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1. Playing Cards (like War)

1. This activity is used to practice place value concepts and identifying greater and lesser numbers. The teacher deals each student's cards from a classic deck of cards. Take out face cards unless students can associate a value with them and Aces. Students flip over one card at the same time, and whoever has the higher number gets to collect both cards. (Virginia Department of Education, et al., 2020). Instructional strategies used are modeling and providing time for guided and independent practice; students also practice social skills playing together and the fast-paced nature helps increase fluency.

2. Rounding with Base-10 blocks

1. Students use manipulative items (base ten blocks) to visually see how to round numbers to the nearest 10. As students explore and decide if a number is rounded to the smaller or larger ten, they keep a record. Next, students can look for patterns in the two columns and write a method for rounding to the nearest 10. It is important to have a group discussion about how students think numbers ending in five should be rounded and teach students that those numbers are rounded to the larger ten (Virginia Department of Education, 2012). Instructional strategies used are modeling, discussion questions that promote flexible thinking, time for guided practice, and students working as partners or in small groups.

3. Greater Gator visual and activity

1. Introducing the concept of greater, less than, and equal numbers. Using the greater gator can help students remember that he eats the number that is greater than. Instructional strategies include explicitly teaching vocabulary and using mathematical language, modeling, and providing time for guided practice. The lesson plan included in Sample Activity 2 also provides corrective feedback for the student depending on how they are struggling and what errors are made (National Center on Intensive Intervention, n.d.).

4. Largest Number and Smallest Number

1. Students are provided with random, different numbers by giving each two number cards. They must use the cards to create the largest and smallest double-digit number by putting the largest number in the ten’s place and then one's place. There are coinciding worksheets and discussion questions for the students to share their strategies. The activity also provides time for students to practice adding ten more and 100 more to the numbers they make (Virginia Department of Education, 2012, pp. 1-47-1-54). The activity uses instructional strategies such as direct instruction, modeling, independent practice,

5. Counting and Estimation

1. Students will practice their counting, number sense, and estimation skills when asked to estimate the number of objects in a jar and then count. Instructional strategies to support this lesson are direct instruction, asking questions to promote productive struggle, and modeling strategies to solve the problem. The directed questions will guide students to make an estimate and share strategies together on how to count the objects. More details on instructional sequence and question prompts can be found in the first-grade section of the Number Sense Module (Virginia Department of Education, 2012, pp. 1-55-1-57).

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1. S.T.A.R. mnemonic.

1. Students learn this mnemonic to remind them of problem-solving strategies when presented with word problems. When students translate the words into a visual or manipulative, they practice using the strategies in pairs. Hott, et al. (2014) provides a visual on page 4. Using this activity requires direct instructional, modeling, and guided practice so ultimately students can use this strategy independently.

S— Search the word problem.

T— Translate the words into an equation in picture form

A— Answer the problem

R— Review the problem

2. Graphic Organizers.

1. Students identify the process/equation needed to solve the word problem and insert numbers into the graphic organizers depending on what type of equation (wrong word) is needed to solve. (Virginia Department of Education, Berry, K., & Powell S., 2020, p. 32-34). The 'total' graphic organizer provides space for the two parts below the sum, and 'difference' graphic organizer provides space for the lesser number, difference, and greater number. These graphic organizers can help students understand what the word problem is asking of them after they are explicitly taught how to use the organizers.

3. "Zim and Zog" activity

1. Students must share coins with two video game giants and find all possible ways with three coins, then four, and then ten. This activity promotes the skill of drawing a diagram to solve word problems and finding multiple solutions to a problem as they, "guess and check" (Watters & Logan, n.d., p. 25). While completing this activity the teacher should provide direct instruction, modeling, guided practice, and allow students to work together and share strategies during independent practice.

4. Logic problems

1. The cinema deduction problem is an example of a logic problem that can be solved with students getting up and acting it out, another word problem solving strategy (Watters & Logan, n.d., p. 33). Logic puzzle questions help students use deductive reasoning by eliminating options as they progress; this activity goes hand in hand with direct instruction, modeling and guided practice before students are expected to complete them independently. Some more examples of logic problem clues are in the Think About It lesson plan (Watters & Logan, n.d., pp. 67-69).

