For those of you who are looking for ways to play together and build mathematical thinking and skills at the same time, consider this simple hopscotch game. You’ll need sidewalk chalk and a small stone. Children can play alone or in partners.
Go outside. Draw a large square on the pavement. Divide the square into at least 9 smaller squares, as shown below. This is called a matrix.
In each of the smaller squares record a number from 1 to 9. You can put them in any order. Now take a small stone and toss it onto the matrix. This is your starting square. From here, you must jump to the number that adds to give you 10.
In the game below, a child has thrown a stone onto the number 8. She stands on the number 8 then and has to jump to get to the number 2 — the missing part to get to 10.
If there’s another child nearby, they should record the equation that matches the jump. (8 + 2 = 10)
Player 2 (if there is one) takes his turn, throwing a stone and jumping from that number to the missing part to make ten. Player A records the equation.
The first player to hop on all the combinations is the winner. (And yes, landing on a 5 gets you a double jump!)
If you’re stuck inside, make the matrix on a sheet of paper and toss coins — or even Cheerios! — instead of jumping from number to number. Toss the first coin, say the number you’ve landed on, then say what the missing part is to get to the desired sum.
Of course you can change the numbers to suit the age and stage of the players…
Consider a double-digit version (Get to 100!) or even a decimal version (Get to 5.0!). The sky’s the limit. I’ve included line masters for each of these games — and a blank grid, too — for you to use as inspiration.
Have fun… stay safe…
Hello to my friends near and far… It has been a long time since I have posted anything to my blog, and for that I am truly sorry. To my faithful visitors, I offer you my thanks. I hope this latest instalment has been worth the wait!
My newest collaboration — as always, co-created with the inimitable Sandra Ball — is entitled Financial Literacy In Primary: Thinking About Money in the Canadian Classroom. This full-colour, 50 page resource is free to download – but you’ll need a password to access it. Please use the form below to contact me for the secret code. Read on to learn more. Enjoy! Carole
Financial Literacy — An Important Aspect of Numeracy
Beginning in the fall of 2016, concepts addressing financial literacy are being introduced to the Western Canadian mathematics curriculum. Although they have been included at the middle school level for a number of years, this is the first time that financial literacy as been highlighted in elementary — and most notably at the primary level. This raises some important questions. What is financial literacy at the primary level anyway? Certainly it is more than recognizing and naming Canadian coins! Structured instead around notions of earning, saving and spending and giving money, curricular outcomes dedicated to financial literacy are intended to look more deeply at what it means to be financially responsible.
Our youngest learners need support and explicit teaching to reach these goals. Engaging, authentic and meaningful tasks are critically important. Learning about money should be fun, of course, but should include notions of social responsibility — earning, saving and giving — as well as spending!
Playing with Money: Connecting to Number Sense
In this new resource, Sandra and I have crafted a series of lessons to support teachers in introducing and developing ideas around financial literacy in Kindergarten through Grade 3. Currently there are few — if any — resources devoted to these ideas for primary students. We are hopeful this resource will fill that need!
Rich tasks, literature connections and games for practice in this resource are laid out along a continuum and are intended to be used across grades. In alignment with our new curriculum, these lessons are connected to both the core competencies (Thinking, Communicating and Personal and Social Responsibility) as well as to the curricular competenciesfor mathematics. By integrating financial literacy into our math program in primary, we create meaningful contexts for the math we are learning.
Think of the mathematical expertise our students will build as we represent and describe money amounts, compare and order values, skip count with coins and bills, use place value understandings and add and subtract dollar amounts!
The Math Big Ideas for Financial Literacy
This teacher resource is structured around a set of Big Math Ideas for earning money, saving money and spending and giving money. These enduring understandings apply across the primary grades and beyond. By addressing these Big Math Ideas in developmentally appropriate and engaging ways we can ensure students have fun while they lay the foundations for ensuring financially responsible decision-making.
Sandra and I hope that this resource proves useful to you and fun for your students!
To download the materials, visit my online store (https://mindfull.ecwid.com) and click on the FREE DOWNLOADS icon.
I’ve said it before… Cuisenaire rods rock. I was first introduced to Cuisenaire rods in 2006 by my dear friend and mentor John Van de Walle. In February of that year I was invited to join him in Spokane, Washington and to observe as he did demonstration lessons in primary and intermediate classrooms. His problem-based lessons featured Cuisenaire rods, and while I watched the students responding to the openness of the tasks and the richness of the manipulatives I knew I was witnessing something powerful. The proportional relationships between the pieces and the colour wheel connections make Cuisenaire rods both aesthetically pleasing and mathematically significant. I was hooked. It took some time and experimentation to figure out how to best introduce the materials and to sort out what tasks and questions would promote thinking across the grades. But in the end, I’ve managed to compile a series of open-ended tasks, games, lessons and practice opportunities that are developmentally sequenced and laid out from Kindergarten to grade 7. I’ve compiled these lessons in 2 full-colour volumes – a primary resource (grades K-3) and an intermediate resource (grades 4-7). All of the tasks have been tested and refined to ensure they are classroom-ready and engaging for all! So it is with great humility (and no small sense of accomplishment!) that I announce the release of my latest resources – Remarkable Cuisenaire Rods: Mathematical Tasks for Primary Classrooms and Cuisenaire Rods Rock: Exploring Multiplication and Proportionality in Grades 4-7. These resources would not exist if it weren’t for the mentorship of John Van de Walle. He shaped my mathematical practice more than he knew in his all-too-short lifetime. And so I dedicate my student-centered and pedagogically grounded efforts to his memory. I hope you will enjoy the tasks and games, the investigations and the open-ended problems posed in these resources. They are intended to promote big thinking in elementary – from addition and subtraction to skip counting and multiplication, from fractions to division and more… The full colour primary resource, Remarkable Cuisenaire Rods: Mathematical Tasks for Primary Classrooms is intended for Kindergarten through Grade 3 can be ordered by clicking here or on the image on the left. The resource is $40 plus shipping. Click on the link below to preview lesson titles and the intended grade levels for the tasks. Cuisenaire Rod Resource K-3 Table of Contents The full colour intermediate resource, Cuisenaire Rods Rock! Exploring Multiplication and Proportionality in Grades 4-7 is designed for intermediate students and can be ordered by clicking here or on the image at the right. This resource is $50 plus shipping. Click on the link below to preview lesson titles and the intended grade levels for the tasks. Cuisenaire Rod Resource 4-7 Table of Contents As always, thank you for your support! Carole
Here’s a fun little game for primary classrooms… The Magic Squares game provides students with a total for each row and column, as well as a few key starting numbers. Use the magic wand to place the correct digits from the set of numbers at the bottom of the screen. Double click to grab and then place the correct numerals in the grid.
