Estimation

Activities

Lesson 1

Objectives

• To explore the difference between 1 and 10 through linear measurement using base-10 manipulatives
• To measure items around the classroom in centimeters using base-10 manipulatives
• To report lengths as estimates between two precise measurements when using non-standard measuring tools
• To record information gathered in order to informally assess understanding

Materials

• math journals
• ten base-10 cubes and one base-10 rod per student
• up to 50 base-10 cubes for teacher to display
• 1 centimeter ruler for every 2 students

Procedure

The lesson begins with a whole group discussion about a tens rod. (We would have already discussed the manipulatives and used them in building two digit numbers.) Give each child a base-10 tens rod and ask, "How many cubes are in a rod?" Show the whole group 10 ones and ask, "Which manipulatives are easier to handle, the rods or the cubes? If you had 30 or 40 cubes, would you rather have them in separate cubes or grouped together in tens?" Let the class discuss, but make sure to reinforce that one tens rod is ten ones neatly packed into a form that is easy to handle. (The Cuisenaire rod activity described in Appendix B under Composing and Decomposing 10 would be a good activity to do prior to this lesson.)

Now pair the students up and give each pair 1 base-10 cube and 1 rod. Ask them to measure both in centimeters using the centimeter ruler with their partner (you may need to guide them with this, depending on their prior experience). Have them trace each one in their math journal and record the length next to each outline. After they try to measure on their own, discuss that the cube is 1cm and the rod is 10-cm/1 decimeter.) Then ask, "If one rod is ten centimeters, how long is 2 rods? How long is 3 rods? How long is 4 rods? How long is 5 rods?" They should be able to figure out that you can count by tens, so 2 rods is 20 cm, 3 rods are 30 cm, etc.

Lesson 2

Objectives:

• To explore powers of ten through linear measurement using base-10 manipulatives
• To construct a 50 cm ruler that can be used to measure items around the classroom

Materials

• 1 base-10 tens rod for each child
• base-10 cubes
• 5 base-10 tens rods taped together
• strips of cardstock precut measuring 1 inch wide and 50 cm long with a straight line pre-drawn down the middle

Procedure

Show the class the extra long rod that is 5 base-10 rods taped together. Ask, "How many rods did I use to make this extra long rod? If I used 5 rods, how many centimeters long is this?" Then prove that the rod is actually 50 centimeters by measuring it with a meter stick.

Next, explain that everyone is going to make his/her own 50 cm ruler to use for the next few weeks. Demonstrate how to make the ruler by lining up one rod at one end of the strip along top of the pre-drawn line and marking the other end of the rod with a pencil line. Write "10 cm" under the pencil mark. Then move the rod down to the pencil line you just made and measure out another 10 cm length. Do this until you have measured and marked 50 centimeters in 10-centimeter increments. You can then go back with the tens rod and mark each individual centimeter along the ruler using the lines built into the rod, and then label all 50 centimeters. Then give each student a strip, a tens rod and a pencil and ask them to make it themselves. Find a safe place to store the ruler until the next lesson (they can be folded and stored in Ziploc bags), or you can have them temporarily tape them to the top of their desks.

Lesson 3

Objectives

• To compare 10 centimeters with 100 centimeters
• To introduce the terms "decimeter" and "meter"
• To visually see the difference between 10 and 100
• To associate 10 tens with 1 hundred
• To see 100 as ten times bigger than 10
• To introduce the prefix deci-
• To reinforce fractions as a pieces of a whole through a concrete exploration
• To see fractions as directly applied in everyday life

Materials

• math journals
• 2 previously made 50 cm rulers per pair of students
• a few meter sticks for display
• one extra long rod created by 10 tens rods taped together
• 10 tens rods per pair of students

Procedure

Call the class to the rug to make a circle. Have each student bring his or her 50 cm ruler with him or her. Pair students up with a person sitting next to them. Give each pair 10 tens rods and ask them to line them up end to end. Ask "How many centimeters long is one rod? (10cm). How many rods do you have all together? (ten) Can you figure out a way to quickly count how many centimeters you have in 10 rods?" They should be able to count by tens to find that there are 100 centimeters total. Explain that 100 centimeters is equal to 1 meter. Show a meter stick and line it up underneath one groups train of tens rods. They should be exactly the same length. Pass out a few meter sticks and have the groups take turns aligning their 10 tens rods with the meter stick. Summarize again that 100cm is equal to 1 meter. Then say, "How many rods made up a meter? (ten) So, each rod is 1 out of 10 pieces. That means each rod is 1/10 of a meter. There is a special name for 10 centimeters. We call it a decimeter. Deci- is a prefix that means one tenth (1/10). So, a decimeter is 1/10 of a meter. Thus, each tens rod is a decimeter. A ones cube is a centimeter, a tens rod is a decimeter (or 10 cm), and 10 tens rods is a meter (which is the same as 100 cm or 10 decimeters)."

