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School City of Hobart |
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School City of Hobart Mathematics |
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Mathematics - Mathematics - Grade 4 |
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Number Sense
The learner will be able to
understand the place value of whole numbers* and decimals to two decimal places and how whole numbers and decimals relate to simple fractions. *whole numbers: 0, 1, 2, 3, etc.
| Strand |
Scope |
Source |
| Number Sense |
Master |
IDOE |
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4.1.1
The learner will be able to
read and write whole numbers up to 1,000,000.
Example: Read aloud the number 394,734.
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| Strand |
Scope |
Source |
| Number Sense |
Master |
IDOE |
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4.1.2
The learner will be able to
identify and write whole numbers up to 1,000,000, given a place-value model.
Example: Write the number that has 2 hundred thousands, 7 ten thousands, 4 thousands, 8 hundreds, 6 tens, and 2 ones.
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| Strand |
Scope |
Source |
| Number Sense |
Master |
IDOE |
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4.1.3
The learner will be able to
round whole numbers up to 10,000 to the nearest ten, hundred, and thousand.
Example: Is 7,683 closer to 7,600 or 7,700? Explain your answer.
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| Strand |
Scope |
Source |
| Number Sense |
Master |
IDOE |
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4.1.4
The learner will be able to
order and compare whole numbers using symbols for "less than" (<), "equal to" (=), and "greater than" (>).
Example: Put the correct symbol in 328 __ 142.
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| Strand |
Scope |
Source |
| Number Sense |
Master |
IDOE |
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4.1.5
The learner will be able to
rename and rewrite whole numbers as fractions.
Example: 3 = 6/2 = 9/3 = ?/4 = ?/5.
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| Strand |
Scope |
Source |
| Number Sense |
Master |
IDOE |
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4.1.6
The learner will be able to
name and write mixed numbers, using objects or pictures.
Example: You have 5 whole straws and half a straw. Write the number that represents these objects.
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| Strand |
Scope |
Source |
| Number Sense |
Master |
IDOE |
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4.1.7
The learner will be able to
name and write mixed numbers as improper fractions, using objects or pictures.
Example: Use a picture of 3 rectangles, each divided into 5 equal pieces, to write 2 3/5 as an improper fraction.
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| Strand |
Scope |
Source |
| Number Sense |
Master |
IDOE |
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4.1.8
The learner will be able to
write tenths and hundredths in decimal and fraction notations. Know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 = 0.50, 7/4 = 1 3/4 = 1.75).
| Strand |
Scope |
Source |
| Number Sense |
Master |
IDOE |
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4.1.9
The learner will be able to
round two-place decimals to tenths or to the nearest whole number.
Example: You ran the 50-yard dash in 6.73 seconds. Round your time to the nearest tenth.
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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, subtraction, multiplication, and division of whole numbers and understand the relationships among these operations. They extend their use and understanding of whole numbers to the addition and subtraction of simple fractions and decimals.
| Strand |
Scope |
Source |
| Problem Solving |
Master |
IDOE |
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4.2.1
The learner will be able to
understand and use standard algorithms* for addition and subtraction.
Example: 45,329 + 6,984 = ?, 36,296 - 12,075 = ? *algorithm: a step-by-step procedure for solving a problem.
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| Strand |
Scope |
Source |
| Add/Subtract Whole Numbers |
Master |
IDOE |
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4.2.2
The learner will be able to
represent as multiplication any situation involving repeated addition.
Example: Each of the 20 students in your physical education class has 3 tennis balls. Find the total number of tennis balls in the class.
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| Strand |
Scope |
Source |
| Multiplication Story Problems |
Master |
IDOE |
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4.2.3
The learner will be able to
represent as division any situation involving the sharing of objects or the number of groups of shared objects.
Example: Divide 12 cookies equally among 4 students. Divide 12 cookies equally so that each person gets 4 cookies. Compare your answers and methods.
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| Strand |
Scope |
Source |
| Division Story Problems |
Master |
IDOE |
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4.2.4
The learner will be able to
demonstrate mastery of the multiplication tables for numbers between 1 and 10 and of the corresponding division facts.
Example: Know the answers to 9 x 4 and 35 / 7.
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| Strand |
Scope |
Source |
| Multiply Whole Numbers |
Master |
IDOE |
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4.2.5
The learner will be able to
use a standard algorithm to multiply numbers up to 100 by numbers up to 10, using relevant properties of the number system.
Example: 67 x 3 = ?
