Unit 6 Measurement and Data: Area and Volume

Save this PDF as:

Size: px
Start display at page:

Transcription

1 Unit 6 Measurement and Data: Area and Volume Introduction In this unit, students will learn about area and volume. As they find the areas of rectangles and shapes made from rectangles, students will need to multiply fractions. When solving problems that require conversion between units, students will add, subtract, multiply, and divide numbers, including fractions and decimals. Therefore, they need to be able to convert between mixed numbers and improper fractions, and fluently multiply fractions, mixed numbers, and decimals. For details, see the prior knowledge required for each lesson. Capacity vs. Volume Volume and capacity are concepts that are sometimes interchanged. Volume is the amount of space taken up by a three-dimensional object, and capacity is defined as how much a container can hold. While volume is measured in cubic units such as cubic centimeters (cm 3 ) or cubic feet (ft 3 ) capacity is measured in fluid ounces (fl oz), cups (c), gallons (gal), liters (L), etc. Units of capacity are also used to measure the volume of any pourable substance, such as water. Liters are not strictly part of the metric system; the SI or International System of Units has basic units and derivatives and steers clear of multiple units for the same thing. However, liters are compatible with the use of the metric system, specifically for the volume of pourable substances. Liters are commonly used and appealing because they are human-sized, not too large and not too small. Materials Throughout the unit, collect various sizes of boxes (such as shoe boxes, small food and medication packaging boxes, facial tissue boxes) so that students can measure and calculate their volumes in Lessons MD5-29 and MD5-31. Invite students to add to your collection of boxes by bringing some in from home. In Lesson MD5-34, you will also need a rectangular aquarium. Measurement and Data Q-1

2 MD5-23 Area of Rectangles Pages STANDARDS preparation for 5.NF.B.4b Goals Students will find the area of rectangles with whole-number sides and review units of area learned in previous grades. Vocabulary area column row square centimeter (cm 2 ) square inch (in 2 ) square foot (ft 2 ) square kilometer (km 2 ) square millimeter (mm 2 ) square meter (cm 2 ) square yard (yd 2 ) PRIOR KNOWLEDGE REQUIRED Knows the relative size of units of length measurement within the metric and customary US system Can use multiplication to find the number of objects in an array Can multiply and divide mentally up to Can multiply two 2-digit numbers MATERIALS meter sticks or yard sticks pattern block square 1 cm cube 1 ft square floor tile old newspapers or wrapping paper rulers Review counting squares in a rectangular array. Remind students that, when they have an array of rows and columns of the same length, they can use skip counting, repeated addition, or, more efficiently, multiplication to find the total number of squares. To find the number of squares in an array such as the one in the margin, students usually multiply the number of squares along the length of the array (5) by the number of squares along the width of the array (4) for the total (20). Introduce square centimeters as units of area. Explain that squares that have sides of 1 cm each are called square centimeters, and that we write 1 cm 2 for 1 square centimeter. Explain that, when we cover a flat shape with squares of the same size so that there are no gaps or overlaps, the number of squares needed to cover the shape is called its area. A square centimeter is then a unit for measuring area. Draw a rectangle and a square as shown in the margin. ASK: Which shape has a larger area? How do you know? (the square is covered by 4 squares and the rectangle is covered by 3 squares, so the square has a larger area) Determining area of rectangles covered by squares. On the board, draw several rectangles and mark their sides at regular intervals, as shown in the margin, so that students will be able to extend the marks into squares. Ask volunteers to divide the rectangles into squares by using a meter stick or a yardstick to join the marks. Ask students to find the area of the rectangles. Q-2 Teacher s Guide for AP Book 5.2

4 Ask students if they know of anything that is exactly 1 square unit of some kind. If the following examples are not offered, point them out and, if possible, show them: a face of a centimeter cube is 1 cm 2, a pattern block square is 1 in 2, and some floor tiles are 1 ft 2. ACTIVITY (MP.2) Making and comparing unit squares. Assign different square units (1 cm 2, 1 in 2, 1 ft 2, 1 yd 2, 1 m 2 ) to students and have them use wrapping paper or old newspapers to make and label squares of the given size. Have students who are working on the small units (square inch, square centimeter, square foot) make as many squares of the same size as they can, while their peers create single large squares. Have students work in groups to compare and order the units by trying to place one unit on top of the other. Then have them make rectangles from the squares they created to answer questions such as the following: Will a rectangle that is 5 cm by 4 cm fit inside 1 square meter? (yes) Will a rectangle that is 3 ft by 2 ft fit inside 1 square yard? (yes) Will a rectangle that is 4 ft by 1 ft fit inside 1 square yard? (no) Does a rectangle that is 4 ft by 1 ft have a larger area than 1 square yard? (no) How can you show that with unit squares? (a rectangle 4 ft by 1 ft is made of 4 square feet, which all fit together inside a square yard) (MP.1, MP.4) Students can also use a ruler to draw rectangles in small units on the rectangles representing larger units to see if they fit inside. They might ask, for example: Will a rectangle that is 7 mm by 9 mm fit inside 1 cm 2? (yes) Will a rectangle that is 11 in by 7 in fit inside 1 square foot? (yes) How about a rectangle that is 13 in by 7 in? (no) Have students try to cover the part of the rectangle that sticks out from the 1 ft square in square inches, and then see that the leftover part fits inside the 1 ft square together with the rest of the rectangle. Have students conclude that a rectangle measuring 13 in by 7 in has an area smaller than 1 ft 2. Finding area of rectangles in different units. Work through the following problem as a class. Ensure students pay attention to the numbers as well as the units in part b). a) Calculate the area of each rectangle. Include the units. Rectangle D R E V O Length 3 km 8 mm 15 cm 13 cm 21 m Width 2 km 7 mm 6 cm 7 cm 15 m (area: 6 km 2, 56 mm 2, 90 cm 2, 91 cm 2, 315 m 2 ) Q-4 Teacher s Guide for AP Book 5.2

5 b) Jake thinks that rectangle O fits inside rectangle D. Is he correct? Explain. (yes, because 21 m and 15 m are both smaller than 1 km; 1 km = 1,000 m, so this rectangle will fit inside a rectangle that is 3 km long and 2 km wide) c) List the rectangles from greatest area to least area. What state capital does your answer spell? (Dover) Bonus: For what state is it the capital? (Delaware) A B (MP.3) Extensions 1. On grid paper or a geoboard, make as many shapes as possible with an area of 6 squares. For a challenge, try making shapes that have at least one line of symmetry a line that divides a shape into two identical parts that are mirror images of each other. For instance, the shapes in the margin each have an area of 6 square units and one line of symmetry, shown as a thin line. 2. Mario says that shape A in the margin has an area of 4 squares and shape B has an area of 3 squares, so shape A has a larger area than shape B. Explain his mistake. Answer: Each square in shape B is larger than each square in shape A, and three larger squares can have a larger total area than four smaller squares. 3. Explain that perimeter is the distance around a shape. Students should be familiar with this concept from earlier grades. Have them investigate connections between area and perimeter of rectangles using BLM Area and Perimeter (p. Q-66). Measurement and Data 5-23 Q-5