Then ask the students to line up both of their 50-centimeter rulers end to end. These two rulers should be the same length as the 10 tens rods because 50 cm + 50 cm = 100 cm. If they wanted to measure things using a meter stick, they could just combine their 50 centimeter rulers to make one 100 centimeter ruler = 1 meter.

Lesson 4

Objectives

• To relate previous experiences measuring in centimeters with opportunities for estimating lengths of objects
• To create a visual display of objects about 1 cm long, 10 cm long or 100 cm long in order to make it easier to compare relative lengths
• To give students a chance to estimate lengths of items and distances in the school

Materials

• three lengths of thick yarn, 1 cm, 10 cm and 100cm
• slips of paper to write on
• plastic bags
• digital camera(s)
• push pins
• 1 ones cube, 1 tens rod, and 2 50cm rulers taped together for each pair of students

Procedure

Explain that the class will make a display by finding objects and distances in the school that are about 1 centimeter, 10 centimeters/ 1 decimeter, and 100 centimeters/ 1 meter. Pair up the students and give each pair 1 ones cube and 1 tens rod. Have them tape each of their 50-centimeter rulers together to make a meter stick (or they could each create a line of 10 tens rods taped together to use as a meter stick). They are going to use these manipulatives to find items around the room that are about this length. Demonstrate how to use the different measuring tools to measure objects around the room. Then show them that they should leave the tool next to the object in order to take a picture of the object for the bulletin board. If they find portable items that are 1 cm or 10 cm, they may opt to collect the item in it's own plastic bag instead of taking a photograph of it. They can also measure distances between two things/places. They may find that it is 1 meter between the rug and the bookcase. They can lay a meter stick in that space and take a photo of the distance between two points.

After the class has finished, print the photographs. Ask each pair of students to make a caption for each photo using small strips of paper. The caption should say "The __________ is about ____ centimeters." or "It is about _____ cm from ____________ to __________." Pin the lengths of string on a bulletin board, leaving room to add the pictures above each length. Add a label under each yarn declaring how many centimeters long it is (you may also want to add "decimeter" and "meter.") Pin the photos above the length of string corresponds the measured length of the object/distance. You can continue to add to this display on later dates.

Lesson 5

Objectives

• To make polygons that have perimeters of 10 cm, 20 cm, 30 cm, 40 cm, 50 cm, etc. up to 100cm
• To integrate linear measurement with a study of perimeter and plane shapes
• To provide further exposure to lengths that increase by powers of ten in order to improve student ability to estimate lengths

• Wikki Stix (or pipe cleaners) cut or combined into lengths of 10cm, 20cm, 30cm, 40cm, 50cm, 60cm, 70cm, 80cm, 90cm, and 100cm - enough for each student to have 2 different lengths
• strips of paper to make labels
• ten 10 cm Wikki Stix for demonstration

Procedure

In a whole group setting, display the different lengths of Wikki Stix (WS). Point out that they are cut into lengths that are multiples of ten. Show the 10 cm WS and then the 20 cm WS. Line up two 10 cm WS alongside of the 20 cm WS. Explain, "The 20 cm WS is two times bigger than the 10 cm WS. It is the same length as two 10 cm WS, so we say that it is two times bigger." Show the 30 cm WS next. "This WS is the same as three of the 10 cm WS, so we say that it is three times bigger. 30 is three times bigger than 10." Continue this until you get to the 100 cm WS. "This WS is the same length as ten 10 cm WS, so we know that this WS is ten times bigger than the 10 cm one. SO, 100 must be 10 times bigger than 10!"

Now explain that you are going to use all of these different lengths to make different polygons. Demonstrate how to bend a WS to make a triangular shape, a rectangular shape or a trapezoidal shape. Explain that each student will get two different lengths of Wikki Stix. They should trace the length of each WS in their math journal. Then, they should use their 50 cm ruler to measure the length and record it under the line segment they just drew for each WS. This should look something like this (not to scale):

____________________________________________________________

10 cm 30 cm

After they have recorded this information, they can bend the WS to make whatever polygon they would like. Once they have made their two shapes, they will draw models of the shapes in their math journal. They will then use their 50 cm rulers to measure the length of each side of their shapes. They should record the length of each side on the drawings like so (not to scale):

Next, they need to add up all the measurements of each side to find the perimeter of their shape. 10 cm + 5 cm + 10 cm + 5 cm = 30 cm. The perimeter should be the same as the length the Wikki Stix were before they were bent into a polygon.