4.6: Critter Trades
Critter Trades – Proportional Reasoning
Students reason proportionally as they trade critters (e.g., 1 scorpion for 4 wasps.) All trades are 1 for 2, 3, 4 or 5. As they trade, students record numbers on the traded items, and then skip count or use repeated addition to solve the problems.
In the Extras for Experts, the trading is “backwards,” that is, many to one. For example, if you can get 2 ants for 1 bee, then to get 6 ants, how many bees will you need?
Solutions
Critter Trades 1
1. 6
2. Write 2 on each spider.
Then, \begin{align*}2 + 2 + 2 = 6\end{align*}.
Critter Trades 2
1. 20
2. Write 5 on each grasshopper
Then, \begin{align*}5 + 5 + 5 + 5 = 20\end{align*}.
Critter Trades 3
1. 15
2. Write 3 on each fly.
Then, \begin{align*}3 + 3 + 3 + 3 + 3 = 15\end{align*}.
Critter Trades 4
1. 40
2. Write 4 on each scorpion.
Then, \begin{align*}4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 40\end{align*}
Critter Trades: Centipedes and Moths
For 4 centipedes, how many moths will you get?
\begin{align*}& \mathbf{Describe:} && \text{There are two different critters.}\\ &&& \text{For 1 centipede I get 3 moths.}\\ & \mathbf{My \ Job:} && \text{Figure out how many moths I can get for 4 centipedes.}\\ & \mathbf{Plan:} && \text{Write 3 on each of the 4 centipedes.}\\ &&& \text{Then add the 3s.}\\ & \mathbf{Solve:} && \text{(ART: Show the 4 centipedes in a row with the number 3 written on each)}\\ &&& \text{For 4 centipedes, I will get 12 moths.}\\ & \mathbf{Check:} && 3 + 3 + 3 + 3 = 12\end{align*}
Critter Trades 1: Spiders and Bees
- For 3 spiders, how many bees will you get?
- How did you figure it out?
Critter Trades 2: Grasshoppers and Butterflies
- For 4 grasshoppers, how many butterflies will you get?
- How did you figure it out?
Critter Trades 3: Flies and Ants
- For 5 flies, how many ants will you get?
- How did you figure it out?
Critter Trades 4: Scorpions and Wasps
- For 10 scorpions, how many wasps will you get?
- How did you figure it out?
Extras for Experts: Critter Trades – Proportional Reasoning
Solutions
Extra for Experts: Critter Trades 1
1. 3
2. 1 daddy long legs is 2 worms.
1 daddy long legs is 2 worms.
1 daddy long legs is 2 worms.
You need \begin{align*}1 + 1 + 1\end{align*}, or 3 daddy long legs to get \begin{align*}2 + 2 + 2\end{align*}, or 6 worms.
Extra for Experts: Critter Trades 2
1. 4
2. 1 lizard is 5 ants.
1 lizard is 5 ants.
1 lizard is 5 ants.
1 lizard is 5 ants.
You need \begin{align*}1 + 1 + 1 + 1\end{align*}, or 4 lizards to get \begin{align*}5 + 5 + 5 + 5\end{align*}, or 20 ants.
Extra for Experts Critter Trades 1: Daddy Long Legs and Worms
- To get 6 worms, how many daddy long legs will you need to trade?
- How did you figure it out?
Extra for Experts Critter Trades 1: Lizards and Ants
- To get 20 ants, how many lizards will you need to trade?
- How did you figure it out?
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