**Puzzles that Promote Mathematical Reasoning**

**Strategies for Engaging Algebra Learners**

**A Habits of Mind Approach**

**Transition to Algebra**

a full-year intervention course designed to be taken

concurrently with first-year algebra

(aka double period algebra)

Why Puzzles?

Focuses on a few key mathematical ways of thinking or

Quickly gives students the

mathematical knowledge, skill,

and confidence to succeed in a

first-year algebra class

Puzzling and Persevering

Seeking and Using Structure

Using Tools Strategically

Describing Repeated Reasoning

Communicating with Precision

TTA is a 4-year research and development project funded by the National Science Foundation.

TTA has is also being used in other settings including

summer school and middle school as

pre-algebra

Mary Fries

,

mfries@edc.org

Paul Goldenberg,

pgoldenberg@edc.org

Jane Kang,

jkang@edc.org

**ttalgebra.edc.org**

mathematical habits of mind

Consistent with Common Core State Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Who Am I? Puzzles

You can make up your own puzzles using clues with relevant content.

parity: evens and odds

squares and roots

inequalities

algebraic expressions

factoring (shown right)

Mathematical Puzzles

:

are

genuine problems

support

number sense

encourage

logical reasoning

help students develop

strategy

in problem solving

are

fun

and engaging

allow for

social collaboration

in solving

encourage

perseverance

as solution method may not be known before starting

Bridge from mobile puzzles to systems of equations and properties of numbers and operations

Think of a Number

Tricks

Students

reason abstractly about variables

use notation logically

work with tables to organize information

How did I know your number?

Area Models

Mystery Number Puzzles

Students learn systems of equations intuitively

Mobile Puzzles

MysteryGrid Puzzles

Use the clues to fill in each grid so that every row and every column contains all of the numbers in the title.

provide a visual model for the distributive property

support "seeing" like terms

**NCTM 2013**

"[When] students were given the opportunity to look at a book, they would

immediately go for the puzzles

." - TTA Teacher

Students indicated that

area models

,

Think-of-a-Number tricks

, and

mystery grids

were among the

most useful

activities in helping them

understand algebra.

Classroom Use

Teachers who

taught both

algebra 1 and the intervention class

were better able to

make connections

between them.

Discussion

How was your experience exploring these activities today?

How do you see these experiences translating to students?

How do you see these ideas taking place in your school?