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2017_National Catalog_NewPath

Math Math Posters Grades 5 – 9 STANDARDS Visual Overview of Key Math Concepts! Each poster provides a detailed look at a core, standards-based topic. Laminated for years of use! 23” x 35” All About Fractions Poster A graphic overview of equal parts of a whole; equivalent fractions; fractions on a number line; mixed numbers; and adding & subtracting fractions. 33-6101 ............................. $19.95 Area, Volume & Perimeter Area Area formula width (w) width (w) length ( ) length ( ) Area = length x width Area = x w Volume formula height (h) width (w) length ( ) Volume = length x width x height Volume = x w x h Perimeter formula width (w) width (w) length ( ) length ( ) Perimeter = (2 x length) + (2 x width) Perimeter = 2 + 2w Area is the number of square units needed to cover the inside of a figure. A = l x w A = 9 x 5 A = 45 Area = 45 square feet Volume is the number of cubic units that fill up a solid figure. 3ft 3ft V = x w x h V = 4 x 3 x 3 V = 36 Volume = 36 cubic feet Perimeter is the distance around a plane figure. P = 2 + 2 P = 2(12) + 2(6) P = 24 + 12 P = 36 12m 6m 6m Perimeter = 36 meters 9ft Volume 4ft Perimeter 5ft 12m To find the perimeter you may also add the lengths of all sides. P = 12 + 6 + 12 + 6 = 36 www.newpathlearning.com © Copyright NewPath Learning. All Rights Reserved. 34-6801 Ratio, Proportions & Percent 80 100 Step 2 Ratio A ratio is a comparison of two numbers. These numbers are called the terms of the ratio. Write a ratio to compare the number of girls and boys in your classroom. = boy = girl A proportion is an equation showing that two ratios are equal. Ratios that are equal to each other are called equivalent fractions. All About Decimals 78 100 Tenths Hundredths 0. 7 0 0. 7 8 1. 0 4 1. 4 0 Base Blocks Word Fraction Decimal 1 1. 3 2 Seven tenths Seventy-eight hundrendths One and four hundrendths One and four tenths Eleven and thirty-two hundrendths Subtracting Decimals Decimals & Fractions: 0.7 1 1 Subtract the Finding Volume Add the Volume of Prisms Volume of Cylinders V = x w x h V = r 0.78 diameter (d) = 8 cm radius (r) = radius (r) = r = 4 cm 3.14 • 4 2 • 9 Base area (B) Height (h) b • h, or • 4 • 7 = 14 12 12 V V Volume of Cones Volume of Spheres Volume of Pyramids 8 cm 4 3 V = r 3 13 3 • 3.14 • 33 • 3.14 • 9 • 8 4 3 • 3.14 • 27 V = 13 (B) = B = • 3.14 • 32 • 8 4 • w 4 • 6 = 24 The Pythagorean Theorem Pythagoras was a Greek mathematician and philosopher who made important contributions to mathematics and astronomy. The Pythagorean Theorem was Pythagoras’ most famous mathematical contribution. Using the Pythagorean Theorem Square C b c www.newpathlearning.com 54 All About Fractions 15 0 1 + = – = To add fractions with the same denominator: To subtract fractions with the same denominator: All About Decimals Poster Comprehensive coverage of decimals & fractions; place value; ordering & comparing decimals; and adding & subtracting decimals. 33-6102 ............................. $19.95 Area, Volume & Perimeter Poster Features illustrated instruction on the formulas used to determine these key measurements along with graphic examples of calculating the area of a rectangle; perimeter of a plane; and the volume of a solid. 33-6103 ............................. $19.95 Customary & Metric Units of Measurement Poster A detailed look at key customary and metric units to include length, capacity, weight and temperature. 