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| Strand |
Scope |
Source |
| Multiply Whole Numbers |
Master |
IDOE |
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4.2.6
The learner will be able to
use a standard algorithm to divide numbers up to 100 by numbers up to 10 without remainders, using relevant properties of the number system.
Example: 69 / 3 = ?
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| Strand |
Scope |
Source |
| Divide Whole Numbers |
Master |
IDOE |
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4.2.7
The learner will be able to
understand the special properties of 0 and 1 in multiplication and division.
Example: Know that 73 x 0 = 0 and that 42 / 1 = 42.
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| Strand |
Scope |
Source |
| Multiply/Divide Whole Numbers |
Master |
IDOE |
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4.2.8
The learner will be able to
add and subtract simple fractions with different denominators, using objects or pictures.
Example: Use a picture of a circle divided into 6 equal pieces to find 5/6 - 1/3 .
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| Strand |
Scope |
Source |
| Add Fractions |
Master |
IDOE |
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4.2.9
The learner will be able to
add and subtract decimals (to hundredths), using objects or pictures.
Example: Use coins to help you find $0.43 - $0.29.
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| Strand |
Scope |
Source |
| Add/Subtract Decimals |
Master |
IDOE |
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4.2.10
The learner will be able to
use a standard algorithm to add and subtract decimals (to hundredths).
Example: 0.74 + 0.80 = ?
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| Strand |
Scope |
Source |
| Add/Subtract Decimals |
Master |
IDOE |
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4.2.11
The learner will be able to
know and use strategies for estimating results of any whole-number computations.
Example: Your friend says that 45,329 + 6,984 = 5,213. 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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4.2.12
The learner will be able to
use mental arithmetic to add or subtract numbers rounded to hundreds or thousands.
Example: Add 3,000 to 8,000 without using pencil and paper.
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| Strand |
Scope |
Source |
| Reasoning/Estimation |
Master |
IDOE |
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Algebra and Functions
The learner will be able to
use and interpret variables, mathematical symbols, and properties to write and simplify numerical expressions and sentences. They understand relationships among the operations of addition, subtraction, multiplication, and division.
| Strand |
Scope |
Source |
| Number Sentence |
Master |
IDOE |
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4.3.1
The learner will be able to
use letters, boxes, or other symbols to represent any number in simple expressions, equations, or inequalities (i.e., demonstrate an understanding of and the use of the concept of a variable).
Example: In the expression 3x + 5, what does x represent?
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| Strand |
Scope |
Source |
| Expressions |
Master |
IDOE |
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4.3.2
The learner will be able to
use and interpret formulas to answer questions about quantities and their relationships.
Example: Write the formula for the area of a rectangle in words. Now let l stand for the length, w for the width, and A for the area. Write the formula using these symbols.
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| Strand |
Scope |
Source |
| Formulas |
Master |
IDOE |
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4.3.3
The learner will be able to
understand that multiplication and division are performed before addition and subtraction in expressions without parentheses.
Example: You go to a store with 90¢ and buy 3 pencils that cost 20¢ each. Write an expression for the amount of money you have left and find its value.
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| Strand |
Scope |
Source |
| Expressions |
Master |
IDOE |
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4.3.4
The learner will be able to
understand that an equation such as y = 3x + 5 is a rule for finding a second number when a first number is given.
Example: Use the formula y = 3x + 5 to find the value of y when x = 6.
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| Strand |
Scope |
Source |
| Formulas |
Master |
IDOE |
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4.3.5
The learner will be able to
continue number patterns using multiplication and division.
Example: What is the next number: 160, 80, 40, 20, ...? Explain your answer.
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| Strand |
Scope |
Source |
| Operations: Multiply/Divide |
Master |
IDOE |
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4.3.6
The learner will be able to
recognize and apply the relationships between addition and multiplication, between subtraction and division, and the inverse relationship between multiplication and division to solve problems.
Example: Find another way of writing 13 + 13 + 13 + 13 + 13.
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| Strand |
Scope |
Source |
| Problem Solving |
Master |
IDOE |
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4.3.7
The learner will be able to
relate problem situations to number sentences involving multiplication and division.
Example: You have 150 jelly beans to share among the 30 members of your class. Write a number sentence for this problem and use it to find the number of jelly beans each person will get.
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| Strand |
Scope |
Source |
| Number Sentence |
Master |
IDOE |
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4.3.8
The learner will be able to
plot and label whole numbers on a number line up to 100. Estimate positions on the number line.
Example: Draw a number line and label it with 0, 10, 20, 30, ..., 90, 100. Estimate the position of 77 on this number line.
