Vocabulary

Vocabulary Workshop, Tools for Comprehension
Grades 1–5

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Grades 6–12+

Reading

From Phonics to Reading
Grades K-3

Math games and activities can be an excellent tool to supplement and support math instruction. Using math games in your classroom allows students to practice mathematics in fun but also impactful ways. Students love games because they are engaging and exciting, and teachers love games because they help students practice what they've learned.

First-grade students will extend their comprehension of mathematics by counting up to larger numbers and developing their skills in addition and subtraction while using base-ten blocks, coins, connecting cubes, number lines, pattern blocks, Venn diagrams, dominoes, and spinners. These activities will also offer additional practice and understanding of 2-digit numbers and sequencing.

To model a number such as 4, children should be asked to place one counter in the ten frame and then add one more at a time. With each step, ask which group has more and which has fewer to emphasize number relationships.

Invite children to fill the ten frame across the first row, starting from the left just as they read a book. When they fill the first row, anchor the number 5 so that children can use 5 as a reference when they model numbers 6–9. After the first row is full, have children begin placing counters in the bottom row, again starting on the left.

Have children use a blue counter for the last counter in the model. This change introduces part-part-whole relationships—that there are different combinations that make the same number. Children who can represent a number in a ten frame with different color combinations will be able to translate this skill to addition concepts.

Children will need to place counters outside the ten frame for modeling numbers 11 and 12.

Children can extend this pattern for other numbers to 20 and beyond, and when they model sums greater than ten.

To model 2-digit numbers, children can use ten rods and ones cubes. Be sure children recognize that a ones cube is a single unit that represents the number 1 and belongs in the ones place in the base-ten system. A ten rod is comprised of ten connected ones cubes and represents 10 and the tens place.

The number of ten rods corresponds to the digit in the tens place of a number. The number of ones cubes corresponds to the digit in the ones place of a number.

To model a number, children should identify the digit in the tens place and lay out that many ten rods. Then, they should identify the digit in the ones place and lay out that many ones cubes.

To identify a number represented by a model, children should count the number of ten rods to find the digit in the tens place. The number of ones cubes tells the digit in the ones place. Children can also count the total number of ones cubes in the entire model, but this brute force method is time-consuming and ignores the merits of place-value concepts.

Two-Digit Subtraction

A concrete activity, such as the following, will help children as they move to the abstract algorithm. Have children work in pairs to practice building 2-digit numbers using rods and cubes. Encourage them to build each number in a variety of different ways and then challenge them to build the number in the most efficient way. The number 56, for example, can be built with 3 rods and 26 cubes, but is most efficiently built with 5 tens and 6 ones.

Then, have children model subtraction problems, such as 42 – 18. Have children build 42 (4 rods and 2 cubes), and invite them to generate strategies for “taking away” 18. Children should see that they can “trade” 1 rod for 10 cubes allowing them to take away 18 (1 rod and 8 cubes). The remaining rods and cubes show the difference. As children gain confidence in their concrete work, encourage them to record their subtraction on a place value mat.

You may wish to challenge children to solve “missing number” problems. Give them a starting number, such as 51, and challenge them to find the number that is subtracted in order to end up with a given difference, such as 35 (16).

Invite children to play a game of *Coins Three Ways*. Begin by giving partners a selection of coins. Then explain that you are going to name an amount and ask them to show that amount in three different ways. You may wish to demonstrate how the game is played by counting out 27 cents as five nickels and two pennies. Then, show the same amount as a quarter and two pennies. Finally, show 27 cents a third way as two dimes and seven pennies. Count each grouping with the class.

Ask children to show you three ways that they can show an amount. Begin by asking partners to show 33 cents three ways. Use children’s coin combinations to build a chart that shows the various combinations. Invite children to identify which combination requires the fewest coins and which combination requires the most. Encourage children to use the data in the chart to describe any trends, patterns, or similarities that they see.

Some possible combinations that make 27 cents:

Give children a different color cube for each addend. The colors will help children visualize the different parts they are joining. For example, children can see that 1 blue cube and 6 red cubes make 7 cubes, as do 2 blue cubes and 5 red cubes, 3 blue cubes and 4 red cubes, and so on.

Have children begin by building the parts completely and then joining the parts to make a whole.

Reading or writing the combinations encourages reflective thought on the “part-partwhole” relationship. You may wish to have children record their work through drawings, numbers written in blanks, or by writing addition sentences.

Children typically begin by noting the addition facts associated with the domino, such as 5 + 4 = 9 and 4 + 5 = 9.

Have them cover one side of the domino with a finger or index card and write the related subtraction fact. Repeat for the other subtraction fact by covering the other side of the domino. Ask: “How much is left when you take away 5? How much is left when you take away 4?” Have children say and record the related subtraction facts: 9 – 5 = 4, 9 – 4 = 5.

After organizing the four written number sentences, have children use different colors of highlighters to mark each number (all of the 5’s, for example, could be yellow). Help them see how the placement of the number changes, and connect the relationship between the whole and the parts in the addition and subtraction sentences.