33-6104 ............................. $19.95 Ratio, Proportion & Percent Poster An illustrated overview of the key concepts of ratio, proportion and percent as well as the relationship between them. 33-6105 ............................. $19.95 Customary & Metric Units of Measure 9 1 2 3 4 5 6 7 8 cm 100 90 80 70 60 50 40 30 20 10 0 -10 -20 -30 -40 1 quart (qt) 2 pints 1 quart 4 cups Temperature 200 180 160 140 120 100 80 60 40 20 0 -20 -40 1 2 3 4 5 6 7 Inch 1 mL One Gallon MILK One Quart 1,000 mg total mass 5 grams 1 10 centimeters (cm) 10 decimeters 1,000 meters gram 500 mg 500 mg Customary Units Metric Units Degrees Celsius (ºC) are metric units of temperature. Length Capacity Weight Degrees Fahrenheit (ºF) are customary units of temperature. Length Capacity Mass Temperature The Customary System of Measurement is used primarily in the United States. The Metric System of Measurement is used primarily in most parts of the world. It is a base-ten system. Comparing Metric & Customary Measures Length Capacity Weight & Mass 1 in. = 2.54 cm 1 m ≈ 39.37 in. 1 m ≈ 1.09 yd 1 km ≈ 0.6 mi 1 mi ≈ 1.6 km 1 L ≈ 1.06 qt 1 gal ≈ 3.8 L 1 oz ≈ 28 g 1 kg ≈ 2.2 lb 1 foot (ft) 12 inches (in.) 1 centimeter (cm) 10 millimeters (mm) 1,000 milliliters (mL) 1 decimeter (dm) 1 meter (m) 1 kilometer (km) 1 yard (yd) 3 feet 1 yard 36 inches 1 mile (mi) 1,760 yards 1 mile 5,280 feet 1 pint (pt) 2 cups 1 liter (L) 10 deciliters (dL) 1 liter (L) 1 gram (g) 1,000 milligrams (mg) 1 pound (lb) 16 ounces (oz) 1 kilogram (kg) 1,000 grams 1 ton (T) 2,000 pounds water freezes 32ºF water boils 212ºF normal body 98.6ºF temperature water freezes 0ºC water boils 100ºC 37ºC normal body temperature 1 gallon (gal) 4 quarts IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII www.newpathlearning.com © Copyright NewPath Learning. All Rights Reserved. 34-6801 • Mixed numbers have a whole number and a fraction. • A number line can be used to compare fractions. • Fractions that represent the same amount of a whole are called equivalent fractions. – One and one half tomatoes Equal Parts of a Whole Equivalent Fractions Mixed Numbers Fractions on a Number Line 2 equal parts Halves 3 equal parts Thirds 4 equal parts Fourths 5 equal parts Fifths 6 equal parts Sixths represents the example: same amount as 8 equal parts Eighths 10 equal parts Tenths 12 equal parts Twelfths Adding Fractions Subtracting Fractions 1. Only add the numerators 2. Write the total over the same denominator. 1. Only subtract the numerators 2. Write the difference over the same denominator. 14 13 16 18 18 18 18 18 18 18 18 18 18 2 8 3 8 4 8 4 8 5 8 6 8 7 8 8 8 1 10 1 12 1 12 1 12 0 14 2 4 3 4 4 4 0 12 12 2 2 0 14 12 12 14 14 14 1 3 6 2 6 5 6 + = 3 8 2 8 18 – = 1 Numerator 2 Denominator www.newpathlearning.com © Copyright NewPath Learning. All Rights Reserved. 34-6801 10 100 1 10 = = Ratio Fraction form Word form Using a colon boys to girls girls to the total number of students boys to the total number of students 5 to 7 5:7 7 to 12 5 to 12 7:12 5:12 10% 25 100 1 4 5 7 7 12 5 12 = = 25% 50 100 1 2 = = 50% 75 100 3 4 = = 75% 100 100 10 10 = = 100% 20 20 4 5 x = = 15 15 15 15 Step 5 7 1 Equal Ratios: Count the number of boys: Count the number of girls: Write a ratio to compare. Ratios can be written in three different ways. 4 1 = = 12 3 8 2 4 1 = 4 ÷ 1 = 4 12 3 =12÷3= 4 8 2 = 8 ÷ 2= 4 Proportion Percent What percent of this grid is shaded? Lemonade Making Directions Percents show up everywhere in our daily lives – sales tax on purchases, tips at restaurants, discounts at stores, among others. Percent means “per hundred”. It is a ratio that compares a number to 100. For example, 36 percent is a ratio of 36 to 100 or 36 out of 100. = water = lemon juice • Mix 4 parts water with 1 part lemon juice. • change to an equivalent fraction with a denominator of 100. 