School City of Hobart Mathematics - Grade 2 In this technological age, mathematics is more important than ever. When students leave school, they are more and more likely to use mathematics in their work and everyday lives - operating computer equipment, planning timelines and schedules, reading and interpreting data, comparing prices, managing personal finances, and completing other problem-solving tasks. What they learn in mathematics and how they learn it will provide an excellent preparation for a challenging and ever-changing future. |
Number Theory |
Number Sense
The learner will be able to understand the relationships among numbers, quantities, and place value in whole numbers* up to 100. They understand that fractions may refer to parts of a set* and parts of a whole. * whole numbers: 0, 1, 2, 3, etc * set: collection of objects, numbers, etc.
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2.1.1
The learner will be able to count by ones, twos, fives, and tens to 100. Example: Count 74 pencils by groups of tens and twos. .
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2.1.2
The learner will be able to identify the pattern of numbers in each group of ten, from tens through nineties. Example: Where on a hundreds chart are the numbers 12, 22, 32, etc.? .
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2.1.3
The learner will be able to identify numbers up to 100 in various combinations of tens and ones. Example: 32 = 3 tens + 2 ones = 2 tens + 12 ones, etc. .
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2.1.4
The learner will be able to name the number that is ten more or ten less than any number 10 through 90. Example: Name the number ten more than 54. .
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2.1.5
The learner will be able to compare whole numbers up to 100 and arrange them in numerical order. Example: Put the numbers in order of size: 95, 28, 42, 31. .
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2.1.6
The learner will be able to match the number names first, second, third, etc. with an ordered set of up to 100 items. Example: Identify the seventeenth letter of the alphabet. .
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2.1.7
The learner will be able to identify odd and even numbers up to 100. Example: Find the odd numbers in this set: 44, 31, 100, 57, 28. .
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2.1.8
The learner will be able to recognize fractions as parts of a whole or parts of a group (up to 12 parts). Example: Divide a cardboard rectangle into 8 equal pieces. Shade 5 pieces and write the fraction for the shaded part. .
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2.1.9
The learner will be able to recognize, name, and compare the unit fractions: 1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/10, and 1/12. Example: Which is larger, 1/3 or 1/6? Explain your answer.
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2.1.10
The learner will be able to know that, when all fractional parts are included, the result is equal to the whole and to one. Example: What is another way of saying six sixths? Explain your answer. .
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2.1.11
The learner will be able to collect and record numerical data in systematic ways. Example: Measure the hand span in whole centimeters of each student in your class. Keep a record of the answers they give you. .
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2.1.12
The learner will be able to represent, compare, and interpret data using tables, tally charts, and bar graphs. Example: Make a tally of your classmates' favorite colors and draw a bar graph. Name the color that is most popular and the color that is the favorite of the fewest people. .
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Whole Numbers |
Computation
The learner will be able to solve simple problems involving addition and subtraction of numbers up to 100.
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2.2.1
The learner will be able to model addition of numbers less than 100 with objects and pictures. Example: Use blocks to find the sum of 26 and 15. .
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2.2.2
The learner will be able to add two whole numbers less than 100 with and without regrouping. Example: 36 + 45 = ? .
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2.2.3
The learner will be able to subtract two whole numbers less than 100 without regrouping. Example: 86 - 55 = ? .
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2.2.4
The learner will be able to understand and use the inverse relationship between addition and subtraction. Example: Understand that 89 - 17 = 72 means that 72 + 17 = 89. .
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2.2.5
The learner will be able to use estimation to decide whether answers are reasonable in addition problems. Example: Your friend says that 13 + 24 = 57. Without solving, explain why you think the answer is wrong. .
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2.2.6
The learner will be able to use mental arithmetic to add or subtract 0, 1, 2, 3, 4, 5, or 10 with numbers less than 100. Example: In a game, Mia and Noah are making addition problems. They make two two-digit numbers out of the four given numbers 1, 2, 3, and 4. Each number is used exactly once. The winner is the one who makes two numbers whose sum is the largest. Mia had 24 and 31; Noah had 21 and 43. Who won the game? How do you know? Show a way to beat both of them. .
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Functions |
Algebra and Functions
The learner will be able to model, represent, and interpret number relationships to create and solve problems involving addition and subtraction.
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2.3.1
The learner will be able to relate problem situations to number sentences involving addition and subtraction. Example: You have 13 pencils and your friend has 12 pencils. You want to know how many pencils you have altogether. Write a number sentence for this problem and use it to find the total number of pencils. .
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2.3.2
The learner will be able to use the commutative* and associative* rules for addition to simplify mental calculations and to check results. Example: Add the numbers 5, 17, and 13 in this order. Now add them in the order 17, 13, and 5. Which was easier? Why? *commutative rule: the order when adding numbers makes no difference (e.g., 5 + 3 = 3 + 5). Note that this rule is not true for subtraction. *associative rule: the grouping when adding numbers makes no difference (e.g., in 5 + 3 + 2, adding 5 and 3 and then adding 2 is the same as 5 added to 3 + 2). Note that this rule is not true for subtraction. .
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Algebraic Concepts |
2.3.3
The learner will be able to recognize and extend a linear pattern by its rules. Example: One horse has 4 legs, two horses have 8 legs, and so on. Continue the pattern to find how many legs five horses have. .
