Benchmark Fractions
Benchmarks are points of reference used for comparison. In whole numbers, they can be "friendly" or "round" numbers such as 5, 10, or 100. We often use them when we estimate.
Benchmark Fractions are common fractions to which we can compare other, less common fractions. Thinking about Benchmarks helps you perform mental math more easily, as well as know if your answer makes sense. Using a Benchmark insures that you understand the concepts and not just memorize a procedure for solving a problem. Having a clear idea of benchmarks deepens your level of understanding of fractions.
In this unit, you will build a strong foundation in fractions. Below you will find extra practice for the concepts we cover in class.
Benchmark Fractions are common fractions to which we can compare other, less common fractions. Thinking about Benchmarks helps you perform mental math more easily, as well as know if your answer makes sense. Using a Benchmark insures that you understand the concepts and not just memorize a procedure for solving a problem. Having a clear idea of benchmarks deepens your level of understanding of fractions.
In this unit, you will build a strong foundation in fractions. Below you will find extra practice for the concepts we cover in class.
Explore the Concepts and Visual Representations
Explore the fraction-related virtual manipulatives at this site. Click the button link below. Once you're on the site, click the arrow next to the Manipulatives tab. Choose:
1) Fraction Circles or Fraction Tiles - After clicking on the circles or tiles, drag a blank over to the white space. Fill each whole with different combinations to make a whole. Can you predict what piece you will need to finish off the whole? You can select another manipulative without clearing the white space.
2) Number Line - After choosing a Number Line manipulative and dragging it to the white space on the right, choose fractions or decimals and set the minimum (which will appear on the far left) and maximum (which will appear on the far right). Pick an interval (this will be the distance between each hash mark on the line). If you've chosen a range of numbers that is too large to be viewed on the screen, you can click and hold the bar with the small directional arrows. Slide it the direction you want to view. Try this: On scrap paper, name a fraction and show what two numbers it will fall between. Check the number line. Were you correct? Once you've gotten good at whole numbers, try the same prediction for where a negative number.
1) Fraction Circles or Fraction Tiles - After clicking on the circles or tiles, drag a blank over to the white space. Fill each whole with different combinations to make a whole. Can you predict what piece you will need to finish off the whole? You can select another manipulative without clearing the white space.
2) Number Line - After choosing a Number Line manipulative and dragging it to the white space on the right, choose fractions or decimals and set the minimum (which will appear on the far left) and maximum (which will appear on the far right). Pick an interval (this will be the distance between each hash mark on the line). If you've chosen a range of numbers that is too large to be viewed on the screen, you can click and hold the bar with the small directional arrows. Slide it the direction you want to view. Try this: On scrap paper, name a fraction and show what two numbers it will fall between. Check the number line. Were you correct? Once you've gotten good at whole numbers, try the same prediction for where a negative number.
Review Questions:
This graph is lacking in some of the basic components of a graph such as a title and a legend. Ignoring that, you can still use the graph to practice your fractions knowledge. 1) Which two categories together equal a value near one-half? Which three categories together equal a value near one-half? 2) Write a sentence about the graph that uses the phrase "more than half." Write a sentence about the graph that uses the phrase "less than half." |
Raymond picked up the bill for ice cream for his coworkers at The Scoop. Four people ordered Fudge Ripple, five people ordered Strawberry Supreme, and two ordered Chocolate Delight. Use the phrases "more than half" and "less than half" to write one or two sentences about their preference for strawberry or chocolate flavors. |
Watch this Clorox Commercial, then explain how it shows "Twice as Much."
Extra Practice: Here's a two-page extra practice sheet for the Benchmark Fraction One-Half. You can print it out or look at the screen and write down your answers:
Use the knowledge you've gained about using benchmark fractions and you'll have the answer to this challenging question in a flash with mental math! Click the button link below to get started.
Here's a way to play with different visual arrangements to show one-half. It seems easy at first, but once you get past the first seven or so, you really have to start thinking about what new arrangements you can make.
Close to... Two weeks after we were done with this section, groups were able to work together to turn a mass of fractions into an organized poster for our classroom! I was impressed with the explanations of reasoning that I heard as students moved fractions into categories. Some of these were fractions larger than one; those really took some thinking. I heard about lots of pieces "cookies, pies, and pizzas" as students created pictures in their mind of the meaning of the fractions!
Lesson 2 -Benchmark Fracton One-Quarter
Review Questions:
Only twenty-five percent of the people in the movie theater for the latest 'shoot 'em up' action flick were females.
If there were 175 females, how many people were there in the theater? How many males were at the movie? At the late showing, there were 200 people in the theater and the same percentage of females. How many were females? How many were males? |
According to the Pretend Association of National Television Services (PANTS), 25% of children polled watch 4 hours of television on their average day. Make up example numbers that would provide information about the total and the quarter in this situation. Tell the dramatic story using this information as if you were giving the evening news on television. |
STILL UNDER CONSTRUCTION FROM HERE DOWN
As we work toward these concepts in class, I will post more practice.
As we work toward these concepts in class, I will post more practice.
Lesson 3 - Benchmark Three-Fourths
Review Questions: