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5C1.1 Create your own place value mat for numbers as high as hundreds of millions. (Use a ruler and a pencil!) Explain why you grouped the places the way you did. This is how I grouped the places: 5C2.1 A number is divided by 100. The result is 427.4. Explain how you know that the original number does not have 3 as one of its digits. What is the number? 5C2.3 Jake says, “You always get a larger answer when you multiply”. Respond to Jake’s observation. 5C3.1, 5C3.2 Activity 1 Take a rectangular piece of paper. Fold it in half once and then open it up. How many sections do you get? Refold your paper in half and then fold it in half again. How many sections do you get when you open up your paper? Fold your paper up again. How many sections do you think you would get if you folded your paper in half again? And again? And again? Explain how you could predict the number of sections for 8 folds, if it were possible to do it. Activity 2 Predict the numbers in the next two rows: 1 1 1 3 1 2 Explain your thinking: 1 3 1 1 5C4/5C5 Rearranging factors can make mental math easier! 28×250 “I know that 28 is the same as 7×4.” “I can easily multiply 4×250 to get 1000.” “So if I think of 28×250 as 7×1000, I can quickly find the product.” Rearranging factors can be useful in finding products when using pencil and paper too! Watch this: 15×12 15×12 = 3×5×2×6 15×12 = 3×10×6 15×12 = 18×10 15×12 = 180 I see 10! (or you could do 30×6) Now you try: Multiply 45×16 and be prepared to explain to your partner how you rearranged to find the answer. Did you both find the answer the same way? 5C6.1 Measure this line segment using the centimetres scale. Measure it again using the millimeters scale. cm mm Do the digits change? What happens when the unit of measurement is smaller? What happens when the unit of measurement is larger? Decide whether each of the following numbers will increase or decrease as the unit of measurement changes: 0.40 m to centimeters 3.02 cm to metres 0.002 L to milliliters 2.005 km to metres C7.1 Use square tiles to show that if the length of a rectangle is halved and the width is doubled, the area stays the same. Explain how this is like the half-and-double strategy in mental math. Try it: Use what you know about this strategy to find the product of 56×50. 5C8 Using your Fraction Factory pieces, represent 1 in as many ways as you 2 can. Record your findings in the following table: Numerator Denominator 1 2 4 6 8 10 12 … … If you double the numerator and the denominator of any fraction in the table, do you get another fraction in the table? What if you triple the numerator and the denominator? Can you multiply both the numerator and the denominator by any number and have the result still be in the table? Can you predict the numerator if the denominator were 48? Will there be a denominator of 37 in this table? Can you predict the denominator for a numerator of 16? Will there be a numerator of 37 in this table? 5C9.2 5C9.7 1. Use square tiles to build at least six different rectangles that are 2 tiles wide, but of different length. Record and organize your observations in the table below. Width 2 units 2 units 2 units 2 units 2 units 2 units Length Perimeter Area Describe any patterns that you see in the table. What happens to the perimeter when the length increases by one? What happens to the area when the length increases by one? 2. Look closely at the patterns in this table. What shape do you think is being described? Explain your thinking. Side length (in cm) Perimeter (in cm) 1 4 2 8 3 12 4 16 5 20