6 MD5-24 Area of Rectangles with Fractions Pages STANDARDS 5.NF.B.4b Goals Students will find the area of rectangles with fractional sides. Vocabulary area denominator formula fraction numerator square centimeter (cm 2 ) square inch (in 2 ) square foot (ft 2 ) square kilometer (km 2 ) square millimeter (mm 2 ) square meter (cm 2 ) square yard (yd 2 ) PRIOR KNOWLEDGE REQUIRED Can multiply numbers including multi-digit whole numbers, fractions, and mixed numbers Knows what area is Can find the area of a rectangle Knows that division of two whole numbers can produce a fraction MATERIALS rulers NOTE: This lesson assumes that students will use quarter-inch grid paper notebooks = Review multiplying fractions. Draw a square on the board and explain that this is one whole. Divide the square into three equal columns. ASK: What fraction does each column represent? (1/3) Then divide the square into four rows and ASK: What fraction of the whole does each row represent? (1/4) Invite a volunteer to outline 2/3 and to shade 3/4, as shown in the margin. ASK: How can you show multiplying 3/4 2/3 using this picture? (3/4 2/3 = 3/4 of 2/3, so the part that is both shaded and outlined in the picture is 3/4 2/3) ASK: How many parts is the whole square divided into? (4 3 = 12) How many parts are both shaded and outlined? (3 2 = 6) What is 3/4 2/3? (6/12) Show the equation in the margin to summarize. Remind students that, when multiplying fractions, they multiply the numerator by the numerator and the denominator by the denominator. (MP.3) (MP.1) Area of rectangles that are parts of a unit square. ASK: What fraction of the square (in the margin and on the board) is one small rectangle? (1/12) How do you know? (the square is divided into 12 equal pieces) SAY: Imagine this square has a length and a width of 1 inch. Label the sides of the square as 1 in. ASK: What is the area of the square? (1 in 2 ) What is the area of the small rectangle? (1/12 in 2 ) What are the length and the width of the rectangle? (1/3 in by 1/4 in) How do you find the area of a rectangle (multiply length by width) What do you get if you multiply 1/3 in by 1/4 in? (1/3 in 1/4 in = 1/12 in 2 ) On grid paper, have students draw 1 in squares and repeat the discussion above. (Four small squares fit along the edge of a large square. There are 16 small squares in a square inch, so each small square has area 1/16 in 2 and length and width 1/4 of an inch, so length width = 1/4 in 1/4 in = 1/16 in 2.) Emphasize that both methods dividing the unit by the number of small squares and multiplying length by width give the same answer. Q-6 Teacher s Guide for AP Book 5.2

8 Exercises: Find the area of the rectangle. a) length 3 ft, width 7 8 ft b) length 3 8 m, width 3 4 m c) length yd, width 5 8 yd d) length Answers a) 21/8 ft 2 = 2 5/8 ft 2 b) 9/32 m 2 c) 25/16 yd 2 = 1 9/16 yd 2 d) 1,161/100 cm 2 Extensions cm, width cm 1. Find the area of the rectangle. a) length 3 m, width 0.7 m b) length 3.8 m, width 3.4 m c) length 2.55 km, width 0.8 km d) length 4.4 cm, width 2.75 cm Answers: a) 2.1 m 2, b) m 2, c) 2.04 km 2, d) 12.1 cm 2 (MP.1) 2. a) 1 yd = 3 ft. How many square feet are in one square yard? b) Convert the dimensions of the rectangle to feet and find the area of the rectangle. i) 12 ft by 5 yd ii) 10 ft by 2 yd iii) 7 ft by yd c) Convert the dimensions of the rectangle to yards and find the area of the rectangle. d) Use your answer in part a) to check that your answers in parts b) and c) are the same. If they are not the same, find your mistake. Answers a) 1 yd 2 = 9 ft 2 b) i) 180 ft 2, ii) 60 ft 2, iii) 115 1/2 ft 2 c) i) 20 yd 2, ii) 6 2/3 yd 2, iii) 12 5/6 yd 2 Q-8 Teacher s Guide for AP Book 5.2

9 MD5-25 Problems with the Area of Rectangles Pages STANDARDS 5.NF.B.4b, 5.NBT.B.7 Goals Students will solve problems connected to the area of rectangles. Vocabulary adjacent area decimal decimal place decimal point denominator factor fraction numerator perimeter square centimeter (cm 2 ) square inch (in 2 ) square foot (ft 2 ) square kilometer (km 2 ) square millimeter (mm 2 ) square meter (cm 2 ) square yard (yd 2 ) PRIOR KNOWLEDGE REQUIRED Can multiply and divide, including multi-digit whole numbers, decimals, fractions, and mixed numbers Can find the area of a rectangle with fractional sides using the formula for the area of a rectangle Knows that division of two whole numbers can produce a fraction Can solve an equation a x = b Knows that a variable can replace a number Knows that area is additive Can find the perimeter of a rectangle Review using a formula for area of a rectangle. Remind students that they can find the area of a rectangle by multiplying length by width. Since order does not matter in multiplication, they can write the factors in any order. Remind them also that we often use letters instead of whole words in formulas, so instead of writing Area = length width = width length, we can write Area = l w = w l. Write both versions of the formula on the board. Show students how to record the information in a problem and the solution. Explain that it makes it easier to check your own work and to check the work of other people if all the information is written out neatly. For example, show students how to record their work when finding area using a formula: Length = 2.8 m Width = 1.5 m Area = l w = 2.8 m 1.5 m = 4.20 m 2 = 4.2 m 2 Review decimals. This example gives you the opportunity to review multiplying decimals. Remind students that we multiply decimals as if they were whole numbers and then shift the decimal point. We add the number of decimal places in the factors to determine the number of decimal places in the product. Sometimes, as in the example above, the last digit in the product is zero. Since it is in the hundredth place, we do not need to write it, so the area is 4.2 m 2 rather than 4.20 m 2. Exercises: Find the area of the rectangle. Show your calculations. a) length 2 m, width 0.6 m b) length 2.8 cm, width 0.4 cm c) length 1.45 km, width 0.8 km d) length 2.4 mm, width mm Answers: a) 1.2 m 2, b) 1.12 cm 2, c) 1.16 km 2, d) 30.6 mm 2 Measurement and Data 5-25 Q-9

