K-2 Algebraic Thinking

This collection of resources helps to develop algebraic thinking skills for K-2 students. The interactive games and activities emphasize pattern recognition and logical thinking. One activity focuses attention on the patterns in a hundred chart while several others emphasize shape and/or color patterns. Several balance activities introduce basic ideas about equality. Use these resources to begin to build mathematical thinking skills in young students.

Collection Discussion

Replies: 7
Created:04-12-2012 by path
Last Post05-12-2016by leesajohnson
Replies: 2
Created:09-30-2012 by Uncle Bob
Last Post03-16-2013by leesajohnson
Pre-K, K, 1

This interactive Java applet helps students analyze and extend patterns. The applet displays a pattern of beads and the user selects colors in the correct sequence to continue the pattern. The applet acknowledges each correct solution and encourages the user to fix any incorrect ones.

Ten bones are hidden in the squares of a blank 1-100 grid. Students are given the numbers of the squares one at a time. They attempt to locate the numbers in the hundreds chart and find all 10 bones within 60 seconds. Numbers of the incorrectly guessed squares are left in place to help with the search. The game helps students understand the structure and patterns of our base-10 number system. Children can be encouraged to make use of a found bone to locate the next one.

In this activity students are asked to relate the numbers 1- 20 to rectangular shapes. Learners use unit squares or cubes to sort numbers by their 'shapes,' either squares, rectangles or sticks (rectangles of unit width). Ideas for implementation, extension and support are included.

This activity gives students practice naming and using shape and color attributes to create patterned sequences. The first challenge asks students to use attribute differences to extend a sequence. A second, more open-ended challenge asks students to maximize the length of their sequences under a further constraint. An interactive applet is provided as an alternative to physical manipulatives. The Teachers' Notes page includes suggestions for implementation and discussion questions.

This Java applet allows children to explore a balancing tool and thus build their algebraic thinking about equivalency. By placing shapes on each side of the balance and finding equivalent sets of weights, students discover the weight of each shape in one of six built-in sets or a random set.

This interactive applet reinforces students' knowledge of the properties of rectangles and gives them a game in which to form and test hypotheses. In a 5x5 grid in which a rectangle has been hidden, students try to fix the location with the fewest number of probes (Note: press 'Start' to hide a different rectangle). Ideas for implementation, extension and support are included along with printable sheets and video clips of classroom testing.

This problem promotes logical thinking and introduces learners to the trial and error (guess and check) problem solving strategy, especially with the interactive provided. In this problem children need to understand the difference between having a certain number of brothers and the number of boys in a family to answer the question, "How many children are there in the Brown family?" The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, and a link to a down loadable worksheet for students to table their trials.
2, 3, 4, 5

This interactive Flash applet simulates the traditional frog jumping puzzle, which develops logical reasoning and problem solving strategies. The goal is to swap the green and blue fogs to the opposite sides in as few moves as possible –– and to discover a rule for the minimum number of moves necessary based on the starting number of frogs. This version allows the user to adjust the numbers of frogs independently from one to five.
2, 3, 4, 5

This investigation is an opportunity for children to practice sorting, classifying, and organizing information, as well as recognizing, generalizing and predicting patterns. Learners arrange images of houses and teddy bears in an array such that each row and column contains all four colors of each. By progressing gradually from a 3 by 3 grid to a 6 by 6 grid, they develop systematic, strategic thinking. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, and a link to an extension activity, Tea Cups (cataloged separately).
1, 2, 3, 4, 5, 6+

This open-ended interactive Flash applet helps students develop operation and number sense, facility with number facts, and understanding of equations. Users designate single-digit whole numbers or integers and operations on both sides of an equation and test for balance. Users can enter numbers by using the keyboard or arrow buttons or by dragging number tiles. Each element can be hidden and a seesaw may be toggled on/off. Teachers may use this applet to lead instruction, or students may use it independently to perform specific investigations or explore freely. Supplementary documents include Objectives, containing teaching suggestions, and a student recording sheet.