I feel schools and textbooks are in trouble. Audulus makes learning math fun. I’m thinking of getting math textbooks grades 1 - 12 and doing all the lessons in Audulus. All fun and practical like. Any thoughts on this? I hated getting forced into school and don’t want my children (future children) to have to go through the same system. Might as well start laying down the new system now before I have kids, then relax later while they learn though videogames, Audulus, and such later.
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More ride bell!
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Totally, for me there is a game-like crafting element to Audulus. You know how in games like minecraft or zelda: breath of the wild you collect elements and turn them into knew useful items in your inventory? I think of Audulus in those terms quite often. Like I will take some oscillators and a few expressions and suddenly I have a frequency shifter (“you have added +1 weird to your stats”). What happens when I shift the frequency of a drum loop? “New sound added to your inventory”
It definitely helps motivate learning when there is an achievable goal at hand.
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Oh yeah. Dark Cloud 2 had a unique take on that. You take photos and then combine them to make ideas:
You have to collect items to make the ideas after.
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I kind of need to brush up on math anyway…
I forget if i mentioned this already, but i was thinking of making a series of “Know Your Node” style videos on common expressions I use all the time.
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Those are great. I like the jokes you throw in there.
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Btw, for math up to and including grade 5, get the Beast Academy books – not only are they fun (comic book style presentation), but they are deep, too. They are the lead in to the Art of Problem Solving books (which start at pre-algebra) which are amazing. So much better than the math books that existed when I was a kid.
We got them for my son and I must say that I learned a lot, too.
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http://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.txt
Grade 1
The following are highlights of student learning in Grade 1. They are provided to give teachers and parents a quick overview of the mathematical knowledge and skills that students are expected to acquire in each strand in this grade. The expectations on the pages that follow outline the required knowledge and skills in detail and provide information about the ways in which students are expected to demonstrate their learning, how deeply they will explore concepts and at what level of complexity they will perform procedures, and the mathematical processes they will learn and apply throughout the grade.
Number Sense and Numeration: representing and ordering whole numbers to 50; establishing the conservation of number; representing money amounts to 20¢; decomposing and composing numbers to 20; establishing a one-to-one correspondence when counting the elements in a set; counting by 1’s, 2’s, 5’s, and 10’s; adding and subtracting numbers to 20
Measurement: measuring using non-standard units; telling time to the nearest half-hour; developing a sense of area; comparing objects using measurable attributes; comparing objects using non-standard units; investigating the relationship between the size of a unit and the number of units needed to measure the length of an object
Geometry and Spatial Sense: sorting and classifying two-dimensional shapes and threedimensional figures by attributes; recognizing symmetry; relating shapes to other shapes, to designs, and to figures; describing location using positional language
Patterning and Algebra: creating and extending repeating patterns involving one attribute; introducing the concept of equality using only concrete materials
Data Management and Probability: organizing objects into categories using one attribute; collecting and organizing categorical data; reading and displaying data using concrete graphs and pictographs; describing the likelihood that an event will occur
Grade 1: Mathematical Process Expectations
The mathematical process expectations are to be integrated into student learning associated with all the strands.
Throughout Grade 1, students will:
PROBLEM SOLVING
• apply developing problem-solving strategies as they pose and solve problems and conduct
investigations, to help deepen their mathematical understanding;
REASONING AND PROVING
• apply developing reasoning skills (e.g., pattern recognition, classification) to make and
investigate conjectures (e.g., through discussion with others);
REFLECTING
• demonstrate that they are reflecting on and monitoring their thinking to help clarify their
understanding as they complete an investigation or solve a problem (e.g., by explaining to
others why they think their solution is correct);
SELECTING TOOLS AND COMPUTATIONAL STRATEGIES
• select and use a variety of concrete, visual, and electronic learning tools and appropriate
computational strategies to investigate mathematical ideas and to solve problems;
CONNECTING
• make connections among simple mathematical concepts and procedures, and relate mathematical
ideas to situations drawn from everyday contexts;
REPRESENTING
• create basic representations of simple mathematical ideas (e.g., using concrete materials;
physical actions, such as hopping or clapping; pictures; numbers; diagrams; invented
symbols), make connections among them, and apply them to solve problems;
COMMUNICATING
• communicate mathematical thinking orally, visually, and in writing, using everyday
language, a developing mathematical vocabulary, and a variety of representations.
Grade 1: Number Sense and Numeration
Overall Expectations
By the end of Grade 1, students will:
• read, represent, compare, and order whole numbers to 50, and use concrete materials to
investigate fractions and money amounts;
• demonstrate an understanding of magnitude by counting forward to 100 and backwards
from 20;
• solve problems involving the addition and subtraction of single-digit whole numbers, using a
variety of strategies.