10 When students have finished, have them check their work with a partner. Point out that, if students have written the information and the calculations neatly, they will easily see not only if the answers are different, but also why they are different. Using equations for the area of a rectangle to find the missing dimension. Remind students that they can use a letter for an unknown number in a problem. For example, a rectangle has a length of 7 cm and width of w cm. The rectangle s area is 35 cm 2. Have students record this information. SAY: In this case, we can write an equation for the area: w 7 = 35. Write the equation on the board and have students copy it. ASK: What number will make the equation true? (5) How do you know? (5 7 = 35) Remind students that multiplication and division are related, so if 5 7 = 35, there is an equation from the same fact family that has 5 as the answer. ASK: What equation is that? (35 7 = 5) Remind students that they ve learnt to write an equation where the unknown number is by itself, and that s what they could do to solve this equation. Write the solution on the board: w 7 = 35 w = 35 7 = 5 ASK: What units will the answer be in? (cm) How do you know? (the area is in cm 2 and the length is in centimeters, so the width has to be in centimeters) Add the units to the answer: w = 5 cm. Exercises: Write an equation for the area of the rectangle. Then find the unknown length. Bonus a) Width = 5 cm b) Width = 6 km Width = 15 m Length = l cm Length = l km Length = l m Area = 55 cm 2 Area = 96 km 2 Area = 675 m 2 Answers: a) 11 cm, b) 16 km, Bonus: 45 m Review dividing decimals and fractions by a whole number. Exercises: Write an equation for the area of the rectangle. Then find the unknown length or width. a) Width = 5 m b) Width = w in c) Width = 3 ft Length = l m Length = 7 in Length = l ft Area = m 2 Area = in2 Area = 20 ft 2 Bonus: Width = w yd, Length = 6 yd, Area = 1 2 yd2 Answers: a) 8.25 m, b) 2 1/4 in, c) 20/3 ft = 6 2/3 ft, Bonus: 21/12 yd = 7/4 yd = 1 3/4 yd Q-10 Teacher s Guide for AP Book 5.2

14 d) 1 square mile = 640 acres. Use a calculator to find how many square yards and square feet are in one square mile. e) 1 mi = 1,760 yd. How many square yards are in 1 square mile? Did you get the same answer as in d)? If not, find your mistake. Answers a) 4,840 square yards b) 9 square feet c) 43,560 square feet d) 1 square mile = 3,097,600 square yards = 27,878,400 square feet e) 1 square mile = 3,097,600 square yards 3. On a grid, draw a square with sides 7 units long. a) Find the area and the perimeter of the square. (MP.1) b) Inside the square, draw a shape that has an area smaller than the area of the square and perimeter larger than the perimeter of the square. There are many possible answers. Answer: a) area = 49 square units, perimeter = 28 units Sample answer b) The shape below is one possibility, with area = 17 square units and perimeter = 36 units Q-14 Teacher s Guide for AP Book 5.2

16 height width length that the vertical dimension in 3-D objects is called the height. Display the picture in the margin and identify the length, width, and height of the stack. Then write the following equation on the board and use the terms length, width, and height to label the multiplication statement that gives the number of cubes in the stack: = 24 length width height Draw several stacks on the board and ask students to find the number of cubes in each stack by multiplying length, width, and height. Remind students that order does not matter in multiplication, so the number of cubes can be found in other ways, such as height length width or width length height. ACTIVITY Students work in pairs. Each student creates several rectangular stacks of connecting cubes, and then exchange stacks with their partner. Ask students find the number of cubes in the stacks created by their partner by multiplying length, width, and height. (MP.2) Discuss how the dimensions in the formula length width height are related to the layers in a stack. ASK: What part of the formula gives you the number of cubes in one horizontal layer? (length width) Then you multiply by the number of horizontal layers, which is height. Repeat with a vertical layer (width height). Extension (MP.1) Use connecting cubes. a) How many ways can you build a rectangular stack of 36 cubes with a height of 3 cubes? b) How many ways can you build a rectangular stack with 48 cubes? Answers a) 3 ways; dimensions in order of length width height: , 6 2 3, b) 9 combinations of dimensions (with different arrangements of the same dimensions possible): , , , , , 8 3 2, 8 6 1, 6 4 2, Q-16 Teacher s Guide for AP Book 5.2

17 MD5-27 Volume Pages STANDARDS 5.MD.C.3a, 5.MD.C.3b, 5.MD.C.4, 5.MD.C.5a, 5.MD.C.5b Goals Students will develop and use the formula Volume = length width height for the volume of rectangular prisms. PRIOR KNOWLEDGE REQUIRED Vocabulary area cubic centimeter (cm 3 ) cubic inch (in 3 ) cubic foot (ft 3 ) cubic kilometer (km 3 ) cubic meter (cm 3 ) cubic millimeter (mm 3 ) cubic yard (yd 3 ) formula height rectangular prism volume Can find the area of a rectangle using the formula Can find the number of blocks in a rectangular stack Can multiply two-digit numbers Is familiar with units for measuring length and can convert between the units within the same system MATERIALS connecting cubes BLM Cube Skeleton (p. Q-67) old newspapers or wrapping paper tape centimeter cubes for demonstration cubic inch cubes constructed from the net on BLM Cubic Inch (p. Q-68) glue prism sample, such as a facial tissue box Introduce volume. Remind students that area is the amount of twodimensional (flat) space a shape takes up. We measure area in square units squares that have all sides 1 length unit long. Hold up two shapes made from connecting cubes, one made from 3 cubes and another made from 4 cubes. ASK: Which shape takes up more threedimensional space? (the shape made from 4 cubes) How do you know? (it is made from more cubes) Explain that the space taken up by a box or a cupboard or any other three-dimensional object in other words, an object that has length, width, and height is called volume. We measure volume in cubic units: units that are cubes. Introduce standard cubic units. Draw several cubes on the board and mark the sides as 1 cm for one cube, 1 in for another cube, 1 m for another cube, and so on. Explain that these represent different cubic units: cubic centimeter, cubic inch, cubic meter, etc. Show the abbreviated form for each unit: cubic centimeter (cm 3 ) cubic inch (in 3 ) cubic meter (m 3 ) Measurement and Data 5-27 Q-17

18 1 ft ACTIVITY 1 unit 1 unit Divide students into three groups and assign a unit to each group: ft 3, yd 3, or m 3. Have students roll old newspapers or wrapping paper into tubes slightly longer than the unit they were assigned (to allow for binding at the ends). Mark the unit on each tube as shown in the margin. Students might need to combine several newspapers to produce a longer tube. Have each group produce 12 tubes. Give each group tape and BLM Cube Skeleton and have them create skeletons of their assigned units to scale (see sample cube skeleton in margin). (MP.5) Comparing cubic units. NOTE: To prepare, have a centimeter cube to show 1 cm 3 and create a cube from BLM Cubic Inch to show 1 in 3. Compare the relative sizes of the units with students: cubic inch, cubic centimeter, cubic foot, cubic yard, and cubic meter. Point out that cubic meters and cubic yards are very large. For example, to fill an aquarium with a volume of one cubic meter or one cubic yard, you would need about 100 large pails of water! 5 m 4 m Finding the volume of rectangular prisms. Explain that a threedimensional object, such as a cupboard or a box, has length, width, and height. Show a stack of centimeter cubes, and review how to find the number of cubes in a stack. (multiply length, width, and height) ASK: How many cubes are in the stack? (3 4 2 = 24) Explain that the volume of this stack is 24 cubic centimeters. Draw several stacks of cubes on the board and explain that the cubes in each stack are unit cubes. Mark the size of each cube drawing, using different units for different pictures. Have students find the volume of each stack. On the board, draw the rectangular prism shown in the margin. Explain that mathematicians call rectangular boxes rectangular prisms. ASK: What is the length of this prism? (5 m) What is the width of this prism? (3 m) What is the height of this prism? (4 m) Record the information on the board: 3 m Length = 5 m Width = 3 m Height = 4 m SAY: Imagine this is a container, and I want to pack it with cubes that each measure 1 m by 1 m by 1 m. How many cubes would fit along the length of this container? (5) Width? (3) Height? (4) How many cubes in total would fit in the container? (60) How do you know? (5 3 4 = 60; volume = length width height) Have students write the multiplication statement. What is the volume of the prism? (60 m 3 ) Point out that students found the volume of the prism even though you did not draw the cubes that filled it. ASK: What did you do to find the volume? (multiplied the dimensions: length width height) Write the formula Volume = length width height on the board, and explain that it is also convenient to use the short form V = l w h. Q-18 Teacher s Guide for AP Book 5.2

