
  • Encourage communication by asking the how and the why– can use the words , convince me, prove it, how do you know?
  • Number sense is a MUST to develop in order to enhance mathematical problem solving in our students
  • Do not teach traditional algorithms until later elementary years (Gr. 4-6) when number sense is developed.
  • Speed is not always better, nor does it mean the student is smarter.
  • Productive struggle is crucial to students growth and learning. It pushes them to think further and harder.
  • Number sense is the understanding of number and number relationships; and the ability to use number flexibly, creatively and efficiently.
  • The equal symbol is about ‘balance’ NOT computation
  • Contextualize number equations for all operations. This means have students tell stories connected to the equations.
  • The unknown in equations has to be in every place holder, not just at the end for the answer.  Eg. 5 + 5 = x ,  14- x = 8,  a x 8 = 40,  x = 25 divided by 5

I wanted to share this and I am hoping this is helpful to your own teaching.

Please do not hesitate to ask questions. As I continue on my journey, I am always learning and growing. I am so excited in having the time this Fall to pursue my passion in helping students, teachers and parents. Together, we can make a difference and improve the mathematics learning for children of all ages and throughout the entire world.

 

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Hundreds Chart Challenge

Highlights:

  • Hundreds chart builds number sense

  • Building mental mathematics

Using the hundreds chart in your classroom helps build number sense. The hundreds chart, if understood, helps children develop the understanding of a relationship of numbers which helps with skip counting, factors, adding, subtracting, multiplying, dividing, even and odd, fractions, etc.

I have my grade 3 students use their  hundreds chart from Day 1 of school. They have a hundreds chart in their math duotang and then when they have marked up one they recycle it and get another. From Day 1 we use the hundreds chart to see what factors there are for every school day. From this we can see patterns and relationships between numbers.

For example:

  • They become aware that 2 and 5 are factors of 10
  • When determining how many twos in 44, they know that there are 5 twos in 10 so for every 10 they count by 5’s and at 40 that is 20  two’s
  • From there they count on 21 groups of 2 at 42 and 22 groups of 2 at 44

Many now have gained the understanding of the factors for the multiples of 10 which helps find factors more efficiently.

For example:

  • On Day 75 of school (January 11th, 2017),  many students could tell me they know there are 10 fives in 50
  • From 50 to 75 is 25 so that is another 5 groups of 5
  • There are 15 groups of 5 or 5 groups of 15 in 75

Through our daily work students have made the connection that when you move to the right within a row numbers increase by 1 and if you move to the left within a row numbers decrease by 1. To add, they understand that if you move down within a column numbers increase by 10 and if you move upwards within a column numbers decrease by 10. With this understanding we can add and subtract using a hundreds chart.

Following many different activities using a hundreds chart, we played a game using a die and a hundreds chart. I gave each student a hundreds chart and I had the die. I modelled how to play with my educational assistant and she showed and explained her thinking on the interactive hundreds chart on my Smartboard file.

The rules are:

  1. You will have 10 rolls of the die and you must use all 10 rolls.
  2. You can decide if the number that lands face up on the die when rolled will be given the value of ones or the value of tens.
  3. The goal is to reach as close to 100 as possible or 100.
  4. The work will be recorded within a Tens and Ones games chart (see the example below).

Our  score was -5 from 100 in the example below:

 

Tens

Ones

1 (first roll player chose 1 as 10)

 
 

6 (2nd roll, 6 ones was chosen so total is 16)

3

(total is 46)

1

(total is 56)

 

5  (total is 61)

1

(total is 71)

 

6  (total is 77)

 

3 (total is 80)

 

5 (total is 85)

1

Total is 95

 

I told the students they need to strategize throughout the 10 rolls, knowing if to choose the value to be ones or if to choose the value to be tens.

After the game they were asked to reflect on their decisions to determine if they would have strategized differently at a roll or rolls to reach a score of 100. If we reached a score greater than 100 before or on the 10th roll then we busted and they need to reflect on this as well. This builds mental mathematics as well as allows the students the opportunity to use the 100’s chart.

After we played together, they played independently:

 

Due to the students having challenges keeping the rows aligned I created a game sheet and have provided this for your classroom use.

Click here to download the game sheet: Game Sheet for Hundreds Chart

 

Your Turn!

Try it with your students

If your students are in Kindergarten you can modify:

  • Give each student a number line 1 to 10, a die and some sort of counters.
  • Tell them they have 3 rolls.
  • After each roll, they need to show the count of the die using the counters.
  • Once they have completed the third roll they need to strategize to determine if the sum of all three counts is 10, less than 10 or greater than 10.
  • They are not allowed to put the counters along the number line to see.
  • What they then have to do is determine if they will choose the sum of  2 rolls or all 3 rolls for a sum of 10 or as close to 10 as possible.
  • When this is done, they can lay the counters down along the number line to see if their thinking/reasoning was correct 

If your students are in Gr. 1 perhaps you can use half of the hundreds grid, 1 to 50.