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| Strand |
Scope |
Source |
| Functional Relationships |
Master |
IDOE |
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Geometry
The learner will be able to
show an understanding of plane and solid geometric objects and use this knowledge to show relationships and solve problems.
| Strand |
Scope |
Source |
| Geometric Concepts |
Master |
IDOE |
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4.4.1
The learner will be able to
identify, describe, and draw rays, right angles, acute angles, obtuse angles and straight angles using appropriate mathematical tools and technology.
Example: Draw two rays that meet in an obtuse angle.
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| Strand |
Scope |
Source |
| Angles |
Master |
IDOE |
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4.4.2
The learner will be able to
identify, describe and draw parallel, perpendicular, and oblique lines using appropriate mathematical tools and technology.
Example: Use the markings on the gymnasium floor to identify two lines that are parallel. Place a jump rope across the parallel lines and identify any obtuse angles created by the jump rope and the lines.
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| Strand |
Scope |
Source |
| Lines: Parallel/Perpendicular |
Master |
IDOE |
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4.4.3
The learner will be able to
identify, describe, and draw parallelograms*, rhombuses*, and trapezoids*, using appropriate mathematical tools and technology.
Example: Use a geoboard to make a parallelogram. How do you know it is a parallelogram? *parallelogram: a four-sided figure with both pairs of opposite sides parallel
*rhombus: a parallelogram with all sides equal
*trapezoid: a four-sided figure with one pair of opposite sides parallel
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| Strand |
Scope |
Source |
| Figures: Identify |
Master |
IDOE |
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4.4.4
The learner will be able to
identify congruent* quadrilaterals* and give reasons for congruence using sides, angles, parallels and perpendiculars.
Example: In a collection of parallelograms, rhombuses, and trapezoids, pick out those that are the same shape and size and explain your decisions. *congruent: two figures that are the same shape and size
*quadrilateral: a two-dimensional figure with four sides
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| Strand |
Scope |
Source |
| Congruence |
Master |
IDOE |
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4.4.5
The learner will be able to
identify and draw lines of symmetry in polygons.
Example: Draw a rectangle and then draw all its lines of symmetry.
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| Strand |
Scope |
Source |
| Symmetry |
Master |
IDOE |
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4.4.6
The learner will be able to
construct cubes and prisms* and describe their attributes.
Example: Make a 6-sided prism from construction paper. *prism: solid shape with fixed cross-section (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 |
| Constructions |
Master |
IDOE |
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Measurement
The learner will be able to
understand perimeter and area, as well as measuring volume, capacity, time, and money.
| Strand |
Scope |
Source |
| Measurement Concepts |
Master |
IDOE |
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4.5.1
The learner will be able to
measure length to the nearest quarter-inch, eighth-inch, and millimeter.
Example: Measure the width of a sheet of paper to the nearest millimeter.
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| Strand |
Scope |
Source |
| Length |
Master |
IDOE |
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4.5.2
The learner will be able to
subtract units of length that may require renaming of feet to inches or meters to centimeters.
Example: The shelf was 2 feet long. Jane shortened it by 8 inches. How long is the shelf now?
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| Strand |
Scope |
Source |
| Length |
Master |
IDOE |
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4.5.3
The learner will be able to
know and use formulas for finding the perimeters of rectangles and squares.
Example: The length of a rectangle is 4 cm and its perimeter is 20 cm. What is the width of the rectangle?
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| Strand |
Scope |
Source |
| Perimeter |
Master |
IDOE |
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4.5.4
The learner will be able to
know and use formulas for finding the areas of rectangles and squares.
Example: Draw a rectangle 5 inches by 3 inches. Divide it into one-inch squares and count the squares to find its area. Can you see another way to find the area? Do this with other rectangles.
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| Strand |
Scope |
Source |
| Area |
Master |
IDOE |
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4.5.5
The learner will be able to
estimate and calculate the area of rectangular shapes by using appropriate units, such as square centimeter (cm2), square meter (m2), square inch (in2), or square yard (yd2).
Example: Measure the length and width of a basketball court and find its area in suitable units.
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| Strand |
Scope |
Source |
| Area |
Master |
IDOE |
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4.5.6
The learner will be able to
understand that rectangles with the same area can have different perimeters and that rectangles with the same perimeter can have different areas.
Example: Make a rectangle of area 12 units on a geoboard and find its perimeter. Can you make other rectangles with the same area? What are their perimeters?