5. Lists and pattern seeking

1. Activities that require students to systematically list answers and find patterns promote their word problem solving skills; one activity is the "Crazy Painters" lesson where students find how many ways someone can paint two colors on a wall depending on how many colors they have (Watters & Logan, n.d., pp. 99-103). As students list their answers, they can be given questions to promote productive struggle, such as, 'how many ways could you paint it if you had 100 colors?' which asks for students to identify the pattern and a formula. Direct instruction of the question, explicit parameters (they can use one color to paint both halves of the wall), modeling, and time for independent practice are used with this activity

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Omaha Public Schools. (December 26, 2018). Math tips: What is subitizing? [Video]. YouTube. https://www.youtube.com/watch?v=j0ceWNFCuUQ

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1. Subitizing different representations of numbers 1-10

1. Using dominoes, number cards, and other visual cards (pictures of fingers holding up a certain word, written number words, or pictures shown a certain number of times) have students identify cards with matching amounts. The embedded video provides further explanation on the concept behind subitizing (Omaha Public Schools, 2018). Some variations to these activities are playing a memory game with cards lying face down and students looking for pairs of two cards at a time, or providing students with multiple cards of the same value and one that is different for them to find the outlier. Instructional strategies paired with subsidizing is small group instruction, time for guided practice, and corrective feedback.

2. Number puzzles

1. Students solve a variety of equations where numbers have been swapped out for repeated visuals (e.g., two hamburgers added together equal 8, an ice cream added with a hamburger equals 7, and the two multiplied together equals 12, so students can deduce that a hamburger represents the number 4 and an ice cream the number 3). This activity can be completed as a warm-up or early finisher activity; before students have independent access, the process should be directly taught, modeled and the students should receive guided practice working on a number puzzle.

3. Counting by groups

1. Using hundred boards or other manipulative items, have students count forward to and backwards from 100 counting by 1s, 5s, and 10s. As students' progress and before learning multiplication concepts they can also use this strategy to learn to count by 2s, 3s, and other common multiples (Virginia Department of Education, 2012, pp. K-31-K-32). Instructional strategies paired with this activity are direct instruction, modeling, and guided practice until students can independently count.

4. Number Boards

1. Students receive a number board (almost like a bingo board) and are tasked with covering squares based on clues provided by the teacher (e.g., "cover the number that is one less than four,"). The teacher can assess while watching what number students cover and provide additional clues and corrective feedback if needed. Some number board examples and print outs are provided by the Virginia Department of Education (2014) on pages K-5-K-7.

5. Counting On to add and subtract

1. When teaching computation, this strategy can help students learn early addition and subtraction facts and increase their fluency. Teachers directly instruct students to count on to add or subtract and can turn the activity into a competition where the student tries to answer more flashcards in one minute than they did the first time.

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Visual for the first activity, Fraction Fish and Fraction Peanut (Virginia Department of Education, 2012, p. 2-24).

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1. Pattern blocks creating Fraction Fish and Peanut

1. Have students view the Fraction Fish and Peanut images and ask them to recreate the fraction fish with pattern blocks (Virginia Department of Education, 2012, p. 2-26). Through trying different solutions, eventually ask the students to create the patterns with only one block (trapezoids and triangles) and accomplish this working together in guided practice. Use this model as a visual to directly instruct how fractions are a part of a whole. The next step of the activity is for students to create their own traced Fraction Image using only rhombuses.

2. Sharing treats

1. The materials suggested for the activity are treats like an orange, candy bar, and/or cookie and dividing them unequally before taking student suggestions for how to divide it equally so everyone can have a piece. Then students work in pairs to solve a word problem of two students needing to share an orange equally. There are further assessment questions and variations such as dividing two oranges equally that can be used to extend the activity (Virginia Department of Education, 2012). Other instructional strategies used are modeling and guided practice.

3. People Fractions

1. Use a read aloud story with at least five characters to lead into a discussion finding differences and similarities between characters. The discussion at the end of the story allows students to break groups of people into fractions, from the read aloud and from real life experiences. Students can act out fractions of their class by answering questions and noting what fraction of their class likes cats, dogs, and other opinions. Direct instruction, modeling and guided practice are required strategies.

4. Fractions and Decimals . . . Out to dry

1. Students have a deck of cards with varying digits on them such as 1/3, 1.5, .25, etc. for students to go through and order from least to greatest as a team. The activity helps students recognize fractions as numbers by writing and ordering them in fraction and decimal form, and further understanding where fractions and decimals fall on the number line. More number combination examples and print out resources to literally 'clothesline' the numbers are provided by the Virginia Department of Education (2012) in the fifth-grade section K-5 Mathematics Module on pages 7-9. This independent activity would come later in a unit after explicit lessons on comparing fractions and decimals and finding them in a number line.