Specific Expectations
Quantity Relationships
By the end of Grade 1, students will:
– represent, compare, and order whole numbers to 50, using a variety of tools (e.g., connecting cubes, ten frames, base ten
materials, number lines, hundreds charts) and contexts (e.g., real-life experiences, number stories);
– read and print in words whole numbers to ten, using meaningful contexts (e.g., storybooks, posters);
– demonstrate, using concrete materials, the concept of conservation of number (e.g., 5 counters represent the number 5, regardless whether they are close together or far apart);
– relate numbers to the anchors of 5 and 10 (e.g., 7 is 2 more than 5 and 3 less than 10);
– identify and describe various coins (i.e., penny, nickel, dime, quarter, $1 coin, $2 coin), using coin manipulatives or drawings, and state their value (e.g., the value of a penny is one cent; the value of a toonie is two dollars);
– represent money amounts to 20¢, through investigation using coin manipulatives;
– estimate the number of objects in a set, and check by counting (e.g.,“I guessed that there were 20 cubes in the pile.
I counted them and there were only 17 cubes. 17 is close to 20.”);
– compose and decompose numbers up to 20 in a variety of ways, using concrete materials (e.g., 7 can be decomposed using
connecting cubes into 6 and 1, or 5 and 2, or 4 and 3);
– divide whole objects into parts and identify and describe, through investigation, equal-sized parts of the whole, using
fractional names (e.g., halves; fourths or quarters).
Counting
By the end of Grade 1, students will:
– demonstrate, using concrete materials, the concept of one-to-one correspondence between number and objects when counting;
– count forward by 1’s, 2’s, 5’s, and 10’s to 100, using a variety of tools and strategies (e.g., move with steps; skip count on a number line; place counters on a hundreds chart; connect cubes to show equal groups; count groups of pennies, nickels,
or dimes);
– count backwards by 1’s from 20 and any number less than 20 (e.g., count backwards from 18 to 11), with and without the use of concrete materials and number lines;
– count backwards from 20 by 2’s and 5’s, using a variety of tools (e.g., number lines, hundreds charts);
– use ordinal numbers to thirty-first in meaningful contexts (e.g., identify the days of the month on a calendar).
Operational Sense
By the end of Grade 1, students will:
– solve a variety of problems involving the addition and subtraction of whole numbers to 20, using concrete materials and
drawings (e.g., pictures, number lines) (Sample problem: Miguel has 12 cookies. Seven cookies are chocolate. Use counters
to determine how many cookies are not chocolate.);
– solve problems involving the addition and subtraction of single-digit whole numbers, using a variety of mental strategies (e.g., one more than, one less than, counting on, counting back, doubles);
– add and subtract money amounts to 10¢, using coin manipulatives and drawings.
Grade 1: Measurement
Overall Expectations
By the end of Grade 1, students will:
• estimate, measure, and describe length, area, mass, capacity, time, and temperature, using non-standard units of the same size;
• compare, describe, and order objects, using attributes measured in non-standard units.
Specific Expectations
Attributes, Units, and Measurement Sense
By the end of Grade 1, students will:
– demonstrate an understanding of the use of non-standard units of the same size (e.g., straws, index cards) for measuring
(Sample problem: Measure the length of your desk in different ways; for example, by using several different non-standard
units or by starting measurements from opposite ends of the desk. Discuss your findings.);
– estimate, measure (i.e., by placing nonstandard units repeatedly,without overlaps or gaps), and record lengths, heights, and distances (e.g., a book is about 10 paper clips wide; a pencil is about 3 toothpicks long);
– construct, using a variety of strategies, tools for measuring lengths, heights, and distances in non-standard units (e.g., footprints on cash register tape or on connecting cubes);
– estimate, measure (i.e., by minimizing overlaps and gaps), and describe area, through investigation using non-standard
units (e.g.,“It took about 15 index cards to cover my desk, with only a little bit of space left over.”);
– estimate, measure, and describe the capacity and/or mass of an object, through investigation using non-standard units
(e.g.,“My journal has the same mass as 13 pencils.” “The juice can has the same capacity as 4 pop cans.”);
– estimate, measure, and describe the passage of time, through investigation using nonstandard units (e.g., number of sleeps;
number of claps; number of flips of a sand timer);
– read demonstration digital and analogue clocks, and use them to identify benchmark times (e.g., times for breakfast, lunch, dinner; the start and end of school; bedtime) and to tell and write time to the hour and half-hour in everyday settings;
– name the months of the year in order, and read the date on a calendar;
– relate temperature to experiences of the seasons (e.g.,“In winter,we can skate because it’s cold enough for there to be ice.”).
