Number concepts to 20 • counting: - counting on and counting back - skip-counting by 2 and 5 - sequencing numbers to 20 - comparing and ordering numbers to 20 - Numbers to 20 can be arranged and recognized. - subitizing - base 10 - 10 and some more • books published by Native Northwest: Learn to Count, by various artists; Counting Wild Bears, by Gryn White; We All Count, by Jason Adair; We All Count, by Julie Flett (nativenorthwest.com) using counting collections made of local materials; counting in different languages; different First Peoples counting systems (e.g., Tsimshian) • Tlingit Math Book (yukon-ed-show-me-your-math.wikispaces.com/file/detail/Tlingit Math Book.pdf)
Ways to make 10 • decomposing 10 into parts • Numbers to 10 can be arranged and recognized. • benchmarks of 10 and 20 • Traditional First Peoples counting methods involved using fingers to count to 5 and for groups of 5. • traditional songs/singing and stories
Change in quantity to 20, concretely and verbally • verbally describing a change in quantity (e.g., I can build 7 and make it 10 by adding 3)
Meaning of equality and inequality • demonstrating and explaining the meaning of equality and inequality • recording equations symbolically, using = and ≠
Addition and subtraction to 20 (understanding of operation and process) • decomposing 20 into parts • mental math strategies: - counting on - making 10 - doubles • Addition and subtraction are related. • whole-class number talks • nature scavenger hunt in Kaska Counting Book (yukon-ed-show-me-your-math.wikispaces.com/file/detail/Kaska Counting Book.pdf)
Addition with a Specific Number
Addition with a Specific Number Up to 10
Add Two Numbers Up to 20
Add Two Numbers Up to 100
Subtracting Zero and All
Subtraction with a Specific Number
Subtract Two Numbers Up to 18
Which Sign Makes the Number Sentence True?
Addition and Subtraction Up to 18
Repeating patterns with multiple elements and attributes • identifying sorting rules • repeating patterns with multiple elements/attributes • translating patterns from one representation to another (e.g., an orange-blue pattern could be translated to a circle-square pattern) • letter coding of pattern • predicting an element in repeating patterns using a variety of strategies • patterns using visuals (ten-frames, hundred charts) • investigating numerical patterns (e.g., skip-counting by 2s or 5s on a hundred chart) • beading using 3–5 colours
Direct measurement with non-standard units (nonuniform and uniform) • Non-uniform units are not consistent in size (e.g., children’s hands, pencils); uniform units are consistent in size (e.g., interlocking cubes, standard paper clips). • understanding the importance of using a baseline for direct comparison in linear measurement • using multiple copies of a unit • iterating a single unit for measuring (e.g., to measure the length of a string with only one cube, a student iterates the cube over and over, keeping track of how many cubes long the string is) • tiling an area • rope knots at intervals • using body parts to measure • book: An Anishnaabe Look at Measurement, by Rhonda Hopkins and Robin King-Stonefish (strongnations.com/store/item_display.php?i=3494&f=) • hand/foot tracing for mitten/moccasin making
Comparison of 2D shapes and 3D objects • sorting 3D objects and 2D shapes using one attribute, and explaining the sorting rule • comparing 2D shapes and 3D objects in the environment • describing relative positions, using positional language (e.g., up and down, in and out) • replicating composite 2D shapes and 3D objects (e.g., putting two triangles together to make a square)
Likelihood of familiar life events, using comparative language • using the language of probability (e.g., never, sometimes, always, more likely, less likely) • cycles (Elder or knowledge keeper to speak about ceremonies and life events)
Concrete graphs, using one-to-one correspondence • creating, describing, and comparing concrete graphs
Values of coins, and monetary exchanges • identifying values of coins (nickels, dimes, quarters, loonies, and toonies) • counting multiples of the same denomination (nickels, dimes, loonies, and toonies) • Money is a medium of exchange. • role-playing financial transactions (e.g., using coins and whole numbers), integrating the concept of wants and needs • trade games, with understanding that objects have variable value or worth (shells, beads, furs, tools)