5. Go Fish for Decimals and Fractions

1. Cards with equivalent fraction and decimal numbers are needed to play this version of Go Fish where students ask their classmates for a card to make pairs or 'go fish'. During this activity, students can connect fractions and decimals as numbers. Card printouts and the activity plan were found in the fifth-grade section on pages 2-4 in the Virginia Department of Education (2012) Module. Teachers should model for and play along with the students.

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Hott, B., Isbell, L., Montani, T. O. (2014). Strategies and interventions to support students with mathematics disabilities. Council for Learning Disabilities.

McLeskey, J., Barringer, M-D., Billingsley, B., Brownell, M., Jackson, D., Kennedy, M., Lewis, T., Maheady, L., Rodriguez, J., Scheeler, M. C., Winn, J., & Ziegler, D. (2017, January). High-leverage practices in special education. Arlington, VA: Council for Exceptional Children & CEEDAR Center.

National Center on Intensive Intervention. (n.d.). Sample counting concept activity. American Institutes for Research, U.S. Office of Special Education Programs.

National Center on Intensive Intervention. (n.d.). Mathematics sample lessons to support intensifying intervention. American Institutes for Research. https://intensiveintervention.org/implementation-intervention/math-lessons

Omaha Public Schools. (December 26, 2018). Math tips: what is subitizing? [Video]. YouTube. https://www.youtube.com/watch?v=j0ceWNFCuUQ

Pattern Blocks. (2024). Class Playground. https://classplayground.com/pattern-blocks/#printables

Pellegrini, M., Lake, C., Neitzel, A., & Slavin, R. (n.d.). Effective programs in elementary mathematics: a meta-analysis. John Hopkins University. www.bestevidence.org/math/elem/elem_math.htm

Virginia Department of Education, Berry, K., & Powell S. (2020). Evidence-based specially designed instruction in mathematics resource guide. Virginia Department of Education.

Virginia Department of Education. (2012). K-5 Mathematics module number and number sense. Commonwealth of Virginia Department of Education.

Watters, S., Logan, P. (n.d.). "I can solve problems" 5-14 mathematics problem solving support pack. Glasgow City Council, Education Services.

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Visual for the first activity, Fraction Fish and Fraction Peanut (Virginia Department of Education, 2012, p. 2-24).

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1. Name of Activity: Fraction Fish and Peanut

2. Math Area Used: Fractions as Numbers, Number Sense

3. Age Appropriateness: 7-9 or 2nd-3rd grades; a shorter version could be differentiated for younger students and a more complex version could be provided for older primary and secondary students.

4. Materials needed: A classroom set of the wooden pattern block manipulative. Alternatively, color pattern block printable sheets can be found on the Pattern Blocks page on Class Playground (2024) and be cut out to use for the activity. More details on the vocabulary, instructional sequence, extended activities, the fish and peanut print out, as well as block pattern print outs are on pages 24-27 in the second-grade section of the K-5 Mathematic Module (Virginia Department of Education, 2012).

5. High-Leverage Practices:

1. HLP14: Teach cognitive and metacognitive strategies to support learning and independence. Working through the activity teaches students to organize their thoughts and materials and adjust their strategies to improve learning and relate the image to fractions. Teachers will use explicit instruction, modeling, and the goal of making the image out of only one shape to guide students to find other strategies (McLesky, et al., 2017).

2. HLP16: Use explicit instruction. The fish and peanut examples are strategically chosen to facilitate explicit instruction of how fractions are parts of a whole number. Throughout the lesson the teacher is expected to model and scaffold the steps of the activity, the problem-solving skills needed, strategies, and how to complete the independent task of making their own shape with rhombuses at the end of the lesson (McLesky, et al., 2017).

3. HLP22: Provide positive and constructive feedback to guide students’ learning and behavior. Throughout the lesson all student answers are received and given validation - every solution they find to making the images is taped and displayed to encourage student motivation and engagement. As students find what single shape can be used to create the image, the teacher will provide ongoing feedback that guides students closer to their goal (McLesky, et al., 2017).

6. Evidence-Based Practice: The opportunity for students to work together in small groups and receive constructive, corrective feedback from their teacher following effective practices. The activity and instructional strategies use of traditional curricula such as physical manipulative items, visuals, posing the questions in different ways, and students being able to demonstrate answers in multiple ways also follow evidence-based practices that have shown to promote growth in mathematics. Further evidence-based practices that have a significant effect size to use alongside this strategy and activity is professional development in using traditional curriculum and classroom management (Pellegrini, et al., n.d.).