Base-Ten Block Sketches

Explicit Instruction/Teacher modeling

• Choose volunteers to restate the problem, or what you are trying to find out, in their own words.
• Underline the word "more." Reflect that since you are adding more rocks to your collection, the total number of rocks that you have after your hike will be greater than the number of rocks that you had before your hike.
• Ask students to share ideas for different strategies to solve the problem. Model drawing a picture, first drawing 12 rocks, then 10 additional rocks. Count the total number of rocks.
• Show students how to count on from the number 12 using both the number line and the hundreds chart. Although students may notice that 22 is below 12 on the hundreds chart, count by ones initially to build understanding.
• Write the number sentence 12 + 10 = 22. Reflect, "I have 22 rocks now. Twenty-two is 10 more than 12."
• Tell students that today they will learn a way to sketch a picture that will make adding multiples of 10 faster than counting by ones.

Guided Practice

• Instruct students to flash all 10 fingers as you count chorally by tens from 10 to 100.
• Show students base-ten blocks, and explain that they are used to help solve math problems.
• Tape a base-ten rod on the board, and label it "ten."
• Tape a base-ten cube on the board, and label it "one." Line up 10 cubes next to the rod so that students can see that the 10 cubes equal one rod.
• Ask students if they know what a "sketch" is. Define sketch as a quick drawing. Tell students that today they will sketch base-ten blocks to solve problems.
• Show students how to draw a stick, or short vertical line, to sketch a tens rod. Next, draw a small circle to represent a ones cube.
• Model solving the addition problem 24 + 5. Ask students to show you on their fingers how many tens are in the number 24, and draw two sticks. Ask how many ones are in the number 24, and draw four small circles.
• Notice the plus sign as you think aloud, "The plus sign tells me that I need to add another part. I need to add five more." Add five small circles to the sketch.
• Count chorally, "Ten, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29" as you point to the blocks in the picture.
• Repeat the procedure with the problem 45 + 20. Identify the total number of tens and ones in each part, and sketch base-ten blocks using sticks and circles (six sticks and five circles total). Count the sticks by ten (ten, 20, 30, 40, 50 60), and the circles by one (61, 62, 63, 64, 65) to solve the problem. Add the solution to the equation 45 + 20 = 65.
• Show a few more examples.

Group work time

• Tell students that today they will work with a partner to sketch base-ten blocks to solve word problems.
• Distribute the Sketch the Solution worksheet, and tell students to point to the first problem as you model pointing to problem #1 on your worksheet.
• Practice reading the problem three times with students, each time with a different focus.
• Say, "Let's read the problem together," and chorally read as a class.
• On the first read, focus on the context, or situation of the problem. Ask students, "What is this problem about?" Allow students think time. Choose volunteers to restate the context of problem in their own words before beginning to solve the problem.
• Ask, "What words in the problem help us understand what the problem is asking?" Write students suggestions (i.e., 32 pages, 10 pages, more, total) on the board. Model underlying these words and phrases on the worksheet.
• Tell students to turn and talk to a partner about how to solve the problem. Model a turn and talk procedure, by turning to face a student and pointing to your mouth. Listen as students share ideas.
• Instruct students to write their answers, by motioning with a pencil above the worksheet. Circulate and notice whether students sketch base-ten blocks to solve the problem, or use other strategies.
• Tell students to solve problems #2 and #3 with their partners, talking to their partner about the problems and underlining important information first.
• Point to the example problem on the board. Instruct students to include a base-ten block sketch and an equation in the solution.
• Students who finish early can write their own story problems on the back of the paper and exchange with their partner.