Brainix Mathematics
6th grade high school
*) Fully available for Bavarian curriculum
Chapter 1: Rational Numbers 1
1
Introduction of the concept of fraction
The school year begins with a visit to Moritz's birthday party! While eating cake with all the children, the concept of fractions is brought to life.
Contents: The fraction, definition of unit fraction, meaning of numerator and denominator
2
Shares and fractions
After eating cake, the children quench their thirst with lemonade and cocoa and delve deeper into the parts and fractions.
Contents: Calculating fractions with unit fractions and any fractions, calculating fractions with any fractions, calculating the whole from a given part and fraction
3
Expanding and shortening fractions
Next, the presents are unwrapped at the birthday party. Two chocolate bars cause a fight between Moritz and his sister. By expanding and reducing fractions, the learner can settle the argument and divide the chocolate fairly.
Contents: Equal fractions, expanding and reducing, coprime
4
Fractions as quotients
Three of four different games are played on the TRAIN-IX game console. They compete against Moritz in a guitar duel and a car race. In the final game, they can optionally choose between a soccer game or a catwalk game.
Contents: Apparent fractions, negative fractions, set diagram of rational numbers, the sign of negative fractions, absolute value of fractions, opposite number of rational numbers, mixed numbers, converting a fraction into a mixed number, fractions as quotients, calculating proportions of a given fraction and the whole
5
Comparing fractions
The students are still at Moritz's birthday party. Now they're going on an exciting scavenger hunt together.
Contents: Comparison of fractions with the same denominator or numerator, comparison of completely different fractions, the lowest common multiple
6
Introduction to Decimal Fractions
Next up is a race in Moritz Garden. Tracking race times allows for comparison of decimals.
Contents: Decimal fractions in the place value table, converting a decimal fraction into a fraction, converting a fraction into a decimal fraction
7
Rounding decimals
Now it's time to test Moritz's new drone! A flight from the garden to Moritz's grandma's house lets the students learn many interesting things. Afterwards, they play a round of City-Country-River with modified categories.
Contents: Rounding rule, rounding decimals
8
Converting fractions to decimals
Moritz's birthday party is serving pizza for dinner. Spooky Halloween cocktails are being prepared until she arrives. Moritz receives a message from his grandma on his cell phone. Before they can eat the pizza, the table is set and cleared.
Contents: Prime factorization, conversion by division, infinitely recurring decimal fraction
9
Comparing decimals
The pizza still hasn't arrived. Until it arrives, they play cards. Moritz receives a gift from his parents – a telescope. After eating pizza, the guests observe the starry sky together and learn about different constellations and the universe.
Contents: Comparing decimals, comparing decimals with the same sign
Chapter 2: Rational Numbers 2
1
Addition and subtraction of fractions
This chapter takes place in a zoo. With an uncle who works there as a zookeeper, the students first visit the dolphins. There, the students assist the uncle in various activities with the dolphins.
Contents: Addition of like and unlike fractions, subtraction of like and unlike fractions
2
Addition and subtraction of decimals
Today we're off to see the lions! Many exciting facts and activities make the day an extraordinary experience.
Contents: Written addition, written subtraction
3
Multiplication of fractions
The next stop is the monkey enclosure. There, they'll not only get to know different monkey species and assist with feeding, but learn much more.
Contents: Repetition: Commutative law, multiplication with an integer & a mixed number, multiplication of fractions, associative law of multiplication
4
Multiplication of decimals
Next, it's the penguins' turn. Students help with feeding, meet a chick, and learn how long penguins can stay underwater.
Contents: Multiplication by a power of ten, multiplication by another decimal number, repetition of escalation
5
Division von Brüchen
This chapter takes place in a zoo. With an uncle who works there as a zookeeper, the students first visit the dolphins. There, the students assist the uncle in various activities with the dolphins.
Contents: Division is the inverse of multiplication, division of fractions, sign rule for the division of fractions, double fractions
6
Division von Dezimalzahlen
The koalas need feeding too! Unfortunately, we're running out of eucalyptus and need to reorder.
Contents: Fractions with higher numbers in the denominator, division of decimals
7
Powers with negative exponents
The students, along with the zoo's veterinarian, enter the next area, the kangaroo enclosure. They administer appropriate doses of medicine to the sick kangaroos, and the healthy kangaroos receive preventative nutrients.
Contents: Powers with negative exponents
8
Combination of basic arithmetic operations
Now the last day at the zoo begins. With short stops and photo stops, you can now explore the remaining animals.
Contents: Repetition of terms, arithmetic rules, solving practical problems
Chapter 3: Area
1
Repetition of areas and surface areas
Through a virtual adventure with VR glasses, the learners embark on a trip to Nymphenburg Palace.
Contents: Area units, converting area units
2
Comparison of area units
While visiting Nymphenburg Palace, the students meet the architect Ömer. He asks them for help with architectural tasks.
Contents: Area comparison by counting, area comparison across area units, decomposition and complement equality
3
Area of the parallelogram
During a second visit to Nymphenburg Palace, the architect asks Ömer for help. He is tasked with renovating the palace and needs assistance selecting a suitable awning for the breakfast terrace. The gardener also needs assistance in properly laying out the palace's flowerbeds.
