California Career and Technical Education Standards

• BTC.A.A1.4 Know conventional cabinetmaking and wood product measurement processes, linear m...

California Academic Content Standards (Reinforced)

• M.5.NS.2.5 Compute and perform simple multiplication and division of fractions and apply th...1
• M.6.NS.1.1 Compare and order positive and negative fractions, decimals, and mixed numbers a...1
• M.7.MG.1.2 Construct and read drawings and models made to scale.11

• Win this bar! (illustrated ruler without numbers) - Hooks / Set

  Students will pick up the pre test handout on measurement (see below) as they walk into the class room. For their daily writing activity, they will take the pre test.  After taking roll, students will see an illustration of a ruler on the white board with several fractional marks labeled A, B, C, etc. with a candy bar taped on the board next to the words “Win this bar!”  There are no numbers on the ruler illustration so the units of measure are not yet known. Ask students to raise their hand if they can name the fraction mark for A, B, or C.  This is a trick question as all answers are right or wrong since we have not establish the fractional divisions (no numbers are on the board so we don’t yet know how many units the inch is broken down into).   The first student that figures out that you need to know what the graduated units are will win the candy bar.

   
• Lecture, Demo, Activity combined - Lecture

  Pass out a small piece of paper (about 2 inches by 8 and1/2 inches) and have students write their name on one side.  Ask the students to fold the piece of paper in half.  Have them unfold and mark the halfway point by drawing a line halfway down the crease (see example) and marking it 1/2.  Tell the students that we are going to pretend that this is an inch.  Show them an example of what you want by drawing it on the white board. They should mark the left side of the paper 0 and the right side 1.

  Ask them to fold the paper at the halfway point again and then fold it in half again. This will locate the ¼ inch marks.  This time they should draw lines in the creases half as long as the ½ mark line (the last line they made) and mark them as ¼ and ¾.  Again draw an example on the white board.  I sometimes mark the ¾ mark as 2/4 and ask the students if this looks correct to them.  Then we can talk about why this is both correct and incorrect.  Explain that the ½  mark is also 2/4 but we call it ½ because it can be reduced.  I ask the students at this point to tell me how many “parts” or “sections” there are to the inch we are making. Show them there are now four parts to our oversized inch.  This is why we call each mark a quarter (1/4). Relate that to a dollar by asking how many quarters are in a dollar. Now ask how many ¼ marks make up an inch (4/4 = 1). 

  Have students fold and continue to fold and mark their oversized inch to 1/8 and then to 1/16 units shortening the line lengths and numbering the lines at each division.   I show them how we are measuring by dividing the whole into sections - first 2 then 4 and so on (8,16 etc.).  Ask them what they notice about the numerator (the number on top of the fraction). They should note that the number is always odd.  Ask them what they notice about the denominator (the number on the bottom of the fraction).  They should note that the denominator is always even.   Remind them that if the top number is even it can be reduce 2/8 = ¼, 2/16 = 1/8, etc.   In the fractional measuring system we always reduce to simplest terms.  

  Explain that the length of each line at each new fold is half as long as the last division and that this will help them determine what unit of measure they are looking at because fractional numbers are not found on a standard ruler.  The length of the line will help determine the fraction. Longer lines represent larger fractions and shorter lines represent smaller fractions. count the units of division.  When trying to figure out what a given fraction on a ruler may be, I tell students to start at the mark in question and count every line that is as long or longer back to the first whole number i.e. at the 3/4 mark you would start at 3/4 and count,  1/2, 1/4, 0 = three divisions making the top number of your fraction 3 and then count forward to the first whole number i.e. 3/4 to 1 = 1.  Add the two numbers 3 and 1 and you get 4. 4 that is your bottom number. You get 3/4. 

  Lecture: There are 36 inches in a yard and 12 inches in a foot. Corresponding units of area and volume are the square inch and the cubic inch. The inch is one of the most common units of length in the United States, and is also widely used in the United Kingdom, and Canada, despite the introduction of metric to the latter two in the 1960s and 1970s, respectively. The inch is sometimes used informally in other Commonwealth nations, such as Australia.

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