Manipulative Paper

Manipulative Paper: Base Ten Blocks Base ten blocks are an exceptional learning tool for elementary and middle school students. They let students easily visualize addition, subtraction, multiplication, and division and offer an alternative way of viewing a problem and developing an answer. For the most part, base ten blocks can be extremely useful in the knowledge and skills portion of the TEKS. The number, operation, and quantitative reasoning section of the knowledge and skills portion of the TEKS offer countless lessons that could incorporate this hands on manipulative.

Base ten blocks, like other manipulatives, allow students to physically use materials to conceptually learn our standard counting system. Children also grasp place value concepts more easily when they can touch and see the units. Most are made of wood, plastic, or foam and are easily accessible for teachers. Virtual manipulative sites have allowed students to work on base ten block activities from home and make learning math easier and more fun.

As students reach fifth grade they begin to “use knowledge of the base-ten place value system to compose and decompose numbers in order to solve problems requiring precision, estimation, and reasonableness. By the end of grade 5, students know basic addition, subtraction, multiplication, and division facts, and are using them to work flexibly, efficiently and accurately with numbers during addition, subtraction, multiplication, and division computation” (TEKS). Base ten blocks are ideal in place value lessons. The fifth grade TEK (1) (A) includes place value to read, write, compare, and order whole numbers.

Students can explore number meanings and their relationships while working with base ten blocks. They can use place value clues to build models of numbers and determine their value. Teachers can begin by modeling how many hundred blocks make a thousand by counting by one hundreds together. The teacher could continue by having students volunteer to share answers and explain their results. Teachers could also turn this activity into a game by including a dice. Each student would roll the dice to see which number would be the first digit that should be placed on the game board. The object would be to make the largest number possible.

Once all students have written down where the first number should go, then another student would roll the dice, and so on until all the digits have been rolled. Fifth grade TEK (1) (B) says that students will use place value to read, write, compare, and order decimals through 999,999,999,999. One activity that teachers could use with base ten blocks would be to see the difference in the place value of a decimal and how it affects the number. Students would complete the problem using the base ten blocks. Another activity using base ten blocks would include students making connections between base ten numerals and the quantities they represent.

They would investigate how many tens it takes to reach one hundred, and so on. Then, students count the largest pieces first and identify what would happen if they counted the ones, then the tens, and then the hundreds. Fifth grade TEK (3) (A) and (B) includes using addition, subtraction, and multiplication to solve problems involving whole numbers (no more than three digits times two digits without technology). Students can use the base ten blocks to model multiplication problems using a hundreds chart. They would begin by placing the desired number of blocks in the correct column according to the given problem.

Then, they would simply read the total amount of blocks to calculate the answer. Fifth grade TEK (5) (C), use division to solve problems involving whole numbers, could use base ten blocks similar to a money form. The student could portray dividing an even amount of money (the base ten blocks) among their group members by breaking the blocks apart. This activity could also work using multiplication and allowing students to determine how much money they would have at the end of a given period by multiplying the amount of blocks placed on a place value chart.

TEK (5) (4) would allow students to use the base ten blocks to estimate to determine reasonable results. Students could use the base ten blocks to build two, three, and four digit numbers. They could round the given numbers to the nearest ten, etc. The TEK (5) (14) (C) and (D) could be used for nearly every middle school grade. It includes selecting or developing an appropriate problem-solving plan or strategy and using tools such as real objects or manipulatives to solve problems. TEK (5) (15) can also be used universally as it includes explaining observations using objects, words, pictures, and numbers.

In grades six through eight students begin building a foundation of basic understandings in number, operation, and quantitative reasoning while using algebraic thinking. Although students may still use base ten blocks in these grades, the TEKS do not easily align with useful lessons. Sixth grade TEK (1) (B) students are expected to generate equivalent forms of rational numbers including whole numbers, fractions, and decimals. Students could use the base ten blocks to investigate fraction and decimal equivalencies.

In this lesson, the student would use base ten blocks and grid paper to determine the relationships between the fractions and decimals. They would compare and order the fractions and decimals to increase their understandings of the concepts. TEK (6) (2) (D) is similar to the lesson based on rounding in that students could use the base ten blocks to show estimation and round the approximate reasonable results where exact answers and not required. This activity could be assessed by having the student draw the blocks on a test or quiz.

The primary focus at grade seven is using direct proportional relationships in number, geometry, measurement, and probability. TEK (7) (1) (B) converts between fractions, decimals, whole numbers, and percents mentally, on paper, or with a calculator. Students could model fractions, decimals, and percents by exploring various methods of representing fractions. They demonstrate situations that represent rational numbers. This lesson also relates to a previous one by allowing the student visually recognize the equivalency between fractions and decimals.

TEK (7) (2) (C) uses models to add, subtract, multiply, and divide integers. In this lesson involving multiplication, students could use the base ten blocks to practice solving problems involving the multiplication of decimals. Using the base ten blocks, they try to find as many instances as possible of decimals that when multiplied give a specific answer. Students explain their solutions in writing and give justification for choosing the numbers they used to solve the problem. Using base ten blocks, or any manipulative for that matter, in the classroom can change the way a student thinks of both math and learning.

When teachers give students different ways of viewing a problem a student’s mind grows in creativity and imagination. It is up to all future teachers to take the initiative to include manipulatives in the classroom for all students. Struggling students will greatly benefit from the use of manipulatives as they often require alternate ways of thinking conceptually. All manipulatives are great, and the use of them plus increasing technology will only make it easier for us to increase our teaching abilities.

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