<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Dismiss
Skip Navigation
Our Terms of Use (click here to view) and Privacy Policy (click here to view) have changed. By continuing to use this site, you are agreeing to our new Terms of Use and Privacy Policy.

2.3: Circles and Arrows

Difficulty Level: At Grade Created by: CK-12

Circles and Arrows – Solve for Unknowns

In these problems, students are presented two-by-two 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*}A, \begin{align*}A\end{align*}A and an arrow pointing to 4, can also be represented by the equation: \begin{align*}A + A = 4\end{align*}A+A=4. Students use the grid relationships to figure out the values of the letters. There are often several ways to begin to solve each problem. Encourage students to consider and talk about alternative approaches. All sums in the first set of problems are 10 or less. In the Extras for Experts, sums are 18 or less.

Solutions

  1. \begin{align*}C = 3, D = 1\end{align*}C=3,D=1
  2. \begin{align*}E = 5, F = 2\end{align*}E=5,F=2
  3. \begin{align*}G = 4, H = 1\end{align*}G=4,H=1
  4. \begin{align*}J = 1, K = 5\end{align*}J=1,K=5
  5. \begin{align*}L = 2, M = 3\end{align*}L=2,M=3
  6. \begin{align*}N = 5, P = 3\end{align*}N=5,P=3
  7. \begin{align*}Q = 2, R = 4\end{align*}Q=2,R=4
  8. \begin{align*}S = 4, T = 2\end{align*}S=4,T=2
  9. \begin{align*}U = 4, V = 6\end{align*}U=4,V=6
  10. \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=5-2, \ \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.

Image Attributions

Show Hide Details
Description
Authors:
Date Created:
Feb 23, 2012
Last Modified:
Apr 29, 2014
Save or share your relevant files like activites, homework and worksheet.
To add resources, you must be the owner of the section. Click Customize to make your own copy.
Reviews
Help us create better content by rating and reviewing this modality.
Loading reviews...
Please wait...
Please wait...
Image Detail
Sizes: Medium | Original