What's the Big Idea??

A few notes about teaching math: 

This week we start looking at our second Big Idea in math. We will continue working in this area well into December. 

 BIG IDEA 2 

Develop an understanding of and fluency with addition and subtraction of fractions and decimals. MA.5.A.2.1: Represent addition and subtraction of decimals and fractions with like and unlike denominators using models, place value, or properties. It is absolutely critical that students really understand that they may not ever add or subtract fractions until the fractions have the same denominator. We will discuss many strategies for finding common denominators. Perhaps, the most important strategy will revolve around multiplying fractions by n/n (any fraction with the same numerator and denominator). For example, 3/5 X n/n could be 3/5 X 2/2 or 6/10. 3/5 could also be looked at a 3/5 X 4/4 or 12/20 if we need to create a fraction with a denominator of 20. 

We will be looking at Least Common Multiples in order to determine what denominator to shoot for. LCM: The LCM of 2 and 5 can be found by listing multiples of 2 and 5. 2: 2,4,6,8,10 5: 5,10 

MA.5.A.2.2: Add and subtract fractions and decimals fluently, and verify the reasonableness of results, including in problem situations. 

 MA.5.A.2.3: Make reasonable estimates of fraction and decimal sums and differences, and use techniques for rounding. 

MA.5.A.2.4: Determine the prime factorization of numbers. 


So far this year we  have been working on division word problems, the traditional division algorithm, order of operations (PEMDAS), adding and subtracting decimal numbers, rules of divisibility (especially 2,3,4,6, and 9), prime factorization, division clusters, and square numbers. 

We have been working on questions like the Harry and David's Fruit Company questions that require more than one step to solve. The Harry and David Fruit Company has been selling gift boxes of fruit since 1910. They sell boxes of fruit and ship them all over the USA. 

The chart below shows the contents and cost of some of their more popular options. 

24 Orange Box $48 
18 Grapefruit Box $52 
28 Tangerine Box $44 
20 Pear Box $54 

How much money could the Harry and David Fruit Company make from selling Grapefruit Boxes if they had a supply of 5,010 grapefruits?

Remember, it takes 18 grapefruits to make a gift box. Hopefully, students will see that they need to divide the 5,010 grapefruits by 18 to see how many boxes could be made. After that, they will need to multiply the number of boxes by $52 to see how much money could be made. 

This may seem very simple to an adult, but experience says that 5th graders have some difficulties recognizing the correct steps to take.