3.4: Circles and Arrows
Circles and Arrows – Solve for Unknowns
In these problems, students are presented twobytwo grids containing circles and arrows. Circles contain numbers or letters that represent unknown quantities. Arrows point to sums of rows and columns. Each row and column represents an equation. For example, a row showing \begin{align*}A\end{align*}
Solutions

\begin{align*}C = 3, D = 1\end{align*}
C=3,D=1 
\begin{align*}E = 5, F = 2\end{align*}
E=5,F=2 
\begin{align*}G = 4, H = 1\end{align*}
G=4,H=1 
\begin{align*}J = 1, K = 5\end{align*}
J=1,K=5 
\begin{align*}L = 2, M = 3\end{align*}
L=2,M=3 
\begin{align*}N = 5, P = 3\end{align*}
N=5,P=3 
\begin{align*}Q = 2, R = 4\end{align*}
Q=2,R=4 
\begin{align*}S = 4, T = 2\end{align*}
S=4,T=2 
\begin{align*}U = 4, V = 6\end{align*}
U=4,V=6 
\begin{align*}W = 2, X = 3\end{align*}
W=2,X=3
Figure out the value of each letter.
\begin{align*}& \mathbf{Describe:} && \text{Two rows and two columns with numbers and letters.}\\ &&& \text{Arrows point to sums.}\\ & \mathbf{My \ Job:} && \text{Figure out the values of letters} \ A \ \text{and} \ B.\\ & \mathbf{Plan:} && \text{Start with the first row. Solve for} \ A.\\ &&& \text{Then figure out} \ B.\\ & \mathbf{Solve:} && A+A=4, \ \text{so} \ A=2,\\ &&& \text{In the first column,} \ A+B=5\\ &&& \text{Replace} \ A \ \text{with} \ 2.\\ &&& \text{Then} \ 2+B=5. \ B=52, \ \text{or} \ 3.\\ & \mathbf{Check:} && \text{Replace all} \ A\text{s with} \ 2.\\ &&& \text{Replace all} \ B\text{s with} \ 3.\\ &&& \text{Add rows and columns. Check with sums.}\\ &&& \text{Row} \ 1: 2+2=4 \qquad \text{Column} \ 1: 2+3=5\\ &&& \text{Row} \ 2: 3+6=9 \qquad \text{Column} \ 2: 2+6=8\end{align*}
1. Figure out the value of each letter.
2. Figure out the value of each letter.
3. Figure out the value of each letter.
4. Figure out the value of each letter.
5. Figure out the value of each letter.
6. Figure out the value of each letter.
7. Figure out the value of each letter.
8. Figure out the value of each letter.
9. Figure out the value of each letter.
10. Figure out the value of each letter.
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