19 6 in 2 in 3 in On the board, draw the prism in the margin. Have students write the multiplication statement for its volume. Explain that, when finding volume, it helps to write the units for each measurement in the multiplication statement to prevent mistakes. For example, for this prism, the multiplication statement should be: Volume = 6 in 2 in 3 in = 36 in 3 Explain that writing the units in the equation helps to see that there are three dimensions. Explain also that a few lessons later, students will see prisms where the dimensions for one prism are given in different units, so writing the units in the equations will be even more important. Point out that the raised 3 that appears in the cubic units is the number of length measurements that were multiplied together to make the cubic unit: you multiplied three measurements length, width, and height to get the volume. All three measurements were in inches, so the result is in cubic inches. Point to the raised 3 in in 3. Point out that, in area, we also use a raised number in the units. In units of area, we multiply two dimensions length and width and the result is square units, for example, square inches. Write in 2 on the board and point to the raised 2. ASK: Where have you seen a similar notation with numbers? (in exponents) Point out the similarity: = 2 3 = 8 2 in 2 in 2 in = 8 in 3 Exercises: Find the volume of the rectangular prism. Include the units in your calculation and answer. 8 ft a) 2 cm b) 7 ft 10 cm 6 cm 2 ft c) 4 km 7 km 3 km 3 m 4 m e) length 11 in, width 6 in, height 11 in f ) length 3 ft, width 3 ft, height 3 ft g) length 12 in, width 12 in, height 12 in h) length 100 cm, width 100 cm, height 100 cm d) 15 m Answers: a) 120 cm 3, b) 112 ft 3, c) 84 km 3, d) 180 m 3, e) 726 in 3, f) 27 ft 3, g) 1,728 in 3, h) 1,000,000 cm 3 Measurement and Data 5-27 Q-19

20 (MP.5) Bonus: Use some of your answers above to convert these units. a) 1 yd 3 = ft 3 b) 1 m 3 = cm 3 c) 1 ft 3 = in 3 Answers: a) 1 yd 3 = 27 ft 3, b) 1 m 3 = 1,000,000 cm 3, c) 1 ft 3 = 1,728 in 3 Show that volume does not depend on orientation. Show students a prism that has different measurements for length, width, and height, such as a tissue box. Write its dimensions to the nearest centimeter on the board. Have students find the volume of the prism. Then turn the prism. ASK: Did the height of the prism change? (yes) The length? (yes) The width? (yes) Do you expect the volume to change? (no) Why not? (rotating the box does not change the volume, the space that the prism takes up; the dimensions are the same but we multiply them in a different order) 2 cm 5 cm 3 cm 3 cm 3 cm 2 cm (MP.4) Extensions 1. Find the volume of the shape in the margin. Answer: (3 cm 2 cm 5 cm) + (3 cm 2 cm 3 cm) = 48 cm 3 2. a) Choose a cubic unit: m 3, yd 3, or ft 3. Guess the volume of the classroom in the unit you chose. b) Estimate the length, width, and height of the classroom in the matching linear unit. For example, if you chose m 3, estimate in meters. c) Measure the length, width, and height of the classroom in your unit. Then calculate the volume of the classroom. How close was your guess? 3. During an excavation of an old military fort from the War of 1812, an underground ammunition storage room was discovered. The room is 10 ft long, 6 ft wide, and 4 ft deep. Several ammunition crates measuring 2 ft by 1 ft by 1 ft each were found in the room. What is the greatest number of crates that would fit in the room? Answer: The 2 ft edge can be placed along any side of the storage room. One way to do so would be to place 5 crates along the length of the storage room, 6 along the width, and 4 along the height. This means 120 crates (5 6 4 = 120) could fit in the room. Q-20 Teacher s Guide for AP Book 5.2

21 MD5-28 Nets of Rectangular Prisms Pages STANDARDS 5.MD.C.4 Goals Students will draw nets for rectangular prisms. Vocabulary back, bottom, front, left side, right side, top face edge face height hidden edges net rectangular prism skeleton vertex, vertices PRIOR KNOWLEDGE REQUIRED Can draw squares and rectangles of given dimensions Can identify rectangles of the same size and shape MATERIALS skeleton of a cube made from toothpicks and modeling clay two paper squares to act as faces four transparency squares to act as faces BLM Net of Rectangular Prism (p. Q-69) boxes (e.g., medication boxes) connecting cubes box labeled with the names of faces (back, bottom, etc.) NOTE: Before the lesson, prepare a cube skeleton from toothpicks and modeling clay. Cut out two paper squares and four transparency squares to act as faces. Label the paper squares bottom face and back face, and the transparency squares front face, top face, left-side face, and right-side face. Also, cut out the net from BLM Net of Rectangular Prism. Introduce faces, vertices, and edges. Explain that the flat surfaces of 3-D shapes are called faces. Hold up a box and have students count how many faces it has. (6) Explain that the line segments along which faces meet are called edges. Run your finger along the edges of the box. Explain that the corners of the shape, where edges meet, are called vertices. Each corner is one vertex. Show the vertices on the box. Introduce the names of different faces. Display the cube skeleton and add the square faces one at a time, emphasizing each face s position and name that is, bottom face and back face and then front face, top face, left-side face, and right-side face. Identifying hidden edges. Trace the edges of the cube with your finger one at a time and ASK: Can you see this edge directly or only through the transparent face? If the transparent faces were made of paper, would you see this edge? Students can signal the answer with thumbs up or thumbs down. Explain that the edges that would be invisible if all the faces were non-transparent are called the hidden edges. Draw a picture of a skeleton of a cube. Have a volunteer show the vertices of the actual cube. Point out that the vertices are the only places where the Measurement and Data 5-28 Q-21

22 edges of the cube meet. Explain to students that hidden edges are often drawn using dashed lines. Have volunteers draw the edges, showing the hidden edges as dashed lines, as shown in the margin. Point out that, in the picture on the board, the dashed lines and the solid lines seem to intersect but the edges don t intersect in this way on the actual cube. In other words, where the arrows point in the diagram below, there is no vertex. Not a vertex Introduce nets. Explain to students that a net of a 3-D shape is a pattern that can be folded to make the shape. Show a cut-out from BLM Net of Rectangular Prism and show how it folds to produce a prism. Ahead of time, label faces of a box with the names of the faces. Use the box to demonstrate how to make a net of it by tracing the bottom face onto paper, then rolling the box so that the front face can be traced onto the paper adjacent to the first face, then the top face, and then the back face. Then roll the prism to the sides and trace the side faces, so that each side face attaches to a bottom, front, top, or back face. Point out that you could attach the side faces at different places, depending on the face the prism was standing on before you rolled it sideways. Also, point out that both side faces do not have to be attached to the same face. For example, all three nets below fold into the same box. (MP.7) ACTIVITY Producing a net for a rectangular prism. Give each student a different box and have them produce a net the same way you produced the net for a box. Have them fold the net and check that it creates a copy of the box, and then unfold it. Have students assemble in groups of four, exchange boxes, and mix up their nets. Have students find the net for the box that they now have. Discuss matching strategies. For example, students can try to identify the number of square faces the box has, and look for a net with the same number of square faces. Q-22 Teacher s Guide for AP Book 5.2