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| Strand |
Scope |
Source |
| Area |
Master |
IDOE |
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4.5.7
The learner will be able to
find areas of shapes by dividing them into basic shapes such as rectangles.
Example: Find the area of your school building.
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| Strand |
Scope |
Source |
| Area |
Master |
IDOE |
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4.5.8
The learner will be able to
use volume and capacity as different ways of measuring the space inside a shape.
Example: Use cubes to find the volume of a fish tank and a pint jug to find its capacity.
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| Strand |
Scope |
Source |
| Volume |
Master |
IDOE |
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4.5.9
The learner will be able to
add time intervals involving hours and minutes.
Example: During the school week, you have 5 recess periods of 15 minutes. Find how long that is in hours and minutes.
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| Strand |
Scope |
Source |
| Time |
Master |
IDOE |
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4.5.10
The learner will be able to
determine the amount of change from a purchase.
Example: You buy a chocolate bar priced at $1.75. How much change do you get if you pay for it with a five-dollar bill?
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| Strand |
Scope |
Source |
| Money |
Master |
IDOE |
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Data Analysis and Probability
The learner will be able to
organize, represent, and interpret numerical and categorical data and clearly communicate their findings. They show outcomes for simple probability situations.
| Strand |
Scope |
Source |
| Problem Solving |
Master |
IDOE |
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4.6.1
The learner will be able to
represent data on a number line and in tables, including frequency tables.
Example: The students in your class are growing plants in various parts of the classroom. Plan a survey to measure the height of each plant in centimeters on a certain day. Record your survey results on a line plot.
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| Strand |
Scope |
Source |
| Tables/Charts |
Master |
IDOE |
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4.6.2
The learner will be able to
interpret data graphs to answer questions about a situation.
Example: The line plot below shows the heights of fast-growing plants reported by third-grade students. Describe any patterns that you can see in the data using the words "most," "few," and "none."
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X
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X X
X X
X X X
X X X X X
0 5 10 15 20 25 30 35 Plant Heights in Centimeters
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| Strand |
Scope |
Source |
| Analyzing/Evaluating Graphical Forms |
Master |
IDOE |
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4.6.3
The learner will be able to
summarize and display the results of probability experiments in a clear and organized way.
Example: Roll a number cube 36 times and keep a tally of the number of times that 1, 2, 3, 4, 5, and 6 appear. Draw a bar graph to show your results.
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| Strand |
Scope |
Source |
| Data Analysis |
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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4.7.1
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: "Find a relationship between the number of faces, edges, and vertices of a solid shape with flat surfaces." Try two or three shapes and look for patterns.
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| Strand |
Scope |
Source |
| Analyzing Problems |
Master |
IDOE |
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4.7.2
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 cubes and rectangular solids.
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| Strand |
Scope |
Source |
| Analyzing Problems |
Master |
IDOE |
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4.7.3
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 method for cubes and rectangular solids to find what happens to other prisms and to pyramids.
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| Strand |
Scope |
Source |
| Strategies |
Master |
IDOE |
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4.7.4
The learner will be able to
use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, tools, and models to solve problems, justify arguments, and make conjectures.
Example: In the first example, make a table to help you explain your results to another student.
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| Strand |
Scope |
Source |
| Strategies |
Master |
IDOE |
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4.7.5
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 with all the shapes that you tried.
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| Strand |
Scope |
Source |
| Solution |
Master |
IDOE |
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4.7.6
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: You are telling a friend the time of a TV program. How accurate should you be: to the nearest day, hour, minute, or second?
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| Strand |
Scope |
Source |
| Solution |
Master |
IDOE |
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4.7.7
The learner will be able to
know and use appropriate methods for estimating results of whole-number computations.
Example: You buy 2 CDs for $15.95 each. The cashier tells you that will be $49.90. Does that surprise you?
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| Strand |
Scope |
Source |
| Reasoning/Estimation |
Master |
IDOE |
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4.7.8
The learner will be able to
make precise calculations and check the validity of the results in the context of the problem.
Example: The buses you use for a school trip hold 55 people each. How many buses will you need to seat 180 people?
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| Strand |
Scope |
Source |
| Evaluating Solutions |
Master |
IDOE |
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4.7.9
The learner will be able to
decide whether a solution is reasonable in the context of the original situation.
Example: In the last example, would an answer of 3.27 surprise you?
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| Strand |
Scope |
Source |
| Evaluating Solutions |
Master |
IDOE |
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4.7.10
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 look at shapes with curved surfaces.
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| Strand |
Scope |
Source |
| Evaluating Solutions |
Master |
IDOE |
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