All right folks…
If you’re outside (or wish you were!) here’s another math game worth playing. It’s called Testing the Limits — and I’ve adapted it from BEAM Maths of the Month.
To play, you need sidewalk chalk and a die (6-sided is fine, 10-sided is better!). You can play this game with a partner or alone. Here’s how…
ROUND 1: Roll the die 3 times and make a 3-digit number. Roll 3 more times and make a second 3 digit number. Put both numbers on the same number line. These are your “limits”.
ROUND 2: Now roll 6 more times. Make 2 different 3-digit numbers that fit within the limits from ROUND 1. Plot them on the same number line as ROUND 1. If you can do it, these new numbers become your new limits and you can move onto ROUND 3. If not… the game is over! Check out my sample game below.
Try using just two 2-digit numbers for younger students, or even decimal numbers for older students. Consider trying this with negative numbers, or even one negative and one positive to explore both sides of zero.
Enjoy! Stay safe…
My sincere appreciation to all of you who have waited for the publication of this book. As you know, I’ve had a pretty remarkable year. I hope you’ll forgive me, knowing that only good distractions delayed its completion!
But I am pleased as punch to announce the release of Place Value For Intermediate: Building Number Sense for Grades 3-5, available now from my online store for $50.
This resource for teachers of Grades 3 through 5 features lessons designed to support deep learning of number. A wide range of both open-ended and directed tasks focus on representing, describing, comparing and ordering numbers to 100 000, as well as explorations of decimal numbers to thousandths.
Measurement experiences make up a big part of this series of tasks. The metric system and all of its place value connections is featured in explorations of linear measurement (mm, cm, m, km), perimeter (cm, mm), area (square cm and square m), mass (g, kg) and capacity (mL, L).
Addition and subtraction of large numbers and decimals are also addressed in this volume. Lessons at the grades 4 and 5 level focus on multiplication of 1 by 2- and 3-digit factors as well as 2 by 2-digit factors using the distributive property (an area model).
Assessment tasks tap into students’ understandings of these numbers and their application in the real world. Being able to see and relate to big numbers and to very small ones, to understand their relative size and to capably use these numbers to estimate is the essence of number sense.
Set up in a developmental continuum intended to facilitate the teaching of combined grades, this 352 page volume is certain to contain material to meet the needs of all learners and to inspire fun and engagement with critically important place value concepts.
When you buy the book online, you also get access to almost 40 pages of digital files and resources, which will be emailed to you as a downloadable pdf!
Thanks for your continued support and inspiration…
Wow. I have had the most extraordinary summer. Truly extraordinary. And somehow between engaging in a series of remarkable, life-affirming adventures I have managed to write another teacher resource book… 😊
It’s all about Place Value (as I’m sure you’ve figured out!) and is intended for teachers of kindergarten through grade 2, with special accommodations for those who teach in combined grades settings. There are 230 pages of developmentally framed lessons designed to address the diversity in our primary classrooms. Each one supports students to represent and describe quantity, to compare and order sets, to use referents to estimate and to skip count. Lessons devoted to measurement — an ideal practical application of place value in the world — are also featured. Whole class lessons, centres tasks and games for practice allow students to connect these important concepts in a seamless way, and can be used both as a unit or spread throughout the year to build and consolidate understanding.
(PS… A companion volume for Grades 2 to 4 is in the works – expect it later this fall!)
For those of you who have been looking for some of the teacher resources and student materials that I have used in my demonstration lessons, I’ve opted to try and put a collection of them all in one post… This collection of materials are intended for teaching place value, for use in lessons involving partitioning (addition, subtraction and multiplication), for comparing and ordering whole numbers as well as decimals, and for the teaching of fractions. As you’ve seen modelled in the lessons I’ve taught, these materials work best in concert with visuals (ten frames, base ten blocks, etc) and with plenty of opportunities for students to write equations, describe their thinking orally, build with models and create real-world situations to match.
The money and Cuisenaire Rods are best printed in colour, of course. I’d recommend sending the pdf’s to Staples.ca for printing. You can specify the weight of the paper (I like 80lb gloss cover) – and they’ll have the materials ready quickly for a reasonable price.
Consider putting magnetic tape on the back of these materials to allow them to be displayed on the white board. Check out the dispenser of magnetic tape available from Poster Pals. It’s great stuff!
I hope these prove helpful.
Happy New Year, Everyone!
I am pleased to announce the release of my latest resource, Sums and Differences – Teaching Addition and Subtraction in Grades 2&3. This teacher resource is matched to the WNCP curriculum and addresses the operations of addition and subtraction to 100 for grade 2 and to 100o for grade 3. Designed to be used by teachers of combined grades – or by anyone who has a range of learners in their classrooms – these lesson sequences focus on the big math ideas of adding and subtracting! Each lesson asks students to engage with place value in concrete, pictorial and abstract ways, while practicing and developing fluency with the operations. Word problems, games and written practice are included to ensure students hone their skills and deepen their understanding of addition and subtraction with bigger numbers.
The resource includes all the line masters, game boards, written practice and teaching materials required to support your students in becoming proficient with addition and subtraction in ways that are consistent with the curriculum and which promote number sense.
This 220 page resource is just $40 plus shipping. Click here to order!
PS – The companion resource for grades 1&2 is also available for purchase. Read about it by clicking here.
PPS – My sincere apologies. I have discovered 2 errors in the book. One comes on page 167, in the game called “Three in a Line – Subtracting hundreds, tens and ones”. The wheel at the top of the page and the differences below don’t match. 😦 I’ve attached the replacement game here for you.
Likewise, I’ve had some feedback about the “I have…, Who has…?” game in the early pages of the resource. I’ve re-created it and uploaded the replacement here.