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Numeration |
2.3.4
The learner will be able to create, describe, and extend number patterns using addition and subtraction. Example: What is the next number: 23, 21, 19, 17, __? How did you find your answer? .
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Geometry |
Geometry
The learner will be able to identify and describe the attributes of common shapes in the plane and of common objects in space.
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2.4.1
The learner will be able to construct squares, rectangles, triangles, cubes, and rectangular prisms* with appropriate materials. Example: Use blocks to make a rectangular prism. *rectangular prism: box with 6 rectangles for sides, like a cereal box .
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2.4.2
The learner will be able to describe, classify, and sort plane and solid geometric shapes (triangle, square, rectangle, cube, rectangular prism) according to the number and shape of faces*, and the number of edges and vertices*. Example: How many vertices does a cube have? *face: flat side, like the front of the cereal box *vertices: corners (vertex: corner) .
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2.4.3
The learner will be able to investigate and predict the result of putting together and taking apart two- and three-dimensional shapes. Example: Use objects or a drawing program to find other shapes that can be made from a rectangle and a triangle. Use sketches or a drawing program to show several ways that a rectangle can be divided into three triangles. .
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2.4.4
The learner will be able to identify congruent* two-dimensional shapes in any position. Example: In a collection of rectangles, pick out those that are the same shape and size. *congruent: same shape and size, like the front and back of the cereal box .
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2.4.5
The learner will be able to recognize geometric shapes and structures in the environment and specify their locations. Example: Look for combinations of shapes in the buildings around you. .
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Measurement |
Measurement
The learner will be able to understand how to measure length, temperature, capacity, weight, and time in standard units.
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2.5.1
The learner will be able to measure and estimate length to the nearest inch, foot, yard, centimeter, and meter. Example: Measure the length of your classroom to the nearest foot. .
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2.5.2
The learner will be able to describe the relationships among inch, foot, and yard. Describe the relationship between centimeter and meter. Example: How many inches are in a yard? .
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2.5.3
The learner will be able to decide which unit of length is most appropriate in a given situation. Example: Would you use yards or inches to measure the length of your school books? Explain your answer. .
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2.5.4
The learner will be able to estimate area and use a given object to measure the area of other objects. Example: Make a class estimate of the number of sheets of notebook paper that would be needed to cover the classroom door. Then use measurements to compute the area of the door. .
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2.5.5
The learner will be able to estimate and measure capacity using cups and pints. Example: Make a reasonable estimate of the number of pints a juice pitcher holds. .
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2.5.6
The learner will be able to estimate weight and use a given object to measure the weight of other objects. Example: About how many jellybeans will you need to put on one side of a balance scale to balance with a box of chalk? Count out the number of jellybeans that you guessed would be needed and see whether your estimate was close. Explain the results of your estimation and weighing. .
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2.5.7
The learner will be able to recognize the need for a fixed unit of weight. Example: Estimate the number of paperclips needed to balance with a box of chalk. Will it be the same as the number of jellybeans? Explain your answer. .
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2.5.8
The learner will be able to estimate temperature. Read a thermometer in Celsius and Fahrenheit. Example: What do you think the temperature is today? Look at the thermometer to check. .
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2.5.9
The learner will be able to tell time to the nearest quarter hour, be able to tell five-minute intervals, and know the difference between a.m. and p.m. Example: When does your favorite TV program start? .
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2.5.10
The learner will be able to know relationships of time: seconds in a minute, minutes in an hour, hours in a day, days in a week, and days, weeks, and months in a year. Example: How many days are in a year? .
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2.5.11
The learner will be able to find the duration of intervals of time in hours. Example: Your trip began at 9:00 a.m. and ended at 3:00 p.m. How long were you traveling? .
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2.5.12
The learner will be able to find the value of a collection of pennies, nickels, dimes, quarters, half-dollars, and dollars. Example: You have 3 pennies, 4 nickels, and 2 dimes. How much money do you have? Explain your answer. .
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Problem Solving |
Problem Solving
The learner will be able to make decisions about how to set up a problem.
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2.6.1
The learner will be able to choose the approach, materials, and strategies to use in solving problems. Example: Solve the problem: "Count the number of squares on the surface of a cube. Put two cubes together and count the number of visible squares. Repeat this step with 3, 4, 5, ... cubes in a line. Find a rule for the number of squares." Use blocks to set up the problem. .
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2.6.2
The learner will be able to use tools such as objects or drawings to model problems. Example: In the first example, place blocks together. Each time you add a block, count the number of squares and record it. .
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2.6.3
The learner will be able to explain the reasoning used and justify the procedures selected in solving a problem. Example: In the first example, notice that the number goes up by 4 each time a block is added. Observe that, as you add each cube, you gain 6 squares but lose 2 where the blocks are joined. .
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2.6.4
The learner will be able to make precise calculations and check the validity of the results in the context of the problem. Example: In the first example, check your results by setting out 10 blocks and counting the number of squares on each long side and then the two at the ends. See how this fits with your rule of adding 4 each time. .
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2.6.5
The learner will be able to understand and use connections between two problems. Example: Use the method of the problem you have just solved to find what happens when the cubes are not all in a line. .
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