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School City of Hobart |
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School City of Hobart Mathematics |
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Mathematics - Mathematics - Grade 3 |
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Number Sense
The learner will be able to
understand the relationships among numbers, quantities, and place value in whole numbers* up to 1,000. They understand the relationship among whole numbers, simple fractions, and decimals. *whole numbers: 0, 1, 2, 3, etc.
| Strand |
Scope |
Source |
| Number Sense |
Master |
IDOE |
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3.1.1
The learner will be able to
count, read, and write whole numbers up to 1,000.
Example: Write 349 for the number "three hundred forty-nine".
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| Strand |
Scope |
Source |
| Number Sense |
Master |
IDOE |
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3.1.2
The learner will be able to
identify and interpret place value in whole numbers up to 1,000.
Example: Understand that the 7 in 479 represents 7 tens or 70.
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| Strand |
Scope |
Source |
| Number Sense |
Master |
IDOE |
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3.1.3
The learner will be able to
use words, models, and expanded form to represent numbers up to 1,000.
Example: Recognize that 492 + 400 + 90 + 2.
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| Strand |
Scope |
Source |
| Number Sense |
Master |
IDOE |
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3.1.4
The learner will be able to
identify any number up to 1,000 in various combinations of hundreds, tens, and ones.
Example: 325 can be written as 3 hundreds, 2 tens, and 5 ones, or as 2 hundreds, 12 tens, and 5 ones, etc.
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| Strand |
Scope |
Source |
| Number Sense |
Master |
IDOE |
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3.1.5
The learner will be able to
compare whole numbers up to 1,000 and arrange them in numerical order.
Example: What is the smallest whole number you can make using the digits 4, 9, and 1? Use each digit exactly once.
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| Strand |
Scope |
Source |
| Number Sense |
Master |
IDOE |
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3.1.6
The learner will be able to
round numbers less than 1,000 to the nearest ten and the nearest hundred.
Example: Round 548 to the nearest ten.
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| Strand |
Scope |
Source |
| Number Sense |
Master |
IDOE |
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3.1.7
The learner will be able to
identify odd and even numbers up to 1,000 and describe their characteristics.
Example: Find the even number: 47, 106, 357, 629.
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| Strand |
Scope |
Source |
| Number Sense |
Master |
IDOE |
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3.1.8
The learner will be able to
show equivalent fractions* using equal parts. Example: Draw pictures to show that 3/5, 6/10, and 9/15 are equivalent fractions. *equivalent fractions: fractions with the same value (e.g. 1/2, 2/4, 3/6, etc.).
| Strand |
Scope |
Source |
| Number Sense |
Master |
IDOE |
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3.1.9
The learner will be able to
identify and use correct names for numerators and denominators.
Example: In the fraction 3/5, name the numerator and denominator.
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| Strand |
Scope |
Source |
| Number Sense |
Master |
IDOE |
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3.1.10
The learner will be able to
given a pair of fractions, decide which is larger or smaller by using objects or pictures.
Example: Is 3/4 of a medium pizza larger or smaller than 1/2 of a medium pizza? Explain your answer.
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| Strand |
Scope |
Source |
| Number Sense |
Master |
IDOE |
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3.1.11
The learner will be able to
given a set* of objects or a picture, name and write a decimal to represent tenths and hundredths.
Example: You have a pile of 100 beans and 72 of them are lima beans. Write the decimal that represents lima beans as a part of the whole pile of beans. *set: collection of objects, numbers, etc.
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| Strand |
Scope |
Source |
| Number Sense |
Master |
IDOE |
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3.1.12
The learner will be able to
given a decimal for tenths, show it as a fraction using a place-value model.
Example: Show the decimal 0.7 as a fraction using pennies.
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| Strand |
Scope |
Source |
| Number Sense |
Master |
IDOE |
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3.1.13
The learner will be able to
interpret data displayed in a circle graph and answer questions about the situation.