23 leftside face top face back face bottom face front face rightside face Labeling faces on a net. Return to the box you used earlier. Place the box on the net so that the bottom face touches the net, and label the faces on the net following the order you traced them in, as shown in the margin. Have students label the faces on the nets they produced. Discuss how some faces are exactly the same for example, the top face and the bottom face are exactly the same. Which other faces match exactly? (back and front, left side and right side) 4 in 6 in 2 in On the board, sketch a box as shown in the margin. ASK: What are the dimensions of the top face? (6 in by 4 in) Have students sketch a rectangle that is 6 squares long and 4 squares wide on grid paper and label it top face. ASK: What faces touch the top face on the prism? (front, back, and both side faces) What face does not touch the top face? (bottom face) If I now draw an identical rectangle right beside the top face and label it bottom face, would that be correct? (no) I want to draw the front face now. Where should I attach it? (to the top or to the bottom edge of the top face) What should the length of the front face rectangle be? (6 squares) The width? (2 squares) How do you know? (The front face dimensions are the length and the height of the prism.) Continue with the other faces. Exercises: On grid paper, draw a net for the prism and label the faces. Use 1 square of the grid for 1 cm 2. a) 5 cm b) 2 cm 2 cm 1 cm 4 cm Answers a) b) 3 cm Measurement and Data 5-28 Q-23

24 Extensions (MP.2) a) Which of these nets will fold into a cube? i) ii) iii) iv) b) Use six squares to make a different net for a cube. c) Use six squares to make a different figure that will not be a net for a cube. Answers: a) i) no, ii) yes, iii) yes, iv) no Sample answers b) c) Q-24 Teacher s Guide for AP Book 5.2

25 MD5-29 Volume and Area of One Face Pages STANDARDS 5.MD.C.5a, 5.MD.C.5b Goals Students will develop and use the formula Volume = area of horizontal face height for the volume of rectangular prisms. Vocabulary back, bottom, front, left side, right side, top face cubic centimeter (cm 3 ) cubic foot (ft 3 ) cubic inch (in 3 ) cubic kilometer (km 3 ) cubic meter (cm 3 ) cubic millimeter (mm 3 ) cubic yard (yd 3 ) edge face formula height horizontal face rectangular prism vertex, vertices volume PRIOR KNOWLEDGE REQUIRED Can use the formula V = l w h to find the volume of a rectangular prism Can multiply and divide multi-digit whole numbers MATERIALS rectangular box for each student box with faces labeled with their names for demonstration colored marker NOTE: In rectangular prisms, any pair of opposite faces can be considered bases. Since in Grade 5 students only deal with rectangular prisms, we have not introduced the term base. Instead, students should develop an understanding that they can find the volume of a rectangular prism by multiplying the area of any face by the dimension that is not one of the dimensions of that same face. Review the names of faces and the fact that opposite faces of a rectangular prism match. Show students a rectangular prism. ASK: In a rectangular box, or in a rectangular prism, can the top face be larger than the bottom face? (no) Can the bottom face be larger than the top face? (no) Can they have different shapes? (no) The top face and the bottom face are always the same rectangles. If some students have difficulty seeing that the top face and the bottom face match exactly, give them a box, have them trace the bottom face of the box, and check that the top face matches the bottom face exactly. Repeat with other pairs of opposite faces. Review the formula V = l w h. Ask students how they can find the volume of their boxes. ASK: What do you need to measure? (length, width, height) Remind students that a formula is a short way to write the instructions for how to calculate something. ASK: What is the formula for the volume of a rectangular prism? (Volume = length width height) How do we write it the short way? (V = l w h) Write both formulas on the board. Remind students that they used a formula to find areas of rectangles and how they recorded the solution. For example, write the solution for a problem Find the area of a rectangle with the length 3 cm and the width 2 cm on the board, as shown on the next page. Keep the formula on the board for future use. Measurement and Data 5-29 Q-25

MD5-26 Stacking Blocks Pages 115 116

MD5-26 Stacking Blocks Pages 115 116 STANDARDS 5.MD.C.4 Goals Students will find the number of cubes in a rectangular stack and develop the formula length width height for the number of cubes in a stack.

Unit 8 Geometry. Introduction. Materials

Unit 8 Geometry Introduction In this unit, students will learn about volume and surface area. As they find the volumes of prisms and the surface areas of prisms and pyramids, students will add, subtract,

Volume of Rectangular Prisms Objective To provide experiences with using a formula for the volume of rectangular prisms.

Volume of Rectangular Prisms Objective To provide experiences with using a formula for the volume of rectangular prisms. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts

Unit 6 Number and Operations in Base Ten: Decimals

Unit 6 Number and Operations in Base Ten: Decimals Introduction Students will extend the place value system to decimals. They will apply their understanding of models for decimals and decimal notation,

G3-33 Building Pyramids

G3-33 Building Pyramids Goal: Students will build skeletons of pyramids and describe properties of pyramids. Prior Knowledge Required: Polygons: triangles, quadrilaterals, pentagons, hexagons Vocabulary:

5 th Grade Math. ELG 5.MD.C Understand concepts of volume and relate volume to multiplication and to addition. Vertical Progression: 3 rd Grade

Vertical Progression: 3 rd Grade 4 th Grade 5 th Grade 3.MD.C Geometric measurement: understanding concepts of area and relate area to multiplication and to addition. o 3.MD.C.5 Recognize area as an attribute

NS6-50 Dividing Whole Numbers by Unit Fractions Pages 16 17

NS6-0 Dividing Whole Numbers by Unit Fractions Pages 6 STANDARDS 6.NS.A. Goals Students will divide whole numbers by unit fractions. Vocabulary division fraction unit fraction whole number PRIOR KNOWLEDGE

RP6-23 Ratios and Rates with Fractional Terms Pages 41 43

RP6-2 Ratios and Rates with Fractional Terms Pages 4 4 STANDARDS 6.RP.A.2, 6.RP.A. Vocabulary equivalent ratio rate ratio table Goals Students will understand that ratios with fractional terms can turn

Assessment Management

Areas of Rectangles Objective To reinforce students understanding of area concepts and units of area. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family

Free Pre-Algebra Lesson 3 page 1. Example: Find the perimeter of each figure. Assume measurements are in centimeters.

Free Pre-Algebra Lesson 3 page 1 Lesson 3 Perimeter and Area Enclose a flat space; say with a fence or wall. The length of the fence (how far you walk around the edge) is the perimeter, and the measure

Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms.

Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game

Objective To introduce a formula to calculate the area. Family Letters. Assessment Management

Area of a Circle Objective To introduce a formula to calculate the area of a circle. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment

Assessment Management

Area Objectives To provide experiences with the concept of area, distinguishing between area and perimeter, and finding areas of rectangular figures by partitioning and counting squares. www.everydaymathonline.com

Author(s): Hope Phillips

Title: Fish Aquarium Math *a multi-day lesson Real-World Connection: Grade: 5 Author(s): Hope Phillips BIG Idea: Volume Designing and building aquariums includes mathematical concepts including, but not

Chapter 8. Chapter 8 Opener. Section 8.1. Big Ideas Math Green Worked-Out Solutions. Try It Yourself (p. 353) Number of cubes: 7

Chapter 8 Opener Try It Yourself (p. 5). The figure is a square.. The figure is a rectangle.. The figure is a trapezoid. g. Number cubes: 7. a. Sample answer: 4. There are 5 6 0 unit cubes in each layer.

Number Models for Area

Number Models for Area Objectives To guide children as they develop the concept of area by measuring with identical squares; and to demonstrate how to calculate the area of rectangles using number models.

2. Length, Area, and Volume

Name Date Class TEACHING RESOURCES BASIC SKILLS 2. In 1960, the scientific community decided to adopt a common system of measurement so communication among scientists would be easier. The system they agreed

Perimeter, Area and Volume What Do Units Tell You About What Is Being Measured? Teacher Materials

Lesson 1 Perimeter, Area and Volume What Do Units Tell You About What Is Being Measured? Teacher Materials Perimeter: The Line Club T1: Before class: Copy one set of student pages for each student in the

4TH GRADE FIRST QUARTER MATHEMATICS STANDARDS. Vocabulary. answers using mental computation and estimation strategies including rounding.

4TH GRADE FIRST QUARTER MATHEMATICS STANDARDS Critical Area: Developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit

OA3-10 Patterns in Addition Tables Pages 60 63 Standards: 3.OA.D.9 Goals: Students will identify and describe various patterns in addition tables. Prior Knowledge Required: Can add two numbers within 20

COMMON CORE STATE STANDARDS FOR MATHEMATICS 3-5 DOMAIN PROGRESSIONS

COMMON CORE STATE STANDARDS FOR MATHEMATICS 3-5 DOMAIN PROGRESSIONS Compiled by Dewey Gottlieb, Hawaii Department of Education June 2010 Operations and Algebraic Thinking Represent and solve problems involving

Lesson 18: Determining Surface Area of Three Dimensional Figures

Lesson 18: Determining the Surface Area of Three Dimensional Figures Student Outcomes Students determine that a right rectangular prism has six faces: top and bottom, front and back, and two sides. They

WHAT IS AREA? CFE 3319V

WHAT IS AREA? CFE 3319V OPEN CAPTIONED ALLIED VIDEO CORPORATION 1992 Grade Levels: 5-9 17 minutes DESCRIPTION What is area? Lesson One defines and clarifies what area means and also teaches the concept

Area of Parallelograms, Triangles, and Trapezoids (pages 314 318)

Area of Parallelograms, Triangles, and Trapezoids (pages 34 38) Any side of a parallelogram or triangle can be used as a base. The altitude of a parallelogram is a line segment perpendicular to the base

VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region.

Math 6 NOTES 7.5 Name VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region. **The formula for the volume of a rectangular prism is:** l = length w = width h = height Study Tip:

Unit 2 Number and Operations Fractions: Multiplying and Dividing Fractions

Unit Number and Operations Fractions: Multiplying and Dividing Fractions Introduction In this unit, students will divide whole numbers and interpret the answer as a fraction instead of with a remainder.

Third Grade Illustrated Math Dictionary Updated 9-13-10 As presented by the Math Committee of the Northwest Montana Educational Cooperative

Acute An angle less than 90 degrees An acute angle is between 1 and 89 degrees Analog Clock Clock with a face and hands This clock shows ten after ten Angle A figure formed by two line segments that end

Voyager Sopris Learning Vmath, Levels C-I, correlated to the South Carolina College- and Career-Ready Standards for Mathematics, Grades 2-8

Page 1 of 35 VMath, Level C Grade 2 Mathematical Process Standards 1. Make sense of problems and persevere in solving them. Module 3: Lesson 4: 156-159 Module 4: Lesson 7: 220-223 2. Reason both contextually

Solving Geometric Applications

1.8 Solving Geometric Applications 1.8 OBJECTIVES 1. Find a perimeter 2. Solve applications that involve perimeter 3. Find the area of a rectangular figure 4. Apply area formulas 5. Apply volume formulas

Scope and Sequence KA KB 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B

Scope and Sequence Earlybird Kindergarten, Standards Edition Primary Mathematics, Standards Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced

Grade 9 Mathematics Unit 3: Shape and Space Sub Unit #1: Surface Area. Determine the area of various shapes Circumference

1 P a g e Grade 9 Mathematics Unit 3: Shape and Space Sub Unit #1: Surface Area Lesson Topic I Can 1 Area, Perimeter, and Determine the area of various shapes Circumference Determine the perimeter of various

Unit 7 The Number System: Multiplying and Dividing Integers

Unit 7 The Number System: Multiplying and Dividing Integers Introduction In this unit, students will multiply and divide integers, and multiply positive and negative fractions by integers. Students will

Using Proportions to Solve Percent Problems I

RP7-1 Using Proportions to Solve Percent Problems I Pages 46 48 Standards: 7.RP.A. Goals: Students will write equivalent statements for proportions by keeping track of the part and the whole, and by solving

CCSS Mathematics Implementation Guide Grade 5 2012 2013. First Nine Weeks

First Nine Weeks s The value of a digit is based on its place value. What changes the value of a digit? 5.NBT.1 RECOGNIZE that in a multi-digit number, a digit in one place represents 10 times as much

3 rd Grade Mathematics Unit #3 : Relating Area to Multiplication and Division Pacing: 29 Days Unit Overview In this unit, students extend their understanding of multiplication and division (Unit 2) by

Perfume Packaging. Ch 5 1. Chapter 5: Solids and Nets. Chapter 5: Solids and Nets 279. The Charles A. Dana Center. Geometry Assessments Through

Perfume Packaging Gina would like to package her newest fragrance, Persuasive, in an eyecatching yet cost-efficient box. The Persuasive perfume bottle is in the shape of a regular hexagonal prism 10 centimeters

Tallahassee Community College PERIMETER

Tallahassee Community College 47 PERIMETER The perimeter of a plane figure is the distance around it. Perimeter is measured in linear units because we are finding the total of the lengths of the sides

Perimeter, Area, and Volume

Perimeter is a measurement of length. It is the distance around something. We use perimeter when building a fence around a yard or any place that needs to be enclosed. In that case, we would measure the

Topic: 1 - Understanding Addition and Subtraction

8 days / September Topic: 1 - Understanding Addition and Subtraction Represent and solve problems involving addition and subtraction. 2.OA.1. Use addition and subtraction within 100 to solve one- and two-step

Vocabulary Cards and Word Walls Revised: June 29, 2011

Vocabulary Cards and Word Walls Revised: June 29, 2011 Important Notes for Teachers: The vocabulary cards in this file match the Common Core, the math curriculum adopted by the Utah State Board of Education,

NF5-12 Flexibility with Equivalent Fractions and Pages 110 112

NF5- Flexibility with Equivalent Fractions and Pages 0 Lowest Terms STANDARDS preparation for 5.NF.A., 5.NF.A. Goals Students will equivalent fractions using division and reduce fractions to lowest terms.