If your students are in Gr. 4, 5 or 6 you can use a hundreds chart to 200, 300 or 400 and they multiply the numbers rolled on the die.

Think about the modifications and/or variations that can be made to meet the needs of your students.

I look forward to hearing how it went with your students! Leave a comment below with your questions and comments.

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Delving into Number Line

Highlights:

  • Understanding relationship of number

  • Young children's understanding of negative & positive numbers

  • Building other number-related skills

Delving deep into number enhances number sense and this of course, is the goal through activities connected to the Big Ideas. One of the Big Ideas for the elementary classroom is number line. Through number line young children can learn number pattern, relationship of number, addition, subtraction, multiplication, division, fraction, decimals… and much more.

In my grade 3 classroom we begin with the very basics to understand relationship of number. Where are numbers located in relationship to other numbers and what the relationship between two numbers are by looking at their location (eg. to the right or to the left of each other tells us if they are greater or less and by how many). We often think elementary children are not ready developmentally to learn specific concepts/outcomes (Eg. negative numbers).

I have learned through my own teaching experiences to never underestimate what young children can learn. One day at the beginning of October during numberline instruction, we were having a conversation about zero and it has meaning just as all the other numbers have. I had one boy raise his hand and ask, Miss Kusick, if zero is represented as nothing then how do we represent negative numbers? At that time we connected it to temperature (which I do daily in my math routine because a thermometer is a vertical number line) and I also discussed being in the black in a bank account. However, I am unsure if my students are making these connections at this time in the year.

Within the next couple of days I was reading an article in one of the  Teaching Childrens Mathematics magazines published by NCTM. I subscribe to this magazine yearly because they are full of rich articles and activities that are written by teachers. At the back of the magazine is always an activity that can be modified at every level Kindergarten to Grade 6. This was unbelievable timing because the activity was showing ideas to help young children understand negative and positive number along a linear number line through personal experiences.

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-10   -9   -8   -7   -6   -5   -4   -3    -2    -1    0   1   2   3    4     5    6     7    8    9     10

Students will label 0 as their time/year of birth. Then if his/her brother was born 2 years before they will label that at -2. If their parents married 5 years before, he or she will label that at -5. If they had ear surgery at age 2 they will label that at 2. If they started kindergarten at 5 they will label that at 5.

I thought what a great way for kids to make meaning of number, both negative and positive, through their own personal experiences. I sent a note home to parents asking them to sit with their child and identify significant times in their lives 10 years before their birth and up to their current age… births of siblings, marriage or meeting of their parents, moving, surgeries, broken bones, special awards or activities they have been involved with. This information came in and the first thing I did was model this for them by choosing significant times in my life. Children love to know about their teacher. Then their work began. Before students could label information along their number line they had to identify 0 by folding the paper in half. Then they had to use finger iterations to identify 1 to 10 and -1 to -10. Finger iterations has been a part of our number line work since September. Learning iterations came from an article I read last year  titled, “Iteration: Unit Fraction Knowledge and the French Fry Tasks". The initial learning is to help children understand the repeat strategy, but lends itself to nurture children's’ understanding of fractions.

The students seemed to really enjoy the activity and I observed many of my 25 students have ‘aha’ moments. For example, one young boy said “this is so cool cause my brother is 4 years old and it is at the number 4 on my number line because he was born 4 years after me. And I am eight now so that is 4 years younger than me.”  

This activity was successful in  helping my students gain further understanding of the negative numbers, but there was also some confusion. Some students couldn’t connect the years of events taking place in relationship to their birth (0). For example, one young girl was born in 2008 and she had a brother born in 2006 which meant he was born 2 years before her, but she labelled this at -6 (taking the last digit in the year rather than making the connection that 0 (her birth) is 2008 so 2006 is 2 spaces to the left of 0. Out of my 25 students I would say approximately 10 weren’t making this connection. |Keep in mind we have been engaging in number line work from the first day of school and some students had numberline instruction in Grade 1 and 2 and there were others that did not.  

This activity was done middle of October. It still shows me further work is needed to master understanding of negative numbers using various strategies and activities. Students need continue practice and repetition to make connection and meaning. Remember teachers, we are working towards conceptual understanding, not memorization.

When I wrote the note home to parents I did specify to identify how many years before or after birth these events happened verses identifying the year in which they took place. For younger students (K to Gr. 3) keep it at the number of years before and after and for older students (Gr. 4 to Gr. 6) ask for the years of events to make it more challenging. But remember you will have students at a Grade 3 level who can connect the years as I had so this is where differentiation  of learning can happen. Even if the parents didn’t right down the years of events you can ask students the year they were born and they can connect the years to the numbers -10 to 10 along the number line.

This was undoubtedly a valuable activity for my students to engage in to enhance their number sense, but there is still much more learning to do to master understanding.  I will continue to work with number line throughout the entire year using other strategies and activities. I am thinking I  will do this activity again but have the students bring in personal information about a family member (mom, dad, grandma, grandpa).  This could be a great way to tie in some Social Studies and learn some history.

Supporting Book Recommendations

Less Than Zero

A Place for Zero

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