Each game sets a different total for the rows and columns, so students can choose a number that makes sense for them before beginning.
The challenge of finding a sum for 3 addends is a good one for late grade 1 (when the digits without images to accompany them make sense) through grades 3.
I had the pleasure of working with K and K/1 teachers in Mission on Monday – a great group of teachers who somehow managed to summon up the energy to attend an after-school workshop with me this week!! Together we looked at ways to support their young students in subitizing and partitioning. Sounds complex, doesn’t it? 🙂 Truth is, children in early primary need opportunities to see numbers at a glance without counting (subtizing) and to recognize that we can break up sets and put them back together again and the set size is the same (partitioning). These concepts and skills are critically important for young children to develop – they underpin the ability to add and subtract, to multiply and divide…
Engaging young children in conversations about how they “see” sets of number is a great way to start. Present an arrangement of 5-8 objects in your daily opening activities, and ask children what they see and how they see it. Talk about the parts and label these smaller sets with numerals to make sense of the digits. Celebrate the fact that, no matter how you slice it, 7 is still 7!
Over time, you might want to make connections to the operations by using the attached “Missing Part Cards”. They include a numeral to indicate the set size, and then dots in familiar arrangements in the form of an equation. The important part of course is to cover up just one of the sets of dots before showing the missing part cards to the children! 🙂 A 6.5 cm x 6.5 cm square of thick paper (bond paper or construction paper – or even sticky notes doubled up) taped across the top creates a flap that will hide one of the parts from view, as indicated below.
Show the card and read it aloud with the children:
“Seven is the same as 4 and…?”
It’s a good idea to say “is the same as” and “and” for “equals” and “plus” here. “Equals” and “plus” are the names for the symbols and are less meaningful to learners than “is the same as” and “and” – which are words that describe what the symbols mean…
Have students say what they think is missing, and why they think so. You’ll be surprised at the strategies students will use to find the missing part! Older learners will benefit from seeing the equation written with a box to indicate the missing part – that is,
This is a great way to introduce algebraic thinking in a visual way!!
Feel free to download the Missing Part Cards for 5, Missing Part Cards for 6 and Missing Part Cards for 7 here. They are best printed in colour of course, and will hold up best if printed on card stock or bond paper. Credit for the idea goes to John Van de Walle, who first showed them to me years ago. A smart man, our John – and one I miss terribly.
PS – If you’re looking for more ideas like this for K and grade 1, consider purchasing a copy of my book: Number Sense – A Combined Grades Resource for K, K/1 and Grade 1 Math Classrooms. It’s set up to support teachers in addressing the number PLOs in mindful ways while keeping their Kindergarten and Grade 1 students together. Games, tasks, problems and meaningful practice opportunities are included in English and in French. To order online, click here.
My apologies to my colleagues in Coquitlam – I promised to post this over the weekend, but ended up riding my bike to the Olympic sites downtown – and was completely overwhelmed by the celebrations…
The 2010 Olympic Games are in full force here in Vancouver, and I for one couldn’t be more excited – or more proud – to live in this city! Kids everywhere are getting right into the games and patriotism is at an unprecedented high. So, with that in mind, I structured a math lesson with an Olympic spin for primary classrooms. The big math ideas of this lesson highlight 2 things: “We can find the sum using 3 addends”, and “We can make ten in many ways.”
I had a great time engaging with students in Kindergarten with this task – but I’d suggest there are ways to extend it all the way through Grade 2, depending on the questions you ask. Here’s what we did.
I told the kinders that I was a volunteer with the Olympics and that my job was to figure out for each event who had won and how many medals each country had in all. I told them that I had to produce a report for the Olympic Committee to show how I had figured it all out. I began by talking about the different kinds of medals we could win, then told them the names of the 3 countries I would be comparing – China, the US and Canada. We modelled a possible solution for one event (the speed-skating event) and figured out a way to record and compare the results.
Students went to tables and, working in partners and alone, modelled and recorded solutions for each of the sports that I was in charge of – namely Snowboarding, Bobsledding, Curling, Skiing and Figure Skating. They were VERY excited to discover that Canada had won each event… With a coincidental score of 10 medals for each and every event! 🙂
Next, we compared the different ways we can make 10 (1+8+1; 3+3+4, 5+3+2, etc) and focussed on how each set made ten, no matter how we added them – a big concept for the primary grades.
To take this context and the math even further, students could compare the number of medals earned by each country and calculate the difference between each country’s total. At later grades, students could sort out how many gold, silver and bronze medals were handed out, and then how many medals were awarded in all.
Hopefully there’s something helpful in these materials for you to use in the next while. Get the results by country and by sports, images of the medals and an image to match each sport here…