STATE GOAL 7: Estimate, make and use measurements of objects, quantities and relationships and determine acceptable

C 1 Measurement H OW MUCH SPACE DO YOU N EED? STATE GOAL 7: Estimate, make and use measurements of objects, quantities and relationships and determine acceptable levels of accuracy Statement of Purpose:

Grade 5 Common Core State Standard

2.1.5.B.1 Apply place value concepts to show an understanding of operations and rounding as they pertain to whole numbers and decimals. M05.A-T.1.1.1 Demonstrate an understanding that 5.NBT.1 Recognize

Grade 2 Math Expressions Vocabulary Words

Grade 2 Math Expressions Vocabulary Words Unit 1, Book 1 Understanding Addition and Subtraction OSPI word: number pattern, place value, value, whole number Link to Math Expression Online Glossary for some

How do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.

The verbal answers to all of the following questions should be memorized before completion of pre-algebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics

Lesson 3.1 Factors and Multiples of Whole Numbers Exercises (pages 140 141)

Lesson 3.1 Factors and Multiples of Whole Numbers Exercises (pages 140 141) A 3. Multiply each number by 1, 2, 3, 4, 5, and 6. a) 6 1 = 6 6 2 = 12 6 3 = 18 6 4 = 24 6 5 = 30 6 6 = 36 So, the first 6 multiples

Geometry Notes PERIMETER AND AREA

Perimeter and Area Page 1 of 57 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter

Formulas for Area Area of Trapezoid

Area of Triangle Formulas for Area Area of Trapezoid Area of Parallelograms Use the formula sheet and what you know about area to solve the following problems. Find the area. 5 feet 6 feet 4 feet 8.5 feet

A Correlation of. to the. Common Core State Standards for Mathematics Grade 4

A Correlation of to the Introduction envisionmath2.0 is a comprehensive K-6 mathematics curriculum that provides the focus, coherence, and rigor required by the CCSSM. envisionmath2.0 offers a balanced

Quick Reference ebook

This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference ebook Click on Contents or Index in the left panel to locate a topic. The math facts listed

Imperial Length Measurements

Unit I Measuring Length 1 Section 2.1 Imperial Length Measurements Goals Reading Fractions Reading Halves on a Measuring Tape Reading Quarters on a Measuring Tape Reading Eights on a Measuring Tape Reading

Common Core Standards for Mathematics Grade 4 Operations & Algebraic Thinking Date Taught

Operations & Algebraic Thinking Use the four operations with whole numbers to solve problems. 4.OA.1. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as a statement that 35

Area of Parallelograms (pages 546 549)

A Area of Parallelograms (pages 546 549) A parallelogram is a quadrilateral with two pairs of parallel sides. The base is any one of the sides and the height is the shortest distance (the length of a perpendicular

TYPES OF NUMBERS. Example 2. Example 1. Problems. Answers

TYPES OF NUMBERS When two or more integers are multiplied together, each number is a factor of the product. Nonnegative integers that have exactly two factors, namely, one and itself, are called prime

Show that when a circle is inscribed inside a square the diameter of the circle is the same length as the side of the square.

Week & Day Week 6 Day 1 Concept/Skill Perimeter of a square when given the radius of an inscribed circle Standard 7.MG:2.1 Use formulas routinely for finding the perimeter and area of basic twodimensional

I Perimeter, Area, Learning Goals 304

U N I T Perimeter, Area, Greeting cards come in a variety of shapes and sizes. You can buy a greeting card for just about any occasion! Learning Goals measure and calculate perimeter estimate, measure,

Progressing toward the standard

Report Card Language: add, subtract, multiply, and/or divide to solve multi-step word problems. CCSS: 4.OA.3 Solve multistep work problems posed with whole numbers and having whole-number answers using

Vocabulary, Signs, & Symbols product dividend divisor quotient fact family inverse. Assessment. Envision Math Topic 1

1st 9 Weeks Pacing Guide Fourth Grade Math Common Core State Standards Objective/Skill (DOK) I Can Statements (Knowledge & Skills) Curriculum Materials & Resources/Comments 4.OA.1 4.1i Interpret a multiplication

Area and Perimeter Man

Area and Perimeter Man MA.C.3.2.1.3.1 and.2; MA.B.3.2.1.3.3 LESSON FOCUS Using counting procedures to determine perimeter and area of rectangles, squares, and other figures. COMPANION ANCHORS LESSONS Perimeter;

ACTIVITY: Finding a Formula Experimentally. Work with a partner. Use a paper cup that is shaped like a cone.

8. Volumes of Cones How can you find the volume of a cone? You already know how the volume of a pyramid relates to the volume of a prism. In this activity, you will discover how the volume of a cone relates

Math Common Core Standards Fourth Grade

Operations and Algebraic Thinking (OA) Use the four operations with whole numbers to solve problems. OA.4.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as a statement

Demystifying Surface Area and Volume Teachers Edition

Demystifying Surface and Volume Teachers Edition These constructions and worksheets can be done in pairs, small groups or individually. Also, may use as guided notes and done together with teacher. CYLINDER

Covering and Surrounding: Homework Examples from ACE

Covering and Surrounding: Homework Examples from ACE Investigation 1: Extending and Building on Area and Perimeter, ACE #4, #6, #17 Investigation 2: Measuring Triangles, ACE #4, #9, #12 Investigation 3:

*1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles.

Students: 1. Students understand and compute volumes and areas of simple objects. *1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles. Review

DIMENSIONAL ANALYSIS #2

DIMENSIONAL ANALYSIS #2 Area is measured in square units, such as square feet or square centimeters. These units can be abbreviated as ft 2 (square feet) and cm 2 (square centimeters). For example, we

Mathematics. Mathematical Practices

Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with

Integrated Algebra: Geometry

Integrated Algebra: Geometry Topics of Study: o Perimeter and Circumference o Area Shaded Area Composite Area o Volume o Surface Area o Relative Error Links to Useful Websites & Videos: o Perimeter and

Pythagorean Theorem Differentiated Instruction for Use in an Inclusion Classroom

Pythagorean Theorem Differentiated Instruction for Use in an Inclusion Classroom Grade Level: Seven Time Span: Four Days Tools: Calculators, The Proofs of Pythagoras, GSP, Internet Colleen Parker Objectives

Measurement: Converting Distances

Measurement: Converting Distances Measuring Distances Measuring distances is done by measuring length. You may use a different system to measure length differently than other places in the world. This

Concepts of Elementary Mathematics Enduring Understandings & Essential Questions

Concepts of Elementary Mathematics & First through Fourth Grade Content Areas: Numbers and Operations Algebra Geometry Measurement Data Analysis and Probability Above all, students should feel enchanted

Unit 1 Number Sense. In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions.

