Mathematics is the foundation of all science and technology.
– David Hilbert
ProgramsOur Logiclasses
Our Programs are designed to build intellectual rigor appropriate for its grade level, starting from concrete and exploratory learning in the younger grades to more abstract, strategic thinking in the older grades. Each LogiClass is designed to foster skills and insights that support future academic and intellectual pursuits. The focus is on developing the habits of mind necessary for mathematical thinking, problem solving, innovation, and articulation of math concepts with clarity and precision at every grade level.
First grade advanced and Second grade Student
This program uses interactive challenges and a playful approach to problem-solving to help students develop a keen eye for recognizing mathematical patterns, reason through steps for tackling math challenges, and communicate their thinking effectively.
STUDENTS CAN EXPECT TO:
- Enhance foundational thinking skills.
- Develop confidence in solving out-of-the-box mathematical problems with logic and creativity.
- Justify their work and explain their reasoning clearly.
- Compete with confidence in the following national and international math contests: Noetic; Math Kangaroo.
TOPICS COVERED:
- Number Sense (basic arithmetic operations; number comparisons; even and odd numbers; place value).
- Logic and Reasoning (if-then relationships; order problems; simple deductions; order relationships, visual patterns).
- Geometry (recognizing shapes, figures and symmetry; area concepts; simple spatial relationships).
- Patterns and Sequences (identifying or completing patterns in numbers of shapes).
- Time and Money (basic money calculations; reading clocks and calendars; time intervals).
- Word problems (real life scenarios requiring mathematical interpretation; drawing conclusions from given information).
CURRICULUM:
Through this curriculum, students will build a solid foundation in math problem-solving skills that are essential for participating in both the Noetic Math and Math Kangaroo competitions. Each session will focus on a specific topic, where we will work through a variety of problems that gradually increase in difficulty. Along the way, we will explore helpful strategies and techniques for approaching challenging and out-of-the-box math problems.
Session 1: Introduction and Assessment
- Overview of Math Kangaroo and Noetic problem-solving strategies.
- Assessment test—40 minutes to solve 15 problems
Session 2: Number Sense Foundations
- Example: Alice pointed at birthday balloons numbered 1–10. She said, “If you add all the numbers smaller than 5, you get my age.” How old is Alice?
Session 3: Time and Money
- Example: Angie arrived at the playground at 11:45 AM. Melissa arrived sixteen minutes later. When did Melissa arrive?
Session 4: Geometry Basics
- Example: How many triangles can you find in this figure (rectangle with two diagonals drawn inside)?
Session 5: Patterns and Sequences
- Example: A magician pulls animals out of his hat in this sequence—parrot, dog, cat, lizard. What is the 15th animal?
Session 6: Logic and Reasoning I
- Example: If ▲=3 and ■=2, what is ▲+■+▲?
Session 7: Logic and Reasoning II
- Example: If Jack is taller than Jane, and John is taller than Jill, and Jane is taller than Jill, who is tallest? (Answer: Cannot be determined.)
Session 8: Word Problems I
- Example: Amanda makes bracelets at a rate of five per hour. How many hours will it take Amanda to make bracelets for herself and her nineteen friends?
Session 9: Word Problems II
- Example: Emmet has a red bow, a blue bow and a yellow bow, and two puppies, Archer and Parker. In how many different ways can Emmet put one bow on each of his two puppies?
Session 10: Mock Competition and Review
- Review of key strategies and concepts
- Practice test—45 minutes to solve 20 problems
Third and Fourth grade Student
This program offers a logical progression through math and discovery-based learning where students explore various approaches to a problem and build the ability to (i) think like problem solvers by breaking down complex problems into smaller, interconnected components, and (ii) articulate their understanding clearly and thoroughly.
STUDENTS CAN EXPECT TO:
- Deepen understanding of how logic and reasoning work in mathematical contexts.
- Tackle challenging mathematical problems in a structured way and support their reasoning with logical explanations.
- Engage in mathematical debates to articulate and defend their solutions to problems.
- Compete with confidence in the following national and international math contests: Noetic; Math Kangaroo; MathLeague.
TOPICS COVERED:
- Number Sense and Operations (place value and number comparisons; operations with regrouping; digit operations).
- Logic and Reasoning (true/false statements; deductive reasoning; working backwards; pattern recognition).
- Geometry and Spatial Visualization (perimeter, area, volume; symmetry and transformations; angles and lines).
- Fractions, Decimals and Measurement (comparing and ordering fractions and decimals; length and distance; capacity; weight; temperature).
- Combinatorics and Counting (counting principles; arrangements and combinations).
- Word Problems (multi-step problems requiring critical thinking; drawing conclusions from data; real world applications of math concepts).
CURRICULUM:
Through this curriculum, students will build a solid foundation in math problem-solving skills that are essential for participating in both the Noetic Math and Math Kangaroo competitions. Each session will focus on a specific topic, where we will work through a variety of problems that gradually increase in difficulty. Along the way, we will explore helpful strategies and techniques for approaching challenging and out-of-the-box math problems.
