A 10-by-10 grid with the numbers 1 to 100 printed in the squares. 

The capacity for logical thought, reflection, explanation, and justification; one of the National Research Council’s five strands of mathematical proficiency.

A branch of mathematics that deals with symbols or variables and uses arithmetic operations (+, –, ×, ÷) to find the unknown quantities represented by these variables. 

Particular ways of thinking, including analyzing relationships between quantities, noticing structure, studying change, generalizing, problem-solving, modeling, justifying, proving, and predicting.

An anxiety management strategy where you tell yourself you’re “excited” instead of “anxious” whenever you feel nervous. Researchers say it works because anxiety and excitement are similar; in both cases, the heart beats faster and the hypothalamus releases cortisol (the “fight or flight” hormone). The difference? Anxiety is a negative emotion that increases awareness of potential threats while excitement is a positive emotion that increases awareness of opportunities.  

A branch of mathematics that deals with the properties and manipulation of numbers.

An arrangement of objects in rows and columns. Math teachers use arrays to help students visualize numbers and operations, like addition, subtraction, multiplication, and division. 

A branch of mathematics that deals with the study of rates of change.

An integrated and functional grasp of mathematical ideas that enables students to learn new ideas by connecting those ideas to what they already know. Conceptual understanding supports retention and prevents common errors. It’s one of the National Research Council’s five strands of mathematical proficiency.

Providing opportunities for students to learn or practice a math concept or skill or a learning strategy in the context of an academic enrichment activity. Embedded instruction can be interdisciplinary and is well suited to out-of-school time environments. 

Direct teaching of math concepts and skills as well as learning strategies (e.g., visual representations, verbalization of thought processes, reflection on problem-solving strategies, and interleaving — alternating between different types of math problems — which improves learning and retention. 

A set of whole numbers formed by adding the last two numbers to get the next number in the sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and so on. Also known as the Golden Ratio. Examples may be found in the petals of flowers like lilies, daisies, and sunflowers; the spiral shapes of shells, galaxies, weather patterns, and animal flight patterns; faces, bodies, and DNA.

A geometric shape that repeats with a complex structure. Examples found in nature are snowflakes, ferns, pinecones, pineapples, and branching trees.

A branch of mathematics that deals with the measurement, properties, and relationships of points, lines, angles, surfaces, and solids.

An advanced calculator that can solve equations, plot graphs, and perform other tasks with variables.

The belief that one’s skills, character, intelligence, and creative ability can be developed with practice over time. Opposite of “fixed mindset.”  

A study strategy where you alternate between two or more related concepts or skills instead of focusing on only one at a time. For example, instead of doing addition problems first, then multiplication problems, you’d go back and forth. This strategy can help learning and retention.

Feelings of tension, apprehension, and fear of situations involving math, regardless of one’s math ability.

A meeting of K-12 students or teachers where they work on problem solving. The lead instructor or facilitator may be a university professor, graduate student, or someone else who’s knowledgeable and passionate about math.

A structured format in which students are supported as they discuss their problem-solving strategies, the reasoning behind their work, questions they may have, and observations about different math approaches and applications.

A small set of ideas and strategies presented in Y4Y’s Math Without Fear course that can help “bust” myths, fears, and stereotypes about math and your ability to learn it. “MUST” is an acronym for “messages, understanding, skills, and thrills.”

The act of busting math myths, fears, and stereotypes to help yourself or others manage math anxiety and build confidence in each person’s ability to learn math.

The study and use of numbers and their operations to describe, measure, predict, and explain occurrences and relationships in the physical world. Branches of mathematics include algebra, arithmetic, calculus, geometry, and trigonometry.

The use of various skills and strategies to do math in your head, without pencil and paper or a calculator. Skills that help you do mental math are being able to recall math facts, estimating, and rounding. Strategies include breaking problems down into steps or breaking numbers down into their components. For example, to add 43 and 52, you could add 40 and 50 to get 90, add 3 and 2 to get 5, then add 90 and 5 to get the answer: 95. 

This literally means “thinking about thinking.” It’s the ability to examine how you process thoughts and feelings, which leads to greater awareness of how you think and learn. 

Development of skills that promote a state of active, open attention on the present. A framework for the practice of social and emotional learning. 

Pairs of numbers that you can add to make another number. For example, number bonds for 5 are 1 + 4 and 2 + 3. 

A line on which numbers are marked at intervals. On a number line, any numbers to the right of the zero are positive, and any numbers to the left of the zero are negative. Rulers and thermometers are examples of number lines.

The ability to understand, connect, and relate numbers. It includes things like understanding quantities and making comparisons, for example.

A short, structured activity where the teacher poses an addition or multiplication problem (like 95 + 95 or 19 x 5), asks students to solve it in their heads, then asks them to share how they did it. Students practice mental math, learn about different problem-solving approaches, rehearse math facts, and develop number sense. 

A set of rules for the sequence you follow to solve a math expression: (1) perform all operations inside parentheses, brackets, and/or above and below a fraction bar in the order specified in steps 3 and 4; (2) find the value of any powers or roots; (3) multiply and divide from left to right; (4) add and subtract from left to right. 

The ratio between the circumference of a circle and its diameter. As a fraction, it’s expressed as 22 over 7, but as an actual number, Pi is unknowable. To find the area of a circle, multiply Pi by the radius squared.

A time management strategy to overcome procrastination and make a task seem less overwhelming. To use this technique, set a timer and work on a task for 25 minutes, take a 5-minute break, and do another 25 minutes. After four times, take a longer break (20 or 30 minutes). 

Applying your math knowledge, skills, and understanding, along with critical thinking and creativity, to solve a problem on paper or in everyday life. 

Skill in carrying out mathematical procedures flexibly, accurately, efficiently, and appropriately. It’s one of the National Research Council’s five strands of mathematical proficiency.

The inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy. It’s one of the National Research Council’s five strands of mathematical proficiency.

The level of effort required to successfully complete a task that’s in the “sweet spot” of being neither too easy nor too hard to achieve. Sometimes called beneficial difficulty or zone of proximal development. This kind of struggle, followed by success, produces new understandings and confidence.

Internal dialogue; studies show negative and positive self-talk can affect one’s psychological state, performance, and sense of well-being.

The ability to formulate, represent, and solve mathematical problems. It’s one of the National Research Council’s five strands of mathematical proficiency.

A level of difficulty that engages students in productive struggle by providing a task that’s neither too hard nor too easy, but “doable” with effort and the right conditions (e.g., sufficient time) or supports (e.g., a calculator), depending on the task. Also called the zone of proximal development. 

A branch of mathematics; a subset of geometry that’s concerned with the length, height, and angles of a triangle. 

A framework, based on brain science and evidence-based practices, that guides the design of learning experiences to proactively meet the needs of all learners.

In math, a variable is a symbol or letter (like x or y) that represents a value you don’t know yet. Variables can be dependent (which means their value depends on other variables) or independent (which means their value doesn’t change even if other variables change).