Measurement Relationships
By the end of Grade 1, students will:
– compare two or three objects using measurable attributes (e.g., length, height, width, area, temperature, mass, capacity),
and describe the objects using relative terms (e.g., taller, heavier, faster, bigger, warmer; “If I put an eraser, a pencil, and a metre stick beside each other, I can see that the eraser is shortest and the metre stick is longest.”);
– compare and order objects by their linear measurements, using the same non-standard unit (Sample problem: Using a length of
string equal to the length of your forearm, work with a partner to find other objects that are about the same length.);
– use the metre as a benchmark for measuring length, and compare the metre with non-standard units (Sample problem: In
the classroom, use a metre stick to find objects that are taller than one metre and objects that are shorter than one metre.);
– describe, through investigation using concrete materials, the relationship between the size of a unit and the number of units needed to measure length (Sample problem: Compare the numbers of paper clips and pencils needed to measure the length of the same table.).
Grade 1: Geometry and Spatial Sense
Overall Expectations
By the end of Grade 1, students will:
• identify common two-dimensional shapes and three-dimensional figures and sort and classify them by their attributes;*
• compose and decompose common two-dimensional shapes and three-dimensional figures;
• describe the relative locations of objects using positional language.
Specific Expectations
Geometric Properties
By the end of Grade 1, students will:
– identify and describe common twodimensional shapes (e.g., circles, triangles, rectangles, squares) and sort and classify
them by their attributes (e.g., colour; size; texture; number of sides), using concrete materials and pictorial representations (e.g.,“I put all the triangles in one group. Some are long and skinny, and some are short and fat, but they all have three sides.”);
– trace and identify the two-dimensional faces of three-dimensional figures, using concrete models (e.g.,“I can see squares
on the cube.”);
– identify and describe common threedimensional figures (e.g., cubes, cones, cylinders, spheres, rectangular prisms) and
sort and classify them by their attributes (e.g., colour; size; texture; number and shape of faces), using concrete materials
and pictorial representations (e.g.,“I put the cones and the cylinders in the same group because they all have circles on
them.”);
– describe similarities and differences between an everyday object and a threedimensional figure (e.g.,“A water bottle
looks like a cylinder, except the bottle gets thinner at the top.”);
– locate shapes in the environment that have symmetry, and describe the symmetry.
Geometric Relationships
By the end of Grade 1, students will:
– compose patterns, pictures, and designs, using common two-dimensional shapes (Sample problem: Create a picture of a
flower using pattern blocks.);
– identify and describe shapes within other shapes (e.g., shapes within a geometric design);
– build three-dimensional structures using concrete materials, and describe the twodimensional shapes the structures contain;
– cover outline puzzles with two-dimensional shapes (e.g., pattern blocks, tangrams) (Sample problem: Fill in the outline of a boat with tangram pieces.).
Location and Movement
By the end of Grade 1, students will:
– describe the relative locations of objects or people using positional language (e.g., over, under, above, below, in front of, behind, inside, outside, beside, between, along);
- For the purposes of student learning in Grade 1, “attributes” refers to the various characteristics of twodimensional
shapes and three-dimensional figures, including geometric properties. (See glossary entries for
“attribute” and “property (geometric)”.) Students learn to distinguish attributes that are geometric properties
from attributes that are not geometric properties in Grade 2.
– describe the relative locations of objects on concrete maps created in the classroom (Sample problem:Work with your group
to create a map of the classroom in the sand table, using smaller objects to represent the classroom objects. Describe
where the teacher’s desk and the bookshelves are located.);
– create symmetrical designs and pictures, using concrete materials (e.g., pattern blocks, connecting cubes, paper for folding), and describe the relative locations of the parts.
Grade 1: Patterning and Algebra
Overall Expectations
By the end of Grade 1, students will:
• identify, describe, extend, and create repeating patterns;
• demonstrate an understanding of the concept of equality, using concrete materials and addition and subtraction to 10.
Specific Expectations
Patterns and Relationships
By the end of Grade 1, students will:
– identify, describe, and extend, through investigation, geometric repeating patterns involving one attribute (e.g., colour, size, shape, thickness, orientation);
– identify and extend, through investigation, numeric repeating patterns (e.g., 1, 2, 3, 1, 2, 3, 1, 2, 3, …);
– describe numeric repeating patterns in a hundreds chart;
– identify a rule for a repeating pattern (e.g., “We’re lining up boy, girl, boy, girl, boy, girl.”);
– create a repeating pattern involving one attribute (e.g., colour, size, shape, sound) (Sample problem: Use beads to make a
string that shows a repeating pattern involving one attribute.);
– represent a given repeating pattern in a variety of ways (e.g., pictures, actions, colours, sounds, numbers, letters) (Sample problem: Make an ABA,ABA,ABA pattern using actions like clapping or tapping.).