Relate the different written forms of notation (vertical and horizontal formats) by having children rewrite their number sentences in the other format.

Separate the class into teams of two and give each team an inch ruler and a pile of paper clips. Ask each team to choose 3 classroom objects to measure. (Objects should be no larger than a desk.)

Ask teams to estimate the length of each object and record their estimate. Then have children measure the length of each object in paper clips. Show children how to record their data in a chart such as the one shown here. You may wish to have children find the difference between their estimates and actual measurements by subtracting the lesser number from the greater.

Have children repeat the activity by estimating and measuring in inches and completing a second chart.

Allow time for the teams to discuss how they made their estimates and how close their estimates came to the actual measurements.

Ask children to consider why the activity would be more difficult with larger objects, such as the distance of a room. Ask for a nonstandard unit (such as a jump rope) and a standard unit (foot) that might be more effective for measuring greater distances.

Create a number line on the floor with the tens labeled. Ask them to count aloud by tens as they walk along the number line, stopping at each “ten.”

Then have children practice locating individual numbers on the number line and establishing which “10” is closest to that number. Given the number 52, for example, children should identify 50 as the closest number on the number line. You can teach children the convention that numbers ending in 5 round “up.”

Finally, show children how to use the number line to estimate sums. The estimate of 52 + 25 is 80, for example, because 52 is closer to 50 than to 60, and so it rounds down to 50. On the other hand, 25 is midway between 20 and 30 and ends in 5, so 25 rounds up to 30. 50 + 30 = 80.

To reinforce the concept of rounding, children can work together to create numbers to round and then add together. Have each partner take turns tossing a number cube twice to make and record a 2-digit number. Then, have partners use their number line to round their number to the nearest ten and record it beside the original 2-digit number. Finally, have children add their rounded numbers.

A game such as *What Shape Am I?* gives children a problem-solving experience with shape identification. To play the game, give each child a selection of pattern blocks. Then, put a shape behind your hand. Tell children you will give them clues to help them guess what shape you are hiding. Explain that after each clue, they are to put aside all of their shapes that do not match the clue. Then, offer clues about the “mystery shape” that you are holding. For example, you might say, “I have four sides.” At that point, children would remove the triangles and hexagons from their piles. Then you might say, “I have square corners.” Children would remove the rhombus, the small rhombus, and the trapezoid, leaving the square. As children eliminate possible shapes, encourage them to verbalize their problem-solving processes.

As you progress through each lesson in this chapter, you can use the pattern blocks and the *What Shape Am I?* game to assess children’s comprehension of concepts. You may wish to challenge advanced learners by offering longer descriptive clues that include terms such as: and, but, and not. For example, you might say. “What Shape Am I? I have no square corners and I do not have four sides.”

Separate the class into groups of two or three. Give each team a spinner divided into three unequal parts. Ask children to describe their spinners and compare the amount of space devoted to each color.

Have each group predict which color will “win” when they spin the spinner 20 times. As children take turns spinning the spinners, have them record their group’s results on a chart such as the one below.

After children have completed their charts, have them discuss the results and report which color “won.” Encourage children to explain why they think a particular color was landed on more often than another color. Guide children to understand that the more space a color takes up on the spinner, the greater the likelihood that the arrow will land on it, and the greater the likelihood that it will “win.”

Have children repeat the activity with different spinners. When children use a spinner with equal-size sections, help them understand that the probability of landing on a particular color is the same for any other color though the results may not be exact for each color.

The addition strategy “make ten” relies on place-value concepts and children’s ability to quickly recognize the number 10. This strategy requires children to break the second addend in a addition sentence into parts, so that the first number and part of the second number make ten. Then, the second part of the second number is added to ten to find the total. This strategy is difficult to explain abstractly, but is quickly understood when demonstrated and experienced with a ten frames and counters as below:

Children can also use two ten frames to add. Give children two numbers, such as 9 + 8, to add. Ask them to model each number in a separate ten frame, and then invite them to suggest ways to use the ten frames to add the two numbers by joining the ten frames. Guide children to understand that they should move counters from one ten frame to fill the other, then add or count on from ten to find the sum. Have children explain what they did, and focus especially on the idea that counters can be taken from a frame that represents one number and put together with the other frame to make 10. Then, there is 10 and some more.

Allow time for children to practice both methods with a variety of problems, including doubles (7 + 7) and near doubles (7 + 8).

Real graphs, such as concrete graphs, use the actual objects being sorted and graphed. Most of the graphs that children work with in Chapter 4 are symbolic graphs, which use something like squares, blocks, tallies, or X’s to represent the things being counted. Sorting actual objects into Venn Diagrams formed with yarn ovals is an excellent activity building a real graph, and will prepare children for the symbolic activity in later lessons.

Have children sort a variety of red shapes and different color triangles into two overlapping yarn circles. They can work with partners or small groups. Allow time for children to discuss different ways to sort the shapes. Challenge them to find a shape that belongs in the overlap area, and discuss why this shape belongs there.

Then, have children sort a collection of coins and challenge them to come up with their own attributes to sort by. Help children label their circles and have them share their results with the class as a method of checking student work.