80% 45 www.newpathlearning.com © Copyright NewPath Learning. All Rights Reserved. 34-6801 Finding Volume Poster Provides a graphic representation of the formulas used to determine volume along with illustrated examples for prisms, cylinders, cones, spheres and pyramids. 33-6106 ............................. $19.95 8 cm (d) (h) (r) 9 cm 5 cm 5 cm 14 • 12 3.14 • 16 • 9 3 cm 3 cm 7cm 3 cm 3 cm 8 cm 3 cm 4 cm 6 cm • Since the bases are triangles, the area of each triangle is Area of rectangular base 3 cm Rectangular Prism Prism (h) ( ) (w) (h) 4 cm (b) 12 cm (h) (h) (r) (h) 2 h V V = V = V = V = V = 45 cm3 3.14 168 cm3 452.16 cm3 d 2 8cm 2 V = r 2 h 13 V = B • h V = 64 cm3 V V V 13 V 13 V 75.36 cm3 V 113.04 cm3 • 24 • 8 B = www.newpathlearning.com © Copyright NewPath Learning. All Rights Reserved. 34-6801 The Pythagorean Theorem Poster What is the Pythagorean Theorem? How is it applied to problem-solving? A detailed overview of this key geometric concept and its uses! 33-6107 ............................. $19.95 The Pythagorean Theorem • Pythagoras was one of the first mathematicians to recognize the relationship between the sides of a right triangle. This special relationship forms the Pythagorean Theorem. • The Pythagorean Theorem states that the sum of the squares of the legs of a right triangle equals the square of the length of the hypotenuse. • According to the Pythagorean Theorem, the sum of the two green squares, is equal to the area of the blue square. Therefore in algebraic terms, the Pythagorean Theorem is stated as: Find the length of the hypotenuse ( ). A right triangle is a triangle with an angle of 90º. The two sides that form the right angle are called legs. The side opposite the right angle is the hypotenuse. Square A a hypotenuse • Area of square A = a2 • Area of square B = b2 • Area of square C = c2 right angle leg leg a2 + b2 = c2 a2 + b2 = c2 32 + 42 = c2 9 + 16 = c2 25 = c2 25 = c2 5 = C Square B C C 3cm 4cm Substitute for the known variables. Take the square root of both sides. The length of the hypotenuse is 5cm. www.newpathlearning.com © Copyright NewPath Learning. All Rights Reserved. 34-6801 Adding Decimals Add 2.74 + 1.52 2.74 + 1.52 Subtract 2.74 – 1.52 Step 1 Step 2 Step 3 Step 4 Step 1 Step 2 Step 3 Step 4 2.7 4 + 1.5 2 6 2.74 + 1.52 26 2.74 + 1.52 4.26 2.74 – 1.52 2.74 – 1.52 2 2.74 – 1.52 22 2.74 – 1.52 1.22 ones tens tenths hundreds hundredths 7 10 1.04 1.4 4 100 1 2 1. 2 0 Place Value Ordering & Comparing Decimals Decimal numbers are another way of writing fractions or mixed numbers. seven tenths one and four tenths seventy - eight hundredths one and four hundredths • The numbers to the left of the decimal point are whole numbers. • The numbers to the right of the decimal point are parts or fractions of whole numbers. • Line up the decimal points. • Compare the digits in each column, starting on the left. One hundred twenty-one and two tenths 4 10 Form Base Blocks Word Fraction Decimal Form Line up the decimal points. hundredths and regroup if needed. Add the tenths and regroup if needed. Add the ones. Place the decimal point in the sum. Line up the decimal points. hundredths and regroup if needed. Subtract the tenths and regroup if needed. Subtract the ones. Place the decimal point in the difference. www.newpathlearning.com © Copyright NewPath Learning. All Rights Reserved. 34-6801 15 15 15 15 BASED!


2017_National Catalog_NewPath
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