Example: Have the students in your class choose the pizza they like best from these choices: cheese, sausage, pepperoni. Use a spreadsheet to enter the number of students who chose each kind and make a circle graph of the data. Determine the most popular and the least popular kind of pizza, and explain what the circle and each pie slice represent.
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| Strand |
Scope |
Source |
| Number Sense |
Master |
IDOE |
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3.1.14
The learner will be able to
identify whether everyday events are certain, likely, unlikely, or impossible.
Example: It is raining in your neighborhood. Is it certain, likely, unlikely, or impossible that the tree in your front yard will get wet?
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| Strand |
Scope |
Source |
| Number Sense |
Master |
IDOE |
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3.1.15
The learner will be able to
record the possible outcomes for a simple probability experiment.
Example: Predict how many heads and tails will occur if a coin is tossed 10 times. Have a partner toss a coin while you keep a tally of the outcomes. Exchange places with your partner and repeat the experiment. Explain your results to the class.
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| Strand |
Scope |
Source |
| Number Sense |
Master |
IDOE |
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Computation
The learner will be able to
solve problems involving addition and subtraction of whole numbers. They model and solve simple problems involving multiplication and division.
| Strand |
Scope |
Source |
| Problem Solving |
Master |
IDOE |
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3.2.1
The learner will be able to
add and subtract whole numbers up to 1,000 with or without regrouping, using relevant properties of the number system.
Example: 854 - 427 = ? Explain your method.
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| Strand |
Scope |
Source |
| Add/Subtract Whole Numbers |
Master |
IDOE |
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3.2.2
The learner will be able to
represent the concept of multiplication as repeated addition.
Example: Lynn made 3 baskets each week for 4 weeks. Draw a picture to show how many baskets she made.
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| Strand |
Scope |
Source |
| Multiplication Story Problems |
Master |
IDOE |
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3.2.3
The learner will be able to
represent the concept of division as repeated subtraction, equal sharing, and forming equal groups.
Example: Bob shared 10 cookies among 5 friends. Draw a picture to show how many cookies each friend got.
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| Strand |
Scope |
Source |
| Division Story Problems |
Master |
IDOE |
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3.2.4
The learner will be able to
know and use the inverse relationship between multiplication and division facts, such as 6 x 7 = 42, 42 / 7 = 6, 7 x 6 = 42, 42 / 6 = 7.
Example: Find other facts related to 8 x 3 = 24.
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| Strand |
Scope |
Source |
| Multiply/Divide Whole Numbers |
Master |
IDOE |
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3.2.5
The learner will be able to
show mastery of multiplication facts for 2, 5, and 10.
Example: Know the answer to 6 x 5.
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| Strand |
Scope |
Source |
| Multiply Whole Numbers |
Master |
IDOE |
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3.2.6
The learner will be able to
add and subtract simple fractions with the same denominator.
Example: Add 3/8 and 1/8 . Explain your answer.
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| Strand |
Scope |
Source |
| Add Fractions |
Master |
IDOE |
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3.2.7
The learner will be able to
use estimation to decide whether answers are reasonable in addition and subtraction problems.
Example: Your friend says that 79 - 22 = 27. Without solving, explain why you think the answer is wrong.
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| Strand |
Scope |
Source |
| Reasoning/Estimation |
Master |
IDOE |
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3.2.8
The learner will be able to
use mental arithmetic to add or subtract with numbers less than 100.
Example: Subtract 35 from 86 without using pencil and paper.
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| Strand |
Scope |
Source |
| Add/Subtract Whole Numbers |
Master |
IDOE |
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Algebra and Functions
The learner will be able to
select appropriate symbols, operations, and properties to represent, describe, simplify, and solve simple number and functional relationships.
| Strand |
Scope |
Source |
| Problem Solving |
Master |
IDOE |
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3.3.1
The learner will be able to
represent relationships of quantities in the form of a numeric expression or equation.