Thanks for your patience and understanding…
Sandra Ball and I have been at it again!
We have just put the finishing touches on another assessment tool for use in fall of the year. It’s a companion to the other “What Do They Know” assessments featured above, but are designed for students in grade 2 and 3.
Focussed on place value, partitioning and skip counting, this tool highlights number sense and the operations. The tool is administered by the classroom teacher and involves the whole class and small groups.
If you’re interested in piloting these materials, please go to my online store (https://mindfull.ecwid.com) and click on the FREE DOWNLOADS icon.
I hope it proves helpful to you in getting to know your learners and what they’re truly capable of!
I almost forgot to post this super fun game called “I have, Who Has…” This particular version allows students to think about place value in tens and ones using money and ten frames. To play the game, hand one (or more) cards to your students for them to read over and practice. It’s important that all the cards be distributed or the game won’t work!! :o)
Then, choose one student to begin by reading aloud both the “I have” side of their card, (“I have 3 tens and 5 ones.” or “I have 35.“) and then have them ask their “Who has…?” question: (“Who has one ten and six ones?”). The person with 16 on the left hand side of their card responds: “I have 16” and asks their question in turn.
If students are careful, the entire class will have a chance to read from their card and ask a question – and the game ends with the person who first read from their card. This is a great game since it links language, pictures, money and place value to make sense of tens and ones. I hope you enjoy it!
I wanted to pass along something that I love using in grades 2, 3 and 4 classrooms when talking about place value and number patterns. series of hundreds charts – that don’t just stop at 100 !
I recall John Van de Walle speaking about the importance of examining number patterns beyond 100, that it was a good idea to expose kids to hundreds charts that bridge the centuries — that is, that extended from one hundred to the next. He used to like to tape all the charts together in a long strip to highlight just how big 1000 is…
I like to play games with these hundreds charts, using a die with the +10, +10, -10, +1, +1, -1 marked on its faces. Have students start on the square with a 1 in it (101, 201, 301, etc) and roll the die, following the instructions. Students should read their die and describe the new sum aloud: “301 and 10 is 311” as they move their counter. The first one to reach the next hundred (400 in this game) is the winner.
In playing the game, there are important patterns to be noticed. Adding one on a hundred chart means moving one space to the right, while subtracting one means moving to the left one space. Adding ten means moving down one line, and subtracting ten means moving upwards one line. In this game, these are the only possible moves! In this way we also highlight the patterns in place value addition – that is, when we add or subtract ones, we affect only the ones; that when we add or subtract tens, we affect only the tens digit. Most importantly, though, that these patterns continue over decades and centuries. Like Van de Walle suggests, tape two of these charts together and have students begin a game at the _50 mark on the first board (say 350) – with the winner being the first to reach 500. Observe as students play and see who struggles with the transition from 300 to 400…
Likewise, consider using these charts as addition and subtraction tools. Once they have played the dice game above, have students place a counter on a number (say 324) and ask them to add 31 more, by moving their counter to show the addition. In this case, it’ll move down 3 rows and then one to the right, landing on 355. Challenge students to add larger numbers, like 29 to their new sum. Do they move down 2 rows and over 9? (20+9) Or do they move down 3 rows and subtract one? (30-1) The latter is more efficient — making fewer moves and resulting in fewer errors – and is also an excellent use of algebraic thinking. Since, in the end, 29 is the same as 30-1.
Subtraction can be modelled in much the same way. Find 2 numbers on the hundreds chart – say 367 and 428 – and mark them with 2 different coloured counters. Ask students to find the difference between the two numbers. It is worth observing to see how many students add up to find the difference — since ultimately it results in the same amount!
Remember to record number sentences to match students’ moving around the board… Otherwise the richness of the mathematics can become lost in a game of “snakes and ladders”!
Hello, my math friends!
I wanted to share something I put together not long ago to support students in understanding the value of the digits when we write decimal numbers. These decimal “tents” as I call them, are made from card stock and are folded in half to form a tent shape. Each one is cut so that the decimals on each card line up one under the other – but the digits themselves are still visible. It’s a bit hard to explain, I fear, but the following pictures should help…
This is what the cards look like, folded. I like to put a strip of magnetic tape on the back of each one so that I can stick them on the board, matching them to a model to show the same amount.
The cards are trimmed so that the decimal point falls at the same location on each of the “expanded” decimal number. On the decimal tents line master, this means you’ll slice off the light grey zeroes…
So when the cards are overlapped, the decimal number itself is clear, and made up of the parts.
It’s a powerful tool to use with students. Helping them to see that we can decompose a decimal number in the same way we do whole numbers is an important connection! This decimal tent set shows that 3 + 0.6 + 0.08 = 3.68.
Imagine a series of these tents strung along a string or wire in your classroom. Have students create a 3 digit decimal number, model it with materials and then order that number along the number line (that is, to hang their cards right on the wire!) placing it relative to the others. It’s a neat way to compare and order decimal numbers!
I had fun playing with place value concepts in Vernon last week with a FABULOUS group of grade 5 students. We modelled large numbers in a place value cart (ones, tens, hundreds, and thousands using magnetized colour replicas of Canadian bills – or rather loonies, tens, hundreds and thousand dollar bills! I built dollar amounts by placing bills of different denominations in their respective columns. It was easy for students to say the total value of the bills when presented in this way – easier still to describe them in terms of expanded form and standard form. :o)
Later we explored the idea of multiplication by 10 – and discovered that every time we multiply a number by ten, we move one place to the left in the place value chart. Kids had fun trading twenty loonies for 2 ten dollar bills and writing the multiplication sentence to match!
I’ve attached pdfs of Canadian bills and coins (thousands, hundreds, tens, loonies, dimes and pennies) so that you can explore place value with tenths and hundredths of dollars as well.