Ask your students to share ways they would group a set of 23 ob- jects to make them easier to count. (Instead of telling them to group by tens and ones.) Ask your students to share what strategy they would use to mentally subtract 82-64 (Instead of showing them the algo- rithm.) Challenge your students to figure out how 3 friends would share 4 cookies equally. (Instead of telling them what a fraction is.)

Tis type of instruction takes care- ful planning of a series of proper- ly sequenced varied experiences paired with strategic questioning and opportunities for meaningful distributed practice.

Once a concept is developed, students should be able to explain their thinking by constructing viable arguments in mathematically precise language.

#5 Math Shift: Students will be required to use ma- nipulatives and other tech- nology enhanced items to demonstrate mathematical concepts.

One way to assist students with concept development is to help them visualize abstract concepts with manipulatives. Manipulatives can be anything from hundreds charts to number lines to deci- mal squares—anything that helps students to visualize mathematical concepts. An obvious example is base-ten blocks. Tese virtual ma- nipulatives allow students to visual- ize the “sizes” of numbers indicated by their places in our number system.

Manipulatives also help students to understand the concepts behind

mathematical procedures such as using base ten blocks to illustrate “regrouping” in a multi-digit addi- tion or subtraction algorithm.

Manipulatives give students a con- crete visualization to hold in their minds when they are computing to understand what is really happen- ing mathematically. Using a variety of manipulatives in your classroom allows students to choose a tool that works best for them.

In addition to traditional manipu- latives, you should also expose your students to virtual manipulatives. Tere are hundreds of online ma- nipulatives available which provide you with a variety of instructional options that would be cost prohibi- tive with traditional manipulatives.

Virtual manipulatives may have added features that bring value to

Assessing Conceptual Knowledge: As you assess your students’ current place value knowledge in order to build on what they already know or to identify gaps in their understanding, be sure you are not just assessing rote knowledge but also conceptual understanding. Your students may be able to state the value of a digit, but do they understand what that value represents? Here are several ways you can use digital con- tent to find out!

1. Use online place value cards to build numbers and visually remind students that there are implied zeros as place holders for each digit.

2. Place the same digit in each place value and use the cards to discuss the relationship between neighbor- ing digits. Guide your students to discover that each digit to the leſt is ten times the value of the digit to its right AND that each digit is one-tenth the value of the digit to its leſt.

3. Ask your students to use their place value knowledge to build the largest number or smallest number possible with given digits in order to determine their understanding of the role of place in determining the value of a digit. What is the largest number you can build with the digits 5, 6, and 3? What is the smallest number you can build? Use base ten blocks to visually represent answers.

4. Ask students to model a number with non-proportional manipulatives. For example, how could you model 356 using pennies? You will quickly learn if your students understand the concept of grouping ten individual objects to create a ten and grouping ten groups of ten to create a hundred.

5. Correct student misconceptions by using online base ten blocks to model solutions. Ask your students: How many tens are in 356? Most students will answer 5; however, that is incorrect. Tere are 35 tens in 356. Use base ten blocks to model this concept. Ten challenge your students to build a three digit number using only tens.

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