Chunk itZ are a visual spatial tool for building “number sense” for quantity to 10.
As they BUILD with the Chunk itz students are Internalizing THE BASICS for knowing, recalling and REASONING about number properties and number facts to 10.
They are using the brain’s ability to see and think in small units: subitizing.
With the Chunk itZ, learners construct and confirm a relational understanding of number BEFORE they move to embedding them in ten frames.
The first introduction is outlining and tracing with accuracy and perseverance. Small muscle development, hand eye co ordination and the ability to grip without strangling the pen and trace without bumps and slips are just a sample of the BASIC skills that impact BASIC FACTS.
As students trace, teachers immerse them in vocabulary of position, space, number properties. Words like vertical, horizontal, rotate to the right, rotate to the left, sides, vertices, area, commutative property, equal emerge as you play with the pieces and the expressions that represent them.
Unitizing is a bigger idea than just subitize. Subitize refers to immediate recognition of small collections. Identify, trace & trust 2s, 3s then 5s. (Four, six and nine can be included as doubles and triples). This builds the foundation for thinking in collections. Without collections thinking students have nothing but counting by ones, a skill that will not build fluency with facts.
Proportional reasoning and unitizing are also embedded in this practice. Coming to understand number engages all the senses.
Link the symbols and practice printing.
If we give students model numbers to study and copy we will see far fewer reversals.
Subitize refers to the building blocks of unitizing. The little collections you know without thinking. Once you are thinking in those small chunks, practice bigger puzzle and holding larger chunks like 5s and 10s. The ChunkitZ can be used for developing magnitude (size change) as students learn with meaning the sequences for multiples of 2, 3 and 5.
Interpreting, describing and “solving” puzzles builds thinking and reasoning skills. Students are challenged to manipulate the pieces in all directions as they fit them together. Gently but consistently, the teacher pushes students to see in their mind and describe without touching. Big ideas like unitizing and proportional reasoning are built into this approach.
Get tracing, talking and reasoning!
We trace two twos and two threes. We trace three twos and three threes. Ideas about 4, 6 and 9 emerge but the focus is on developing the ability to move things in your mind. Equations will come but not right now.
The Chunk itZ support materials include tasks and task sheets to direct teachers and students on a pathway that develops both the physical and the executive control skills students must master if they are to be successful in school K to 12. We are connecting across the grades, across content to develop the whole learner. See ChunkZ Book
These puzzle pages and more are available in the Chunk itZ Book available in pdf. Order from me at firstname.lastname@example.org. Your cost is $39.95.
PROPORTIONAL & SPATIAL REASONING
Students build and trace puzzles. Then as a class or individually ask: “Can you build my puzzle?” Student can trade puzzles and try….
Students can match a puzzle you present:
The final step: Work from a distance.
Automatic Recognition of Quantity
You show me a puzzle and I know at a glance what it represents and start telling you the addends that it is composed of. I see 8. That’s 5 and 3, 6 and 2, 7 and 1 (hard to see but think 3 + 4 + 1). The longer I look, the more I think about.
How many sides, how many vertices does each piece have? What shape does it create? This is an irregular hexagon.
Figuring out what pieces fit where and how?
The literature coming from a steadily developing body of very robust and reliable research focused on the difficulties that are blocking achievement Grades 7 and up makes clear that students do not understand number, number properties and number operations in a connected and meaning- filled way. Too many students believe math to be a set of disconnected answers rather than a way of thinking which can be mastered by anyone. Answers matter but understanding why that is the answer matters more.
Work with the Chunk itZ places the focus on expressions to describe ways students see numbers. As students describe their puzzles, the teacher actively engages them in studying how to connect expressions. the focus is additive composition. What parts make this particular whole and how are they related. This focus on relationships lays a foundation for future grades that is absolutely critical. Teaching that attends to relationships puts a focus on seeing and explaining patterns which leads to the ability to generalize and apply procedures and formulas while it also develops and strengthens memory and recall skills. Students actively engage in their learning: discussing, debating, comparing. Engagement builds attention and attention leads to learning. And just as important, the relationships students are mastering will become the central focus in higher grades as they move into algebra and geometry.
EQUAL & EQUATIONS
The link to equations is made with purpose and clarity. We are not “making” is statements. (Three and two makes five.) The equal sign does not mean “here comes the answer.” In the picture below the focus with the symbolic is not on getting the answer but rather it is on connecting expressions to demonstrate relationships between facts.
The associative property emerges in a meaning filled way, not as a rule to remember. (The associative property is named in an outcome in Grade 2. Young learners are more than capable of attending to it!) If 8 = 2 + 3 + 3 8 = 5 + 3 then
2 + 3 + 3 = (2 + 3) + 3 or 2 + (3 + 3) = 2 + 6
When students just want to write equations, teacher re direct their attention by challenging them to see equations as more than “answers” on the right. This student is excited to write 6 + 1 = 7, the teacher prompt is to push him or her to a richer understanding of the task by suggesting another expression.