Do your math tasks include
Number Space & Shape?
Number sense is foundational to learning math (Baroody et al, 2009) and predicts future success and skill acquisition (Edens & Potter, 2013). It develops through experiences that allow children to examine and compare quantities, link them to symbols, then learn multiple ways to express them using numbers. In the early years, guiding children to know and enjoy expressing numbers is foundational. I am not talking about reading and writing and parroting equations. I am talking about expressing numbers multiple ways. I am not talking about drawing blocks, I am talking about learning to write expressions.
Much research into the connection between body, mind and emotions (Alcock & Haggerty, 2013) point to the need for immersing students in tasks that are tactile, engaging, intellectually motivating and lead to important and authentic mathematics. As primary teachers we need to be confident that practices and resources will foster learning and enjoyment, not simply temporary gains in particular skills.
Chunk-itZ are a tool I have developed to engage the body, mind and emotions. The focus is at once number, space and shape. Puzzling, thinking, writing, reasoning and yes even those “basic facts” emerge. The “Chunk-itZ” hook students immediately.
As students puzzle, teachers observe & listen for opportunities to prompt lessons around number, space and shape.
Do you see 3 and 2? How about 5?
Do you see a staircase? Do you see a decagon?
Ideas that form the foundations for multiplicative reasoning and what teachers refer to as ‘place value’ emerge.
As he was exploring the ChunkZ, a Grade one boy called me over to ask: “Is this 1 “two?” Then turned it over and finished his question: “or two “ones?”
I said: “hmmmm, interesting. How much is each of them worth?”
He responded, “they both are worth 2 but one is a 1 two and the other is 2.”
I asked, “What would this be?”
He responded: “Two ‘twos’. That’s four.
I turned the pieces over and asked: “And now what do I have?”
He responded: ” Two ‘ones’, and that is still four.”
“And what about this?”
He responded: “three ones, that’s 6 cause each one is a 2, or if you turn them over three twos and that is still 6.”
He is demonstrating the ability to unitize. He recognizes that we can talk about numbers as single units or as one unit of… this idea is critical to understanding place value which is based on multiplicative reasoning.
Ideas about what it means to be equal emerge.
Can you “see” 4 and 1 inside 2 and 3?
Do you see how 5 + 2 and 4 + 3 are related in this puzzle?
Ideas about shape and space emerge
Chunk itZ engage learners through visual spatial reasoning. As students rotate, reflect and trace the pieces to make their puzzles, they develop intuitions and insights into how parts are related into wholes. In the hands of a skilled teacher, those wholes can be identified and related using numbers and number expressions. Those wholes can be described and related using the attributes and properties of shape and the vocabulary of space.
This student counted the sides of the three Chunk and said it has 6 sides. He then built a ’12’ puzzle by putting 2 three ChunkZ together and was wondering how many sides it would have. Will it be twice as many sides?
Nearly a century of research confirms the close connection between spatial thinking and mathematics performance. The relation between spatial ability and mathematics is so well established that it no longer makes sense to ask whether they are related.
***Mix & Cheng, 2012
The connection does not appear to be limited to any one strand of mathematics. It plays a role in arithmetic, word problems, measurement, geometry, algebra and calculus. Researchers in mathematics education, psychology and even neuroscience are attempting to map these relationships.
Combined with dot collections, Chunk-it tasks differentiate to challenge ALL learners as they develop, adapt, practice and refine key skills and attitudes that are critical to developing more than just RECALL of facts.
Describe 13 as 10 + 3
4 + 6 + 3
5 + 5 + 3 = 5 + (5+3)
Chunk itZ engage young learners in mathematical REASONING that will make the difference to their success across all the strands and all future grades. In the hands of a skilled teacher, the discussions and drawings form the basis for teaching children to explain their thinking through oral and written communication.
Reading, writing, symbolizing the mathematical relationships, those are the goals. Automatic recall of facts are just a given, it comes and it lasts.
ChunkitZ help develop proportional reasoning which forms the foundation for making sense of multiplication, division, fractions and decimals. Outcomes related to proportional reasoning include comparing size of units to number of units needed when measuring (Grade 2), understanding the relationship between minutes and hours, days and weeks, months and years (these are all ratios), cm to m and mm to cm and m (more ratios) making sense of how multiplication facts are related and how area grows, making sense of how fractions are related and how equivalent fractions are related… the list goes on.
Here is a task for proportional thinking: I show a full size puzzle. In this case it is on the board. Students try to build it from their desk. Then they come up to show their proof.
To increase the challenge, I show a small puzzle on the Smart board or give it to students on a small task card and they build a matching puzzle using Chunk pieces (different scale, same outline.)
In mathematical terms, the outline they create will be similar (the same shape, & equal angles ) but not congruent (equal side lengths) to the puzzle card I showed.
Even students in Grades 5 to 8 enjoy the challenge.
Puzzle cards are now included in the support material that I send out with Chunk itZ orders.