Example: Bill's mother gave him money to buy three drinks that cost 45 cents each at the concession stand. When he returned to the bleachers, he gave 25 cents change to his mother. Write an equation to find the amount of money Bill's mother originally gave him.
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| Strand |
Scope |
Source |
| Equations |
Master |
IDOE |
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3.3.2
The learner will be able to
solve problems involving numeric equations.
Example: Use your equation from the last example to find the amount of money that Bill's mother gave him, and justify your answer.
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| Strand |
Scope |
Source |
| Equations |
Master |
IDOE |
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3.3.3
The learner will be able to
choose appropriate symbols for operations and relations to make a number sentence true.
Example: What symbol is needed to make the number sentence 4 _ 3 = 12 true?
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| Strand |
Scope |
Source |
| Symbols |
Master |
IDOE |
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3.3.4
The learner will be able to
understand and use the commutative* and associative* rules of multiplication.
Example: Multiply the numbers 7, 2, and 5 in this order. Now multiply them in the order 2, 5, and 7. Which was easier? Why? *commutative rule: the order when multiplying numbers makes no difference (e.g., 5 x 3 = 3 x 5), but note that this rule is not true for division
*associative rule: the grouping when multiplying numbers makes no difference (e.g., in 5 x 3 x 2, multiplying 5 and 3 and then multiplying by 2 is the same as 5 multiplied by 3 x 2), but note that this rule is not true for division
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| Strand |
Scope |
Source |
| Operations: Multiplication |
Master |
IDOE |
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3.3.5
The learner will be able to
create, describe, and extend number patterns using multiplication.
Example: What is the next number: 3, 6, 12, 24, ...? How did you find your answer?
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| Strand |
Scope |
Source |
| Patterns: Create |
Master |
IDOE |
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3.3.6
The learner will be able to
solve simple problems involving a functional relationship between two quantities.
Example: Ice cream sandwiches cost 20 cents each. Find the costs of 1, 2, 3, 4, ... ice cream sandwiches. What pattern do you notice? Continue the pattern to find the cost of enough ice cream sandwiches for the class.
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| Strand |
Scope |
Source |
| Functional Relationships |
Master |
IDOE |
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3.3.7
The learner will be able to
plot and label whole numbers on a number line up to 10.
Example: Mark the position of 7 on a number line up to 10.
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| Strand |
Scope |
Source |
| Functional Relationships |
Master |
IDOE |
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Geometry
The learner will be able to
describe and compare the attributes of plane and solid geometric shapes and use their understanding to show relationships and solve problems.
| Strand |
Scope |
Source |
| Figures: Attributes |
Master |
IDOE |
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3.4.1
The learner will be able to
identify quadrilaterals* as four-sided shapes.
Example: Which of these are quadrilaterals: square, triangle, rectangle? *quadrilateral: a two-dimensional figure with four sides
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| Strand |
Scope |
Source |
| Quadrilaterals |
Master |
IDOE |
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3.4.2
The learner will be able to
identify right angles in shapes and objects and decide whether other angles are greater or less than a right angle.
Example: Identify right angles in your classroom. Open the classroom door until it makes a right angle with one wall and explain what you are doing.
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| Strand |
Scope |
Source |
| Angles |
Master |
IDOE |
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3.4.3
The learner will be able to
identify, describe, and classify: cube, sphere*, prism*, pyramid, cone, cylinder.
Example: Describe the faces of a pyramid and identify its characteristics. *sphere: round ball like a baseball
*prism: solid shape with fixed cross-section (a right prism is a solid shape with two
parallel faces that are congruent polygons and other faces that are rectangles)
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| Strand |
Scope |
Source |
| Figures: Identify |
Master |
IDOE |
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3.4.4
The learner will be able to
identify common solid objects that are the parts needed to make a more complex solid object.
Example: Describe and draw a house made from a prism and a pyramid.
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| Strand |
Scope |
Source |
| Figures: Two-/Three-Dimensional |
Master |
IDOE |
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3.4.5
The learner will be able to
draw a shape that is congruent* to another shape.
