Ontario Math Standards

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Ontario Math Standards - 1st Grade

MathScore aligns to the Ontario Math Standards for 1st Grade. The standards appear below along with the MathScore topics that match. If you click on a topic name, you will see sample problems at varying degrees of difficulty that MathScore generated. When students use our program, the difficulty of the problems will automatically adapt based on individual performance, resulting in not only true differentiated instruction, but a challenging game-like experience.

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View the Ontario Math Standards at other levels.

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; (Counting Squares , Order Numbers to 1000 )
• 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. (Fast Addition , Fast Addition Reverse , Fast Subtraction , Basic Word Problems , Mixed Addition and Subtraction )

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); (Counting Squares , Order Numbers to 1000 )
- 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); (Requires outside materials )
- 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); (Skip Counting )
- 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); (Fast Addition , Fast Addition Reverse , Fast Subtraction , Basic Word Problems , Mixed Addition and Subtraction )
- add and subtract money amounts to 10¢, using coin manipulatives and drawings.

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); (Requires outside materials )
- 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.).

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;* (Geometric Shapes )
• compose and decompose common two-dimensional shapes and three-dimensional figures;
• describe the relative locations of objects using positional language.
* 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.

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."); (Geometric Shapes )
- 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; (Requires outside materials )
- 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);
- 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. (Requires outside materials )

Patterning and Algebra

Overall Expectations
By the end of Grade 1, students will:
• identify, describe, extend, and create repeating patterns; (Patterns: Numbers , Patterns: Shapes , Function Tables , Function Tables 2 )
• demonstrate an understanding of the concept of equality, using concrete materials and addition and subtraction to 10. (Fast Addition , Fast Addition Reverse , Fast Subtraction , Mixed Addition and Subtraction )

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); (Patterns: Shapes )
- identify and extend, through investigation, numeric repeating patterns (e.g., 1, 2, 3, 1, 2, 3, 1, 2, 3, …); (Patterns: Numbers )
- 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."); (Function Tables , Function Tables 2 )
- 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?).

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; (Requires outside materials )
• read and describe primary data presented in concrete graphs and pictographs; (Tally 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); (Tally and Pictographs )
- pose and answer questions about collected data (Sample problem: What was the most popular fruit chosen by the students in your class?). (Tally and Pictographs )

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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