Operations and Algebraic Thinking

Write and interpret numerical expressions.

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Resource | Resource Type Grade Level | Rating |
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This activity is a good way of introducing the value of algebraic notation and translating verbal expressions to algebraic expressions. Students are asked "to think of a number," then to do seven consecutive computational steps beginning with their number and to figure out why 2 is always the final result. The teacher's notes, hints, and solution are provided. | Activity Grade Level: 3, 4, 5 | |

This Technology Problem of the Week (tPoW) challenges students to identify the points on the plane that Sam the Chameleon could reach with his tongue if he sticks it out 1 more unit than twice the distance that he walked. It links to the Java applet "Chameleon Applet." Solve and explain your solution; download hints and answer checks. Free registration is required. | Interactive Media, Problem Set Grade Level: 4, 5 | |

This interactive game develops fluency and flexibility with whole number operations. Each round presents a card (flippo) with four single-digit whole numbers. The player uses each number exactly once with the interactive calculator to arrive as close as possible to the target number 24. | Activity, Game, Interactive Media Grade Level: 3, 4, 5 | |

This interactive game develops fluency and flexibility with whole number operations. In each round the player is given 4 single-digit whole numbers, presented in the context of a factory. The player uses each number exactly once with the interactive calculator to arrive as close as possible to a given target number. | Activity, Game, Interactive Media Grade Level: 4, 5 | |

This interactive pan balance allows students to enter numeric or algebraic expressions and investigate the important concept of equivalence as well as practice arithmetic and algebraic skills. Users place an expression in each of the red and blue pans. These expressions may or may not include the variable x. If the expression is algebraic, a value for x is entered or adjusted by moving the slider. As the value of x changes, the results will be weighed and graphed. Instructions and exploration directions and questions are included. | Activity, Interactive Media Grade Level: 3, 4, 5, 6+ | |

This Java tool is used to strengthen student understanding of equality and computation of numerical expressions. The applet also helps students understand that equality is a relationship, not an operation. After entering an expression in both the red and blue pan, the pans will move up and down depending on which expression is greater. When the expressions are equivalent, the pans will balance and the full equation will be entered into the Balanced Equations table. Instructions and exploration directions and questions are included. | Activity, Interactive Media Grade Level: 3, 4, 5 | |

This set of two interactive challenges from the Annenberg Teachers' Lab helps learners develop reasoning skills with number patterns by looking systematically at specific examples, and then by making predictions and generalizations. In "How Many Valentines", students try to figure out the number of valentines sent by an entire class. In "Mystery Operation", solvers try to determine what the computer's mystery operation is by entering a pair of numbers and studying the outputs. Background discussion, a rationale, grade-level information, connections to standards, and solvers' comments are included for each activity. | Activity, Interactive Media Grade Level: 3, 4, 5 | |

This activity promotes students to explore and analyze the number of different ways of achieving each of the specific outcomes when adding and subtracting positive and negative integers while playing the game, "Connect Three." By answering key questions, the players work out a strategy for improving their chances of winning the game. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for support, extension and answers to questions are provided. A pdf of the game board and a spreadsheet to simulate tossing the dice are linked. | Activity, Game, Interactive Media Grade Level: 5, 6+ | |

This interactive Java applet use arrays and three different computational models (Grouping, Common, or Lattice) to help students visualize and understand the process of multiplication of whole numbers. In each method the user drags sliders to adjust the two factors and then observes the resulting changes in the rectangular array and in the respective algorithm and product. | Activity, Interactive Media Grade Level: 2, 3, 4, 5 Resource is part of a PD collection | |

This web page links to a series of 6 pages of number puzzles (141 altogether) which develop flexibility and computational fluency. Puzzles provide a target number and several other numbers, each of which must be used exactly once to arrive at the target. Solvers may use any of the four basic operations (addition, subtraction, multiplication, division) and parentheses. Most puzzles are solvable with whole numbers, but a few solutions involve fractions. Each puzzle contains a hint as well as at least one solution. Red asterisks indicate more difficult puzzles. | Activity, Problem Set Grade Level: 3, 4, 5, 6+ |