Expressions and Equality
By the end of Grade 1, students will:
– create a set in which the number of objects is greater than, less than, or equal to the number of objects in a given set;
– demonstrate examples of equality, through investigation, using a “balance” model (Sample problem: Demonstrate, using
a pan balance, that a train of 7 attached cubes on one side balances a train of 3 cubes and a train of 4 cubes on the
other side.);
– determine, through investigation using a “balance” model and whole numbers to 10, the number of identical objects that
must be added or subtracted to establish equality (Sample problem: On a pan balance, 5 cubes are placed on the left side
and 8 cubes are placed on the right side. How many cubes should you take off the right side so that both sides balance?).
Grade 1: Data Management and Probability
Overall Expectations
By the end of Grade 1, students will:
• collect and organize categorical primary data and display the data using concrete graphs and pictographs, without regard to the order of labels on the horizontal axis;
• read and describe primary data presented in concrete graphs and pictographs;
• describe the likelihood that everyday events will happen.
Specific Expectations
Collection and Organization of Data
By the end of Grade 1, students will:
– demonstrate an ability to organize objects into categories by sorting and classifying objects using one attribute (e.g., colour, size), and by describing informal sorting experiences (e.g., helping to put away groceries) (Sample problem: Sort a collection of attribute blocks by colour. Re-sort the same collection by shape.);
– collect and organize primary data (e.g., data collected by the class) that is categorical (i.e., that can be organized into categories based on qualities such as colour or hobby), and display the data using one-to-one correspondence, prepared templates of concrete graphs and pictographs (with titles and labels), and a variety of recording methods (e.g., arranging objects, placing stickers, drawing pictures, making tally marks) (Sample problem: Collect and organize data about the favourite fruit that students in your class like to eat.).
Data Relationships
By the end of Grade 1, students will:
– read primary data presented in concrete graphs and pictographs, and describe the data using comparative language (e.g.,
more students chose summer than winter as their single favourite season);
– pose and answer questions about collected data (Sample problem: What was the most popular fruit chosen by the students in
your class?).
Probability
By the end of Grade 1, students will:
– describe the likelihood that everyday events will occur, using mathematical language (i.e., impossible, unlikely, less likely, more likely, certain) (e.g.,“It’s unlikely that I will win the contest shown on the cereal box.”).
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Those SVG graphics will come in handy for sure.
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I agree 200% with this. I loved maths before discovering Audulus, but as a kid math class was always a painful and ugly moment. I wonder if such software could help my kids one day.
In that regard I’d say Audulus lacks 2D and 3D plotting. A big part of high-school math is geometry and this is hard to translate into sound.
True. You couldn’t do it it solely on Audulus… Yet. But a vector graphics program, 3D modelling program, or videogame could fill in that area. I make embroidered patches and that software is pure CNC machine x/y graphing. You deal with problems with length, area, density, time, cost…
There are different types of learners: Visual, tactile, readers, listeners, money-see-monkey-do’ers… So I don’t think there could be a one program solution anyway. What I find fun may not be fun for you. I’d just like to provide an “out” for people stuck in a system they do not enjoy.
A Worms 2 type of game would be good to learn about angles, trajectory, velocity, and gravity for example. I play Virtual Pool 4 on my iPad on the bus and I swear it’s an educational game.
Audulus would be good for the earlier grades with making counting machines, multiplying/dividing practical values, arranging and grouping lights… And then there is the whole trigonometric aspect of dealing with waves. That’s the chapter Audulus would excel in.
What worries me is that the system does not want to change. I have a theory that school isn’t about learning everything you need to know in life the most effective way possible. The curriculum leaves out way too many things you actually need to know. How to build a house, how to raise a family, how to grow your own food, how to budget your money, the legal system, your rights… All left out. I think it’s more of an obedience school domestication thing: Get used to going into a building 5 days a week, between these hours, and take breaks when we ring the bell… There’s a good video online about it:
Maybe I’m paranoid, but I smell some serious bullshit being applied to masses of people.
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Killer soundtrack:
Yes yes! Instead of writing convincing essays about how the system is wrong and how it should change, some of us just simply left the cities. There is a lot of work that is just going ahead without everyone, as it always has. I spent years and years going back through a ton of work, to get to the bottom of things. To tell you the truth, it gets to a point where you just realize that becoming formless in social situations will take you the whole way. Becoming militant may get you a genre of friends, but all of the genres seem to be not facing several difficult challenges. The hippy with the van that doesn’t know how an internal combustion engine works, the redneck that turns his nose up at fairtrade organic coffee, which is supposed to help hard working farmers.
I now struggle not to piss people off when I speak – so I basically keep no friend groups, which is fine. When you start chasing the future to become ahead of your time you may not expect the solitude. There are moments when people give up their genres and act as pals. Those are pretty special.
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