# TRACING

### 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.

We cannot leave students to develop grip on their own. Help him.

# UNITIZING

### 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.

What feedback can we give?

### Proportional reasoning and unitizing are also embedded in this practice.   Coming to understand number engages all the senses.

Link the symbols and practice printing.

# REASONING

### 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.

What pieces make my puzzle?

# 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.

What is his understanding of 5?

## EXPRESSIONS

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.

4 +3=5+2

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.

RECORD THE EXPRESSION

BUILD THE PUZZLE

# EQUAL & EQUATIONS

### 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.

## Build CI Puzzles 2019

Email glorway@thinking101.ca