4th grade- Algebraic Thinking DEEPER

4th grade Algebraic Thinking

(Fully explain all reasoning)

  1. A Whitman’s Sampler Box of Candies contains 36 chocolates. These are arranged in 3 equally shaped layers. If each of the layers is a rectangular array, then what are the possible ways this could be done? Which way do you think it was done?
  1. I have 2 pets and my friend Bob has 3 times as many pets. My friend Alice has half as many pets as I do. How many pets do all 3 of us have together? Show your work.
  1. In October I saved 4 times as much money asI saved in September and 6 times as much money as I saved in August. If I saved $30.00 in October, then how much money did I save in total during the 3 months of August, September, and October?
  1. There were two plants. In 2013, Plant A was 6 inches long and plant B was 8 inches long. Between 2013 and 2014, one plant grew 10 inches and the other grew 11 inches. Which plant was taller at the end of 2014? What is the total height of the two plants at the end of 2014?
  1. Grandma baked 5 dozen cookies. She gave each of her friends 7 cookies and she kept 4 cookies for herself. How many friends did grandma share the cookies with?
  1. There are 50 kids going on a field trip. Two private cars are available. Each car holds 4 people (including the adult driver)and each van can hold 8 people (again, including the driver). How many vans will be needed for the fieldtrip? How many adult drivers will be needed? Will all the vehicles be filled to capacity? Explain.
  1. You go to a shop that sells tricycles and unicycles. There are 18 wheels in theWheel Shop. There are 2 more tricycles than unicycles in the shop. How many tricycles are in the shop?Explain how you know.
  1. The Wheel Shop sells other kinds of vehicles. There are bicycles, bicycles built for 2and go-carts in a different room of the shop. Each bicycle has onlyone seat and each go-cart has only one seat, whereas each bicycle built for 2 has two seats. There are a total of 30seats and 24 vehicles in that room.How many bicycles arein that room? How many go-carts are in that room?How many bicycles built for 2 are there in that room? How many wheels are in that room? Explain how you figured it out.
  1. Find threedifferent factors for the number 36 whose sum is 27.
  1. The rule is to add the same number to every input. Find this number to add and then complete the table below.

INPUT / OUTPUT
5 / 12
7 / 14
9
27

What patterns do you notice? If the input is odd, then what is the output?

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