Possible Big Idea Sets to Base Instruction On

(Big Ideas taken from Marian Small’s, Big Ideas from Dr. Small K-3)

Big Ideas: Big Ideas: Big Ideas: NS&N NS&N NS&N  A number tells how many are in a group.  You can represent a number in a variety  The place value system we use is built on You usually count to determine the size of of ways. Each representation of a number patterns to make our work with numbers a group. can focus on a different aspect of the more efficient. Geo&SS number.  Students gain a sense of the size of  Some attributes of shapes are  To compare and order numbers, we can numbers by comparing them to quantitative, others are qualitative (e.g., compare them to more familiar meaningful benchmark numbers. the fact that a circle is round is benchmark numbers. Data Management qualitative; the fact that a triangle has Patterning  When working with data, you usually three vertices is quantitative)  The mathematical structure of a pattern organize or classify the data into Measurement can be represented in a variety of ways. meaningful categories.  The use of standard measurement units Measurement  Concrete graphs, picture graphs, simplifies communication about the size  Familiarity with known benchmark pictographs, tally charts, bar graphs, and of objects. measurements can help you estimate and line plots are useful for comparing the Curriculum Expectations: calculate other measurements. frequency of data in different categories.  Demonstrate using concrete materials,  There is always value in estimating an  There are always many ways to sort of the concept of conservation of number amount (measurement), sometimes organize data. (e.g., 5 counters represent the number 5, because an estimate is all you need or all Curriculum Expectations: regardless whether they are close that is possible, and sometimes because  Relate numbers to the anchors of 5 and together or far apart) an estimate is a useful check on the 10  Identify and describe common two- reasonableness of an amount dimensional shapes (e.g., circles, triangles, (measurement). rectangles, squares) and sort and classify  Area tells how much material is required them by their attributes (e.g., colour, size, to cover a shape on the surface of an texture, number of sides), using concrete object. Shapes that look different can materials and pictorial representations have the same area.  Identify common two-dimensional shapes Curriculum Expectations: and three-dimensional figures and sort  Represent money amounts to 20 cents, and classify them by their attributes through investigation using coin manipulatives  Use ordinal numbers to thirty-first in meaningful contexts (e.g., identify the days of the month on a calendar)  Relate temperature to experiences of the seasons  Demonstrate examples of equality, through investigation, using a “balance” model  Trace and identify two-dimensional faces of three-dimensional figures, using concrete models  Represent, compare, and order whole numbers to 50, using a variety of tools  Read and print in words whole numbers to ten, using meaningful contexts  Identify and describe various coins using manipulatives or drawings, and state their value  Estimate, measure, and describe area, through investigation using non-standard units  Use the metre as a benchmark for measuring length, and compare the metre with non-standard units  Compose and decompose common two- dimensional shapes and three- dimensional figures Big Ideas: Big Ideas: Big Ideas: NS&N NS&N NS&N  A number tells how many are in a group.  There are a variety of appropriate ways to  You can describe the same portion using To count the number in a group, we often estimate sums and differences depending two or more different fractions, or using a create subgroups and count the number on the numbers involved and the context. fraction and a decimal. of subgroups. Estimates are useful for both checking  To compare the numbers of items in two  Counting is fundamental to number. calculations and because sometimes an sets, you can match the items, one to one, Forms of counting include rote counting, estimate is all that is needed. in the two sets to see whether one set has counting all, counting on, skip counting,  A personal ‘invented’ algorithm is often more. Or, you can compare the position and counting back. more meaningful and sometimes equally of the numbers that describe the two Patterning efficient as a conventional algorithm. quantities in the number sequence.  Some ways of displaying data highlight  There are many situations to which an patterns. operation is applied, and there are many Curriculum Expectations:  Patterns represent identified regularities. procedures, or algorithms, for each There is always an element of repetition, operation.  Compose and decompose numbers up to whether the same items repeat, or  There are relationships between the four 20 in a variety of ways, using concrete whether a ‘transformation,’ for example, operations: materials adding 1, repeats. -you can represent subtraction as the Measurement opposite of addition or vice versa  The unit chosen for a measurement -you can represent multiplication as affects the numerical value of the repeated addition and vice versa measurement; if you use a bigger unit, -you can represent division as repeated fewer units are required. subtraction and vice versa  The same object can be described using -you can represent division as the different measurements. opposite of multiplication and vice versa  Any measurement can be determined in Measurement more than one way.  We use units to make measurement Curriculum Expectations: comparisons simpler. This is only  Count forwards by 1’s, 2’s, 5’s, and 10’s to effective if the same unit is used for both 100, using a variety of tools and strategies objects and the unit is uniform. Curriculum Expectations:  Demonstrate, using concrete materials, the concept of one-to-one  Create a set in which the number of correspondence between number and objects is greater than, less than, or equal objects when counting to the number of objects in a given set.  