Unit 1 Number Sense In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions. BLM Three Types of Percent Problems (p L-34) is a summary BLM for the material

1 foot (ft) = 12 inches (in) 1 yard (yd) = 3 feet (ft) 1 mile (mi) = 5280 feet (ft) Replace 1 with 1 ft/12 in. 1ft

2 MODULE 6. GEOMETRY AND UNIT CONVERSION 6a Applications The most common units of length in the American system are inch, foot, yard, and mile. Converting from one unit of length to another is a requisite

Unit 8 Angles, 2D and 3D shapes, perimeter and area

Unit 8 Angles, 2D and 3D shapes, perimeter and area Five daily lessons Year 6 Spring term Recognise and estimate angles. Use a protractor to measure and draw acute and obtuse angles to Page 111 the nearest

4th Grade Common Core Math Vocabulary

4th Grade Common Core Math Vocabulary a.m. A time between 12:00 midnight and 12:00 noon. acute angle An angle with a measure less than 90. acute triangle A triangle with no angle measuring 90º or more.

Three daily lessons. Year 5

Unit 6 Perimeter, co-ordinates Three daily lessons Year 4 Autumn term Unit Objectives Year 4 Measure and calculate the perimeter of rectangles and other Page 96 simple shapes using standard units. Suggest

Exploring Mathematics Through Problem-Solving and Student Voice

Exploring Mathematics Through Problem-Solving and Student Voice Created By: Lisa Bolduc, Aileen Burke-Tsakmakas, Shelby Monaco, Antonietta Scalzo Contributions By: Churchill Public School Professional

Mathematics Grade 5 Year in Detail (SAMPLE)

Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9 Unit 10 Whole number operations Place value with decimals Add and Subtract Decimals Add and Subtract Fractions Multiply and Divide Decimals

Topic 1: Understanding Addition and Subtraction

Topic 1: Understanding Addition and Subtraction 1-1: Writing Addition Number Sentences Essential Understanding: Parts of a whole is one representation of addition. Addition number sentences can be used

Warning! Construction Zone: Building Solids from Nets

Brief Overview: Warning! Construction Zone: Building Solids from Nets In this unit the students will be examining and defining attributes of solids and their nets. The students will be expected to have

Measuring with a Ruler

Measuring with a Ruler Objective To guide children as they measure line segments to the nearest inch, _ inch, _ inch, centimeter, _ centimeter, and millimeter. www.everydaymathonline.com epresentations

BPS Math Year at a Glance (Adapted from A Story Of Units Curriculum Maps in Mathematics K-5) 1

Grade 4 Key Areas of Focus for Grades 3-5: Multiplication and division of whole numbers and fractions-concepts, skills and problem solving Expected Fluency: Add and subtract within 1,000,000 Module M1:

CCSS-M Critical Areas: Kindergarten

CCSS-M Critical Areas: Kindergarten Critical Area 1: Represent and compare whole numbers Students use numbers, including written numerals, to represent quantities and to solve quantitative problems, such

Math - 5th Grade. two digit by one digit multiplication fact families subtraction with regrouping

Number and Operations Understand division of whole numbers N.MR.05.01 N.MR.05.02 N.MR.05.03 Understand the meaning of division of whole numbers with and without remainders; relate division to and to repeated

Fourth Grade Math Standards and "I Can Statements"

Fourth Grade Math Standards and "I Can Statements" Standard - CC.4.OA.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and

Surface Area and Volume

1 Area Surface Area and Volume 8 th Grade 10 days by Jackie Gerwitz-Dunn and Linda Kelly 2 What do you want the students to understand at the end of this lesson? The students should be able to distinguish

DIMENSIONAL ANALYSIS #2

DIMENSIONAL ANALYSIS #2 Area is measured in square units, such as square feet or square centimeters. These units can be abbreviated as ft 2 (square feet) and cm 2 (square centimeters). For example, we

Indicator 2: Use a variety of algebraic concepts and methods to solve equations and inequalities.

3 rd Grade Math Learning Targets Algebra: Indicator 1: Use procedures to transform algebraic expressions. 3.A.1.1. Students are able to explain the relationship between repeated addition and multiplication.

Content Strand: Number and Numeration Understand the Meanings, Uses, and Representations of Numbers Understand Equivalent Names for Numbers Understand Common Numerical Relations Place value and notation

Round Rock ISD Lesson 1 Grade 3 Measurement Kit. Broken Rulers and Line It Up!* - A Length Measurement Lesson

Round Rock ISD 2008-09 Lesson 1 Grade 3 Measurement Kit Broken Rulers and Line It Up!* - A Length Measurement Lesson tech *Lesson is adapted from two activities in Sizing Up Measurement: Activities for

Building number sense and place value and money understanding

Unit: 1 Place Value, Money, and Sense s to be mastered in this unit: 3.N.1 Skip count by 25 s, 50 s, 100 s to 1,000 3.N.2 Read and write whole numbers to 1,000 place 3.N.3 Compare and order numbers to

OA4-13 Rounding on a Number Line Pages 80 81

OA4-13 Rounding on a Number Line Pages 80 81 STANDARDS 3.NBT.A.1, 4.NBT.A.3 Goals Students will round to the closest ten, except when the number is exactly halfway between a multiple of ten. PRIOR KNOWLEDGE

Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. Solve word problems that call for addition of three whole numbers

1 BPS Math Year at a Glance (Adapted from A Story of Units Curriculum Maps in Mathematics P-5)

Grade 5 Key Areas of Focus for Grades 3-5: Multiplication and division of whole numbers and fractions-concepts, skills and problem solving Expected Fluency: Multi-digit multiplication Module M1: Whole

Math-U-See Correlation with the Common Core State Standards for Mathematical Content for Fourth Grade

Math-U-See Correlation with the Common Core State Standards for Mathematical Content for Fourth Grade The fourth-grade standards highlight all four operations, explore fractions in greater detail, and

Activity Standard and Metric Measuring

Activity 1.3.1 Standard and Metric Measuring Introduction Measurements are seen and used every day. You have probably worked with measurements at home and at school. Measurements can be seen in the form

September: UNIT 1 Place Value Whole Numbers Fluently multiply multi-digit numbers using the standard algorithm Model long division up to 2 digit divisors Solve real world word problems involving measurement

What You ll Learn. Why It s Important

These students are setting up a tent. How do the students know how to set up the tent? How is the shape of the tent created? How could students find the amount of material needed to make the tent? Why

MEASUREMENTS. U.S. CUSTOMARY SYSTEM OF MEASUREMENT LENGTH The standard U.S. Customary System units of length are inch, foot, yard, and mile.

MEASUREMENTS A measurement includes a number and a unit. 3 feet 7 minutes 12 gallons Standard units of measurement have been established to simplify trade and commerce. TIME Equivalences between units

Second Grade Math Standards and I Can Statements

Second Grade Math Standards and I Can Statements Standard CC.2.OA.1 Use addition and subtraction within 100 to solve one and two-step word problems involving situations of adding to, taking from, putting