Example: Draw a triangle that is congruent to a given triangle. You may use a ruler and pencil or the drawing program on a computer. *congruent: two figures that are the same shape and size
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| Strand |
Scope |
Source |
| Congruence |
Master |
IDOE |
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3.4.6
The learner will be able to
use the terms point, line, and line segment in describing two-dimensional shapes.
Example: Describe the way a triangle is made of points and line segments and how you know it is a triangle.
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| Strand |
Scope |
Source |
| Two-Dimensional Shapes |
Master |
IDOE |
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3.4.7
The learner will be able to
draw line segments and lines.
Example: Draw a line segment three inches long.
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| Strand |
Scope |
Source |
| Lines |
Master |
IDOE |
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3.4.8
The learner will be able to
identify and draw lines of symmetry in geometric shapes (by hand or using technology).
Example: Use pencil and paper or a drawing program to draw lines of symmetry in a square. Discuss your findings.
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| Strand |
Scope |
Source |
| Symmetry |
Master |
IDOE |
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3.4.9
The learner will be able to
sketch the mirror image reflections of shapes.
Example: Hold up a cardboard letter F to a mirror. Draw the letter and the shape you see in the mirror.
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| Strand |
Scope |
Source |
| Reflections |
Master |
IDOE |
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3.4.10
The learner will be able to
recognize geometric shapes and their properties in the environment and specify their locations.
Example: Write the letters of the alphabet and draw all the lines of symmetry that you see.
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| Strand |
Scope |
Source |
| Figures: Real World |
Master |
IDOE |
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Measurement
The learner will be able to
choose and use appropriate units and measurement tools for length, capacity, weight, temperature, time, and money.
| Strand |
Scope |
Source |
| Measurement Concepts |
Master |
IDOE |
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3.5.1
The learner will be able to
measure line segments to the nearest half-inch.
Example: Measure the length of a side of a triangle.
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| Strand |
Scope |
Source |
| Length |
Master |
IDOE |
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3.5.2
The learner will be able to
add units of length that may require regrouping of inches to feet or centimeters to meters.
Example: Add the lengths of three sheets of paper. Give your answer in feet and inches.
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| Strand |
Scope |
Source |
| Length |
Master |
IDOE |
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3.5.3
The learner will be able to
find the perimeter of a polygon*.
Example: Find the perimeter of a table in centimeters. Explain your method. *polygon: two-dimensional shape with straight sides (e.g., triangle, rectangle, pentagon)
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| Strand |
Scope |
Source |
| Perimeter |
Master |
IDOE |
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3.5.4
The learner will be able to
estimate or find the area of shapes by covering them with squares.
Example: How many square tiles do we need to cover this desk?
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| Strand |
Scope |
Source |
| Area |
Master |
IDOE |
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3.5.5
The learner will be able to
estimate or find the volume of objects by counting the number of cubes that would fill them.
Example: How many of these cubes will fill the box?
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| Strand |
Scope |
Source |
| Volume |
Master |
IDOE |
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3.5.6
The learner will be able to
estimate and measure capacity using quarts, gallons, and liters.
Example: This bottle holds one liter. Estimate how many liters the sink holds.
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| Strand |
Scope |
Source |
| Capacity |
Master |
IDOE |
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3.5.7
The learner will be able to
estimate and measure weight using pounds and kilograms.
Example: Estimate the weight of your book bag in pounds.
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| Strand |
Scope |
Source |
| Weight |
Master |
IDOE |
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3.5.8
The learner will be able to
compare temperatures in Celsius and Fahrenheit.
Example: Measure the room temperature using a thermometer that has both Celsius and Fahrenheit units. If the temperature in the room measures 70ºF, will the Celsius measurement be higher or lower?
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| Strand |
Scope |
Source |
| Temperature |
Master |
IDOE |
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3.5.9
The learner will be able to
tell time to the nearest minute and find how much time has elapsed.