Session 1: Introduction and Assessment
- Overview of Math Kangaroo and Noetic problem-solving strategies.
- Assessment test—40 minutes to solve 15 problems
Session 2: Number Sense and Operations
- Example: What is the greatest 3-digit number that is divisible by 3 and can be created using three of the following digits: 4, 5, 6 and 9?
Session 3: Geometry and Spatial Visualization
- Example: What is the area of a rectangular swimming pool that is 68 feet around (perimeter) and 10 feet wide?
Session 4: Fractions, Decimals and Measurement
- Example: A full glass of water weighs 400 grams. An empty glass weighs 1/4th of the glass full of water. How much does a half-full glass of water weigh?
Session 5: Logic and Reasoning I
- Example: Five girls eat strawberries. Laura eats 2 strawberries more than Sophie. Bettina eats 3 strawberries less than Laura. Clara eats two strawberry more than Bettina and 1 less than Alice. Which two of the girls eat the same number of strawberries?
Session 6: Logic and Reasoning II
- Example: A farmer has cows, cats, sheep and dogs on his farm. There are 20 animals in total. If there are 15 animals that are not cows, and 13 that are not cats, and there are as many sheep as dogs, how many dogs are there?
Session 7: Combinatorics and Counting
- Example: In how many ways can you arrange the letters in the word “MORE”?
Session 8: Word Problems I
- Example: Students are given 9 problems to solve on a math quiz. Each correct answer is 4 points. For each unanswered question 1 point is taken away, and for each incorrect answer 2 points are taken away. Taylor answered 8 questions and got 25 points. How many questions did Taylor answer correctly?
Session 9: Word Problems II
- Example: Last week, Michael rode his scooter from home to the Frozen Yogurt shop to buy a chocolate chip ice cream. After riding 3.5 miles, he realized he had forgotten his wallet at home. He then turned around and rode back 1.5 miles, where he met his sister. She told Michael she was going to buy him the ice cream. So, Michael turned around again and rode another 3.5 miles with his sister, and together they arrived at the Frozen Yogurt shop. What is the distance from Michael’s home to the Frozen Yogurt shop?
Session 10: Mock Competition and Review
- Review of key strategies and concepts
- Practice test—45 minutes to solve 20 problems
Fifth and Sixth grade Student
- Approach mathematics as a powerful tool for innovation, effective communication, and problem-solving.
- Apply their computational fluency and mathematical thinking in understanding and breaking down complex scenarios.
- Deepen intellectual perseverance and creative thinking.
- Articulate their thought process clearly and convincingly.
- Compete with confidence in the following national and international math contests: Noetic; Math Kangaroo; MathLeague; MOEMS.
- Number Sense and Operations (prime numbers, factors, multiples; divisibility rules; fractions, decimals, percents)
- Logic and Reasoning (logical statements; deductive reasoning; truth tables; patterns and sequences)
- Geometry (solid geometry; properties of shapes; angles and symmetry; spatial reasoning)
- Pre-Algebra (variables and expressions; equations and inequalities)
- Combinatorics and Probability (permutations and combinations; basic probability concepts)
- Word Problems (multi-step problems involving real-world contexts; data interpretation; problems requiring critical reading skills)
- Overview of Noetic, Math Kangaroo and MOEMS problem-solving strategies.
- Assessment test—40 minutes to solve 15 problems.
- Example: Which of these fractions is the smallest: 23/12; 22/11; 21/10; 20/9?
- Example: If 2.5% of a number is 15, what is 120% of that number?
- Example: The radius of a circle is twice the length of the side of a square. The square’s perimeter is equal to the diameter of the circle multiplied by what number?
- Example: Noah folds a square piece of paper from left to right, creating a rectangle shape. Then he folds the rectangle shape from top to bottom, creating a square shape. Finally, Noah uses scissors to cut the square shape twice, from left to right and from top to bottom, each time cutting through the middle of the square shape. How many pieces of paper does Noah obtain this way?
- Example: Layla and Zoe play a card game with the following rules: Taking turns, they can take 1, 2, 3, 4 or 5 cards from the pile on each move. Whoever takes the last card loses. At the moment there are 11 cards on the pile and is Zoe’s turn. How many cards should Zoe take so she can be certain to win?
- Example: In how many ways can a family of five sit in a car if both parents must sit in the front?
- Example: Sabrina bought three pumpkin cakes of different sizes. For the first cake she paid half of her money plus $1 more. For the second cake she paid half of her left-over money plus $2 more. For the third cake she paid again half of her left-over money plus $3. After this she had no money left. How much money did Sabrina have to begin with?
- Example: A train crossed a bridge that was 360 meters long in 1 minute. The whole train passed a person standing on the side of the bridge in 12 seconds. How long was the train?
- Review of key strategies and concepts
- Practice test—45 minutes to solve 20 problems