Inhalte: Flächeninhalt des Parallelogramms
4
Area of the triangle
Another task is the redesign of the symbol of the ruling house. A tour of the palace and a lion play a special role in this.
Contents: Area of the triangle
5
Area of the trapezoid
The final preparations are underway! The apprentices are helping the gardener, the architect, and the cook with the preparations for the castle hotel's inauguration ceremony.
Contents: Area of the trapezoid, height of the trapezoid
6
Surface area of bodies
Now event manager Tara needs help with the remaining decorations for the opening party of the new, fictitious hotel complex.
Contents: The surface area of a body
Chapter 4: Volume
1
Measure and compare volumes
An exciting Mediterranean cruise begins. While exploring the massive ship, the apprentices get lost and end up in the storeroom with Lucas, the head of logistics.
Contents: Volume, comparison of volumes
2
Volume units
The first stop is Barcelona! After a sightseeing tour, the students stop by an ice cream parlor. From ice cream vendor Pablo, they learn the unit of volume, the "liter." Together, they make their own ice cream. Back on the ship, they help bartender Bernd prepare non-alcoholic cocktails and convert liter units.
Contents: Unit cube, converting volume units, the unit table, volume unit liter
3
Volume of the cuboid
The cruise ship has arrived at the port of Civitavecchia. On the way to breakfast, the students, together with Lucas, pack the sugar cubes into boxes of different sizes and estimate the dimensions of the different boxes.
Contents: Volume of the cuboid, volume of the cube
4
Volume of other bodies
The final destination remains a mystery for now! Through challenging tasks, students must unravel the mystery surrounding the cruise's final destination.
Contents: Volume of composite bodies, disassembly and completion
Chapter 5: Percentages, Data and Charts
1
Introduction to percentage calculations
Die Schulklasse macht einen Ausflug nach Hamburg. Während der Zugfahrt informieren sich die Lernenden mithilfe ihres Smartphones sowohl über das Wetter als auch über Einkaufs- und Ausflugsmöglichkeiten.
Contents: Percent, Fraction & Decimal, Common Percentages
2
Basic equation of percentage calculation
When we arrived in Hamburg, it was raining heavily. No one was prepared for this, and the search for a suitable rain jacket was our top priority.
Contents: Basic equation, rearrangement of the basic equation
3
The rule of three equation
At the fictional chocolate museum "Schokogalaxie" in Hamburg, visitors can discover interesting facts about the history and production of chocolate. At the end, visitors can even make their own chocolate.
Contents: Rule of three, calculation of percentage, interest, calculation of percentage
4
Calculation of the base value
Of course, the Ocean Wonder Aquarium is a must-visit. Besides learning about interesting sea creatures, you can also feed the sharks.
Contents: Alternative representation of percentages, The base value for percentages, Calculating the base value using the basic equation, Calculating the base value using the rule of three
5
Data and relative frequencies
The students visit a traditional Hamburg apple farm. As part of a tablet duel, they master seven stations spread throughout the farm.
Contents: Random experiments, absolute and relative frequencies, four-field table, the law of large numbers
6
diagrams
The mayor of Hamburg City Hall needs help! With knowledge of diagrams, all problems can be solved.
Contents: Background diagrams, strip chart, pie chart, determining the center angle, column chart, bar chart
7
Data and charts
Arriving at the port of Hamburg, the students take a ferry to the container terminal. Along the way, they see various posters, newspaper articles, and diagrams.
Contents: Percentages, misleading diagrams, pictograms
8
Arithmetic mean
The school trip to Hamburg is coming to an end. There are still many new things to discover at the fish market.
Contents: The arithmetic mean
6. Klasse Mittelschule
Chapter 1: Rational Numbers 1
6
Introduction of the concept of decimal fractions
In the first chapter, the students are on a class trip to Italy. In the 6th lesson, they arrive in Florence. There, they explore many different sights, such as the Boboli Gardens and the statue of Cosimo de Medici. While on the trip, the students learn about the concept of decimal fractions.
Contents: Repetition of greater-lesser relations, addition, subtraction, multiplication and division; decimal fraction concept; place value table
8
Adding and subtracting decimals
The students have now arrived in Rome. There, they will go on a scavenger hunt to the various sights and then go on a short shopping trip. During this activity, the students will learn how to add and subtract decimals.
Contents: Repetition of written addition and subtraction; adding and subtracting decimals
Chapter 2
IN DEVELOPMENT
...
5th grade high school
Chapter 1: Natural and integers
1
Zählen und Ordnen
The students embark on a journey through the Altmühltal Nature Park. They begin by learning about natural numbers at the observatory.
Contents: Natural numbers, naming large numbers, number line, ordering of natural numbers
2
The decimal system
On a bike tour to Prunn Castle, the students discover traces from past times - for example, the Middle Ages or even ancient Rome.
Contents: Decimal system, Roman place value system, powers of ten
Chapter 2