Example: You start a project at 9:10 a.m. and finish the project at 9:42 a.m. How much time has passed?
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| Strand |
Scope |
Source |
| Time |
Master |
IDOE |
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3.5.10
The learner will be able to
find the value of any collection of coins and bills. Write amounts less than a dollar using the ¢ symbol and write larger amounts in decimal notation using the $ symbol.
Example: You have 5 quarters and 2 dollar bills. How much money is that? Write the amount.
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| Strand |
Scope |
Source |
| Money |
Master |
IDOE |
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3.5.11
The learner will be able to
use play or real money to decide whether there is enough money to make a purchase.
Example: You have $5. Can you buy two books that cost $2.15 each? What about three books that cost $1.70 each? Explain how you know.
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| Strand |
Scope |
Source |
| Money |
Master |
IDOE |
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3.5.12
The learner will be able to
carry out simple unit conversions within a measurement system (e.g., centimeters to meters, hours to minutes).
Example: How many minutes are in 3 hours?
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| Strand |
Scope |
Source |
| Converting |
Master |
IDOE |
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Problem Solving
The learner will be able to
make decisions about how to approach problems and communicate their ideas.
| Strand |
Scope |
Source |
| Analyzing Problems |
Master |
IDOE |
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3.6.1
The learner will be able to
analyze problems by identifying relationships, telling relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
Example: Solve the problem: "Start with any number. If it is even, halve it. If it is odd, add 1. Do the same with the result and keep doing that. Find what happens by trying different numbers." Try two or three numbers and look for patterns.
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| Strand |
Scope |
Source |
| Analyzing Problems |
Master |
IDOE |
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3.6.2
The learner will be able to
decide when and how to break a problem into simpler parts.
Example: In the first example, find what happens to all the numbers up to 10.
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| Strand |
Scope |
Source |
| Analyzing Problems |
Master |
IDOE |
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3.6.3
The learner will be able to
apply strategies and results from simpler problems to solve more complex problems.
Example: In the first example, use your results for the numbers up to 10 to find what happens to all the numbers up to 20.
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| Strand |
Scope |
Source |
| Strategies |
Master |
IDOE |
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3.6.4
The learner will be able to
express solutions clearly and logically by using the appropriate mathematical terms and notation. Support solutions with evidence in both verbal and symbolic work.
Example: In the first example, explain what happens to all the numbers that you tried.
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| Strand |
Scope |
Source |
| Solution |
Master |
IDOE |
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3.6.5
The learner will be able to
recognize the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
Example: Measure the length and width of a room to the nearest meter to find how many student desks will fit in it. Would this be an accurate enough method if you were carpeting the room?
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| Strand |
Scope |
Source |
| Solution |
Master |
IDOE |
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3.6.6
The learner will be able to
know and use strategies for estimating results of whole-number addition and subtraction.
Example: You buy 2 bags of candy for $1.05 each. The cashier tells you that will be $1.70. Does that surprise you? Why or why not?
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| Strand |
Scope |
Source |
| Strategies |
Master |
IDOE |
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3.6.7
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, notice that the result of adding 1 to an odd number is always even. Use this to check your calculations.
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| Strand |
Scope |
Source |
| Evaluating Solutions |
Master |
IDOE |
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3.6.8
The learner will be able to
decide whether a solution is reasonable in the context of the original situation.
Example: In the example about fitting desks into a room, would an answer of 1,000 surprise you?
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| Strand |
Scope |
Source |
| Evaluating Solutions |
Master |
IDOE |
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3.6.9
The learner will be able to
note the method of finding the solution and show a conceptual understanding of the method by solving similar problems.
Example: Change the first example so that you multiply odd numbers by 2 or 3 or 4 or 5, before adding 1. Describe the pattern you see.
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| Strand |
Scope |
Source |
| Evaluating Solutions |
Master |
IDOE |
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