NS 2.1 Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation. • Today’s objective: learn how to convert between mixed numbers and improper fractions • Learning target: Convert at least 3 of the 4 mixed numbers and improper fractions correctly on the exit ticket.
A number with an integer and a proper fraction. • Examples: • Non-examples: • What is a mixed number?
A fraction whose numerator is greater than the denominator. • Examples: • Non-examples: • What is an improper fraction?
When you need to see how many whole parts there are. • When we are multiplying or dividing two amounts. • When is it useful to use mixed numbers? • When is it useful to use improper fractions?
Let’s slice up all 4 wholes into 8 pieces each to match the fraction at the end. How many pieces do we have now? The 4 wholes each became 8 pieces, so there are 4×8 = 32 pieces from those. Then add the 7 pieces we started with: 32 + 7 = 39 pieces. It still takes 8 pieces to form a whole circle, so the denominator remains 8.
Multiply the denominator by the whole number and add the numerator to get the new numerator. The denominator remains the same. • How do we convert mixed numbers into improper fractions?
How many wholes can we make out of these pieces? Since the denominator is 4, we need 4 pieces to form one whole. To find how many groups of 4 there are in 13, do the long division: We can form 3 whole circles and will have 1 out of the 4 pieces required to make another circle.
Divide the numerator by the denominator. The quotient is the whole number, the remainder is the new numerator, and the denominator remains the same. • How do we convert improper fractions into mixed numbers?
Direct Station • We will do word problems that involve real-life situations that require converting between mixed numbers and improper fractions.
Collaborative Station • We will play the card game “War” in which each player flips over a card and whoever’s number is greater adds both cards to the bottom of their deck. • Write down the work showing how you figured out whose number was greater. • The goal is to get all of the cards in your deck.
Collaborative Station Example • The cards are evenly divided between Partners A and B. They each hold their decks face down. • Both partners flip over the top card of their deck. Partner A’s card is 7/2 and Partner B’s card is 4 1/2. • The partners calculate that 7/2 = 3 ½ OR The partners calculate that 4 ½ = 9/2. • Partner B’s card is worth more so he puts both cards on the bottom of the deck. • If for one round you compared by turning the mixed number into an improper fraction, for the next round turn the improper fraction into a mixed number instead.
Independent Station • We are continuing ST Math’s unit on fraction addition and subtraction. • Make sure you are writing down your calculations.