Math Math Posters Grades 5 – 9 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” 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 ( ) length width width (w) (w) length ( ) Perimeter = (2 x length) + (2 x width) Perimeter = 2 + 2w The Pythagorean Theorem Pythagoras mathematician who made important and astronomy. The Pythagorean Theorem was was a Greek and philosopher contributions to mathematics Pythagoras’ most famous mathematical contribution. A = 45 Volume is the number of cubic units that fill up a solid figure. V = x w x h V = 4 x 3 x 3 V = 36 P = 2 + 2 12) + 2(6) = meters Using the Pythagorean Theorem 58 All About Fractions A graphic overview of equal parts of a whole; equivalent fractions; fractions on a number line; mixed numbers; and adding & subtracting fractions. All About Fractions 15 14 13 18 18 Numerator Denominator 18 18 Halves 18 18 18 18 14 4 8 1 12 1 0 0 0 12 12 1 2 2 14 12 12 14 14 3 2 5 + = 3 2 18 – = + = – = All About Decimals 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. All About Decimals Decimal numbers are another way of writing fractions or mixed numbers. Tenths Hundredths Word Word hundredths tenths ones 0. 7 0 0. 7 8 1. 4 0 Base Blocks Fraction Decimal 0.7 1 1. 3 2 Seven tenths Seventy-eight hundrendths four One hundrendths and four tenths One and 100 Eleven and thirty-two hundrendths Subtracting Decimals tens 0.78 Decimals & Fractions: four tenths of whole numbers. Customary & Metric Units of Measurement Poster A detailed look at key customary and metric units to include length, capacity, weight and temperature. Area is the number of square units needed A = l x w A = 9 x 5 to cover the inside of a figure. Area = 45 square feet 3ft 3ft Volume = 36 cubic feet 5ft 4ft 9ft Perimeter is the distance around a plane figure. P = 2(P = 24 + 12 P = 36 12m 6m 6m Perimeter 36 Volume Perimeter 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, Proportion & Percent Poster An illustrated overview of the key concepts of ratio, proportion and percent as well as the relationship between them. Customary & Metric Units of Measure The Metric System of Measurement is used primarily in most parts of the world. It is a base-ten system. 9 1 4 7 8 1 2 3 4 5 6 7 The Customary System of Measurement is used primarily in the United States. Inch 1 mL foot (ft) inches (in.) MILK 1,000 mg total mass Customary Units Metric Units 10 centimeters (cm) 10 decimeters 1,000 meters Temperature water freezes ºC water boils 100ºC Degrees Celsius (ºC) are metric units of 16 Length yard (yd) feet yard inches mile (mi) yards Capacity 1 2 1 4 quart (qt) pints quart cups Weight pound (lb) ounces (oz) 1 ton (T) pounds Temperature water freezes ºF water boils ºF normal body 98.6ºF temperature Degrees Fahrenheit (ºF) are customary units of Length Capacity Mass 1 Comparing Metric & Customary Measures Length Capacity L ≈ 1.06 qt 1 gal ≈ 3.8 L Weight & Mass 1 1 1 1 ≈ 1 1 1 1 1 12 1 centimeter (cm) 10 millimeters (mm) 1,000 milliliters (mL) 1 decimeter (dm) 1 meter (m) 1 kilometer (km) 1 3 1 36 1 1,760 1 mile 5,280 feet 1 pint (pt) 2 cups liter (L) 10 deciliters (dL) 1 liter (L) 1 gram (g) 1,000 milligrams (mg) 1 16 1 kilogram (kg) 1,000 grams 2,000 322120371 4 IIIIIIIIIIIIIIIIIIIIIIII IIII III IIIIIIIIIIIIIIIIIIIII in. = 2.54 cm m ≈ 39.37 in. m ≈ 1.09 yd km 0.6 mi mi ≈ 1.6 km oz ≈ 28 g kg ≈ 2.2 lb © Copyright NewPath Learning. All Rights Reserved. 34-6801 • Mixed numbers • A number line can be used to compare fractions. • Fractions that represent the same amount of a whole are called – One and one half tomatoes Equal Parts of a Whole Equivalent Fractions Mixed Numbers Fractions on a Number Line 2 equal parts equal parts equal parts equal parts represents the example: same amount as To add fractions with the same denominator: To subtract fractions with the same denominator: Ratio, Proportions & Percent a colon boys to girls girls boys to the 5:7 to 12 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. 10% 5 7 7 12 5 12 1 ÷ 3 2 25% 50 1 50% 75% 100% 80 100 8 2 5 x = = 15 15 15 5 7 1 Count the number of girls: Write a ratio to compare. Ratios can be written in three different ways. 4 = = 12 4 = 4 1 = 4 12 = 12÷3= 4 8 = 8 ÷ 2= 4 Proportion Percent Lemonade Making Directions Percents show up everywhere in our daily lives – sales tax on purchases, tips at restaurants, discounts at stores, hundred”. It is a ratio that compares a number to 100. For example, 36 percent is a ratio of to or out of = water = lemon juice • Mix 4 parts water with 1 part lemon juice. fraction with a denominator 80% 45 www.newpathlearning.com © Copyright NewPath Learning. All Rights Reserved. 34-6801 100 90 80 70 60 50 40 30 20 10 0 -10 -20 -30 200 180 160 140 120 100 80 60 40 20 0 -20 Finding Volume Finding Volume Volume of Prisms Volume of Cylinders 8cm (d) V = r 2 h V diameter (d) = 8cm 42 r = 4cm Volume of Cones Volume of Spheres Volume of Pyramids (r) 9cm 5cm radius (r) = radius (r) = 3.14 • • 9 ••3cm 3cm 8cm 8cm 4cm 6cm • 3 Rectangular Prism Prism (h) ( ) (w) 4cm (b) 12cm (h) (h) (r) (h) V V = V = V = V = 45cm3 452.16cm3 Base area (B) (h) 12 12 V d 2 8cm 2 V = V = 3 h V = B h (B) = B • 4 • 6 = 24 V = 64cm3 V V V 3.14 32 8 3.14 33 4 3.14 27 3.14 9 8 V 75.36cm3 V 113.04cm3 24 8 B = © Copyright NewPath Learning. All Rights Reserved. 34-6801 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! • Pythagoras was one of the first mathematicians to recognize special relationship forms the Pythagorean • The Pythagorean Theorem states that the sum of the squares of the legs b c • 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 • Area of square B = • Area of square C = right angle leg leg a2 b2 c2 a2 b2 c2 c2 9 16 c2 25 c2 25 c2 5 Square B 4cm Substitute for the known Take the square root of both sides. © Copyright NewPath Learning. All Rights Reserved. 34-6801 Add 2.74 + 1.52 2.74 – 1.52 Step Step Step Step Step Step Step Step 2.74 + 1.52 2.74 + 1.52 26 2.74 + 1.52 4.26 – 1.52 – 1.52 – 1.52 – 1.52 7 1.04 78 1 2 1. 2 0 seven tenths one and 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 • Line up the decimal points. • Compare the digits in each column, starting on the left. hundred Line up the decimal points. Add the 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. Subtract the 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 15 www.newpathlearning.com Poster 33-6101 ............................ $19.95 Poster Comprehensive coverage of decimals & fractions; place value; ordering & comparing decimals; and adding & subtracting decimals. 33-6102 ............................ $19.95 33-6103 ............................ $19.95 33-6104 ............................ $19.95 33-6105 ............................ $19.95 2 3 5 6 cm -40 -40 One Gallon One Quart 5 grams 1 gram 500 mg 500 mg temperature. temperature. ºC normal body temperature gallon (gal) quarts www.newpathlearning.com have a whole number and a fraction. equivalent fractions. 3 Thirds 4 Fourths 5 Fifths 6 equal parts Sixths 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. 18 18 2 8 3 8 4 8 5 8 6 8 7 8 8 8 1 10 1 12 12 0 14 2 4 3 4 4 4 1 6 6 6 8 8 1 2 www.newpathlearning.com © Copyright NewPath Learning. All Rights Reserved. 34-6801 10 100 1 10 = = Ratio Fraction form Word form Using to the total number of students total number of students 5 to 7 7 to 12 5 7:12 5:12 25 100 1 4 = = 100 2 = = 75 100 3 4 = = 100 100 10 10 = = 20 20 4 15 Step Equal Ratios: Count the number of boys: Step 2 1 3 What percent of this grid is shaded? among others. Percent means “per 36 100 36 100. • change to an equivalent of 100. 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 (h) 5cm 14 • 12 3.14 16 9 7cm 3cm 3cm 3cm Since the bases are triangles, the area of each triangle is Area of rectangular base cm (h) V = x w x h V = 3.14 168cm3 Height b • h, or • 4 • 7 = 14 4 r 3 r 2 13 •V = = 13 V 13 13 •• •4 3 •• 3 •• •• •13 • •w www.newpathlearning.com The Pythagorean 33-6107 ............................ $19.95 The Pythagorean Theorem the relationship between the sides of a right triangle. This Theorem. of a right triangle equals the square of the length of the hypotenuse. = a2 b2 c2 + = + = 32 + 42 = + = = = =C Square C C C 3cm variables. The length of the hypotenuse is 5cm. www.newpathlearning.com Adding Decimals 2.74 + 1.52 Subtract 1 2 3 4 1 2 3 4 6 1 1 2.74 2.74 2 2.74 22 2.74 1.22 hundreds 10 1.4 4 100 1. 0 4 Place Value Ordering & Comparing Decimals One twenty-one and two tenths 4 10 Form Base Blocks Fraction Decimal Form © Copyright NewPath Learning. All Rights Reserved. 34-6801 15 15 15
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