Demonstrate an understanding of the use  Solve a variety of problems involving the of non-standard units of the same size addition and subtraction of whole  Describe, through investigation using numbers to 20, using concrete materials concrete materials, the relationship and drawings. between the size of a unit and the  Add and subtract money amounts to 10 number of units needed to measure cents, using coin manipulatives and length drawings.  Estimate measure, and record lengths,  Compare two or three objects using heights, and distances measurable attributes  Count backwards from 20 by 2’s and 5’s  Determine, through investigation using a using a variety of tools ‘balance’ model and whole numbers to  Count backwards by 1’s from 20 and any 10, the number of identical objects that number less than 20 with and without the must be added or subtracted to establish use of concrete materials and number equality lines  Solve problems involving the addition and  Estimate the number of objects in a set, subtraction of single-digit whole numbers, and check by counting using a variety of mental strategies  Describe numeric repeating patterns in a  Compare and order objects by their linear hundreds chart measurements, using the same non-  Identify a rule for a repeating pattern standard unit  Identify and extend, through investigation  Solve problems involving the addition and numeric repeating patterns subtraction of single-digit whole numbers,  Create a repeating pattern involving one using a variety of mental strategies attribute  Represent a given repeating pattern in a variety of ways Big Ideas: Big Ideas: Big Ideas: NS&N Geometry and Spatial Sense Data Management and Probability  A fraction is not meaningful without  Locations can be described using  Graphs are powerful data displays, since knowing what the whole is. positional language, maps and grids. visual displays quickly reveal information  You can use a fraction to describe any  Many of the properties and attributes about data. partitions of a whole. Decimals describe that apply to 2-D shapes also apply to 3-D  To collect good first-hand data, you must partitions of wholes to preserve the shapes. decide what collection method is most pattern of the place value system.  Many geometric properties and attributes suitable and how best to pose any  There are always two fractions involved in of shapes are related to measurement. questions required to collect the data. any single fraction situation- the part you Measurement Measurement are considering and the rest of the whole.  The length of an object is the number of  The capacity of an object tells how much  Fractions can represent parts of regions, units along a line or curve on an object. it will hold as a container. A big object parts of sets, or parts of measures. These Length can be the measurement of a can have a smaller capacity than a smaller meanings are equivalent. single measure of the object, such as the object, depending in thickness of the walls Measurement length of a rectangle, or a combined linear or the dimensions of the containers. Curriculum Expectations: measure.  The mass of an object tells how heavy it is.  Divide whole objects into parts and Curriculum Expectations: A big object can have a smaller mass than identify and describe, through  Create symmetrical designs and pictures, a smaller object. investigation, equal-sized parts of the using concrete materials.  Time is a measurement of how long whole, using fractional names  Construct, using a variety of strategies, something takes. Reading a clock, or tools for measuring lengths, heights, and telling time, is not a measurement unless distances in non-standard units. you relate the time to another event.  Construct, using a variety of strategies, Curriculum Expectations: tools for measuring length, heights, and  Estimate, measure, and describe the distances in non-standard units capacity and/or mass of an object,  Describe the relative locations of objects through investigation using non-standard or people using positional language units  Describe the relative locations of objects  Estimate, measure, and describe the on concrete maps, created in the passage of time, through investigation classroom. using non-standard units  Build three-dimensional structures using  Name the months of the year in order, concrete materials, and describe the two- and read the date on a calendar. dimensional shapes the structures contain  Read demonstration digital and analogue  Describe similarities and differences clocks, and use them to identify between an everyday object and a three- benchmark times dimensional figure  Collect and organize primary data …  Identify and describe common three- dimensional figures and sort and classify them by their attributes using concrete materials and pictorial representations

Big Ideas: Data Management and Probability  In a probability situation, you can never be sure what will happen next.  Categorizing events using terms such as likely, certain, impossible, and unlikely is a way of describing probability  It is important not only to read information from graphs but to make inferences, draw conclusions, and make predictions.  In experimental situations, we base our predictions on past events. Curriculum Expectations  Demonstrate an ability to organize objects into categories by sorting and classifying objects using one attribute and by describing informal sorting experiences  Read primary data presented in bar graphs and pictographs, and describe the data using comparative language  Pose and answer questions about collected data  Describe the likelihood that everyday events will occur using mathematical language.  Collect and organize primary data that is categorical and display the data using one-to-one correspondence, prepared templates of concrete graphs and pictographs and a variety of recording methods