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.
A while back I came across a fun game – Bridging Shuttle – that is aimed at students in grades 1-3. The game is intended to show, through the use of a space shuttle’s flight path, how mathematicians “bridge” through friendly numbers like 10, 20, 50 and 100 while adding. When we talk to students about “making ten and some more” from two addends, we are “bridging” through ten. It involves, of course, breaking numbers up into parts and putting them back together again!
The image below shows the screen for the shuttle’s “flight path” called 8 + 4. Students begin at 8, type in the number that gets them to the next friendly number (2) and then hit the red button to proceed to the satellite. Next they type the number to take them the rest of the way – (2 again) and press the next red button to land.
Consider modeling the action of the space shuttle with ten frames with your students to consolidate the process… This game uses only digits and so is more abstract.
Try the harder versions of this game that bridge through 20 and 50!
I wanted to send along a list of spooky books for math investigations for spreading the Hallowe’en math love. I hope you can find some or all of these in your school libraries… There are so many fun contexts to explore around this season – from notions of pumpkin circumference to skip counting, from growing patterns to playing with the operations and the complements of 5 and 10.
One of my favourite contexts for thinking about parts of 5 stems from a story called Room on the Broom. Just this week I worked in a K/1 classroom and explored the missing part – or complement – of 5. Then we read the book by Julia Donaldson, in which a witch and her friends fly about on a broomstick – adding a friend until there are 5 on the broomstick in all. We “built” some of the book’s illustrations in egg carton 5-frames, and talked about how much room was still left on our broom, if our brooms, like hers, had 5 seats.
Next, I whispered a number from 1-4 in each child’s ear (I left off zero and five for this initial exploration…) and had them build that number in their 5-frame broomstick. Then I asked the children “How much room is on your broom?”. The K/1 kids then had to find the person whose broom “completed” their’s… Click to take a look in the pictures below:
a child with 2 on his broom finds a child with three on her broom:
3 and 2
and they put their brooms together (one on top of the other) to fill it up.
The egg cartons I like best are clear plastic ones – and you can see why… looking through one 5-frame to the other is a powerful way to see the parts of 5!
After a couple of turns with this game, I asked children to record what they did and how they filled up the room on their broom with their partner. You are welcome to use the There’s More Room on my Broom! line master to try this with your students as well. In the photo below, you can see see one of the grade 1 students working to show her thinking on the form…
Have a fun and spooky mathy season!