Pre-Service Mathematics Teacher
MANIPULATIVES
This page has a list of manipulatives across all grades and subjects in mathematics. Each resource listed has a picture of the manipulative itself and a brief description. You will find ones that were already listed in a different section of this website plus many more! These can be used in multiple ways, and not just the examples I listed!
Calculators
While it is important for students to learn how to do concepts by hand, calculators are a great resource for them to check their answers. Once students master a concept, they can use their calculators to quickly get through other problems were previous concepts are used. Graphing calculators are great for students to check their work, or visually see the graph they are working with.
Dominos
Dominos can be used to help students learn algebraic concepts such as fractions. They can randomly pick at least two dominos and add, subtract, multiply, or divide them. Students can also strengthen their knowledge by mastering simplifying fractions using dominos.
Cuisenaire (Algebra) Tiles
Cuisenaire tiles allow students to use tiles to represent variables and constants, learn how to represent and solve algebra problem. Solve equations, substitute in variable expressions, and expand and factor. Flip tiles, remove zero pairs, copy and arrange, and make your way toward a better understanding of algebra.
Tangrams & Pattern Blocks
Tangrams are puzzles that consist of a small square, two small congruent triangles, two large congruent triangles, a medium-sized triangle, and a parallelogram. Students are to put these seven pieces into given shapes. These can be used in geometry investigate area, perimeter, and angles, for example.
Compass, Protractor, and Ruler
Compasses, protractors, and rules can be used in the geometry classroom for students to create their own constructions of given shapes. From there, they can use their knowledge of geometric rules to prove a theorem. For example, students could prove an isosceles triangle has the same base angle measures by drawing an isosceles triangle using the compass to circles and connect the points.
Geoboards
Geoboards are used to explore basic concepts in plane geometry such as perimeter, area and the characteristics of triangles and other polygons. It consists of a board with a certain number of pegs or nails half driven in. Bands can be used to create shapes. Students can explore, formulate, and strengthen their own understanding of geometry through hands-on activities while using these.
Prime Climb is a great game for students to review their basic operations of adding, subtracting, multiplying, and dividing at the beginning of the year! It is also a great review of prime numbers for them. This game requires the players to land both of their pawns at 101. They can't go over the number 101. In order to get here from 0, players can apply any basic operation to the dice rolled. Click the link to watch the video for a full explanation!
Prime Climb
Clocks
Clocks can be used in a variety of ways. They can help students visualize fractions. They can also help students learn about modular arithmetic. Modular arithmetic is also known as clock arithmetic. Students can first begin by doing modular 12 problems. They can move the clock hands around to see how many times the minute hand passes around 12, then move the remaining amount. For example 25 mod 12. They can start at 12:00. Then will then make two revolutions, then move to 1:00. 1:00, or 1, would be the answer to 25 mod 12.
Dice
Dice are very universal in the math classroom. Students can roll two dice to and apply basic arithmetic operations to the numbers to review adding, subtracting multiplying and dividing. They can roll two numbers and create a fraction, and if necessary, simplify them. Students can also compute basic probabilities through trial and error. They can, for example, roll the dice 10 times, and compute the amount of times they rolled an even number. They can then take their results and compute the probability, if this trend continues, of rolling a an even number out of 100 rolls. By doing this, students are also using algebra.
Marbles can be easily utilized in the statistics classroom. Students can randomly draw marbles from a preset bag of marbles, consisting of specific colors. They can compute the probability of their drawings. For example, if a bag had 3 red marbles, 4 green, and 5 blue, students can randomly draw one marble. Say they draw green followed by a red.. They can compute the probability of drawing a green and then a red from the bag.
Marbles
Playing Cards
Playing cards can be used in the statistics classroom to help compute probability. Students can randomly draw cards from the standards 52 card deck, and find the probability of drawing that exact draw. They can also use cards to demonstrate the concept of permutations and combinations.
Fraction & Percent Circles
Fraction and percent circles are a great way for students to visualize fractions and percents. Students tend to struggle with the concept of fractions and percents. By allowing students to use these, they will be able to visually see how what a specific fraction or percent looks like. Teachers can also have students to construct their own.
Fraction War Game
"Students take turns playing “war” using a deck of cards and a pencil to act as the fraction line. The pair of students must then decide who has the larger fraction based on the four cards played. The winner gets to keep all the cards. Player with most cards at end wins."
Review game was found at
X-Y Plane Peg Board
This peg board can be used to help students visualize graphs. For example, when teaching students how to find the equation of a line given two points, they can "graph" the two points on the pegboard, solve for the slope, produce a formula for the line, then graph the line.
Trigonometric Paper Plate Unit Circle
This project has students create their own trigonometry unit circle that can be used as a reference for future lessons! The different colored lines on the plate correspond to different "special triangles." Click on the below above to access this activity!
http://managingandmotivatingmathminds.blogspot.com/2016/03/paper-plate-unit-circle.html?m=1
Trigonometry Reference Trifold
This trifold has basic concepts of trigonometry, including right triangles, reference angles, and unit circle concepts. This is not only a great resource for teachers, but also students. While students are being introduced to trigonometric concepts, the teacher can copy parts of this trifold to pass out as a handout, which students can use until they master the topic!
Trigonometry Identity Manipulatives
These are a great way to teach students how to arrive at a solution given an equation to solve given trig identities. On the left is a picture of these easy to make manipulatives. Each function and number have "grooves" that align with one another. This helps students visually see what matches. To watch the video to explore how these work, click on the link below to see the "Trigonometry" tab.
Slinky
This classic toy can be a great teaching tool for trigonometry. Using this will help students visualize the sine and cosine waves. Teachers can plot a graph on the floor using tape, such as masking or painters tape. They can then have two students hold the slinky at different lengths. Students will then "send" a wave back and forth. From here, they can determine the amplitude, frequency, and periods of different length waves!
Solids with Known Cross Sections
These manipulatives are great visual aids to help students see areas under the curve when using the shell and disk methods! The teacher can make these ahead of time, or the students can do this as an activity. To view more about these, click on the link below!
Sticky Notes
Sticky notes are a great way to teach students about Riemann Sums! Students cut the sticky notes into strips. They then place the strips on the graph paper under the curve. From here, they measure and calculate the area of each rectangle to find the area under the curve. To view more on this, click the link below!
http://teachinghighschoolmath.blogspot.com/2018/01/teaching-riemann-sumsa-post-it-activity.html